# MANAGEMENT APTITUDE TEST 6 DECEMBER

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```					MANAGEMENT APTITUDE TEST
AFTERSCHO☺OL
– DEVELOPING CHANGE MAKERS CENTRE FOR SOCIAL ENTREPRENEURSHIP PGPSE PROGRAMME – World‘ Most Comprehensive programme in social entrepreneurship & spiritual entrepreneurship OPEN FOR ALL FREE FOR ALL

2/8/2009

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

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MANAGEMENT APTITUDE TEST
Dr. T.K. Jain.

AFTERSCHO☺OL
Centre for social entrepreneurship Bikaner M: 9414430763 tkjainbkn@yahoo.co.in www.afterschool.tk, www.afterschoool.tk
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The pth term of an AP is (3p — 1) /6. The sum of the first n terms of the AP is
• Let us assume first term is 2/6 = 1/3 • Let us assume that P is 3, thus the value is : 8/6 • Sum of first 3 terms : N/2 (frst term + 3rd term). 3/2 (1/3 + 8/6) = 3/2 *(10/6) =5/2 answer. (compare with answers).
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 3

The first term of an A.P is 14 and the sums of the first five terms and the first ten terms are equal in magnitude but opposite in sign. The 3 term of the AP is
• Sum = n/2 (2a+ (n-1)d) • 5/2 (28 +4d) = - 5 (28 + 9d) • 70 + 4d + 200 +45 d=0 • +49d = -270 or D = - 5.5 approx. •2/8/2009 term is 14 AFTERSCHO☺OL's=MATERIAL 3rd + ( PGPSE PARTICIPANTS - 11) 3 answer FOR

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Out of 8 persons in a group, find the number of ways of selecting 3 persons and also the number of ways of arranging these 3 selected persons in a row.
• 8C 3 = (8! / (5! * 3!) • =56 • Number of ways of arranging these persons in a row: 3*2*1 = 6 • Total number of ways : 56 *6 = 336.
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There are 6 distinct letters of English alphabet and 4 distinct digits. All possible 6 character alpha — numero codes are generated using any 4 letters of the alphabet and any 2 available digits. If in any given code, the characters are all distinct, then what is the maximum number of such codes that can be generated?
• Here all these can be interchanged – so 6!, we select from groups so 6C4. • 6C4 * 4C2 * 6!= 6! / (4!*2!) * 4/ (2!* 2!) *6! • = 15 * 6 * 720 •2/8/2009 =64800 answer. AFTERSCHO☺OL's MATERIAL 6
FOR PGPSE PARTICIPANTS

In a cricket tournament, each participating team plays once against every other and in all 36 matches are played. Find the number of teams that participated in the tournament.
• • • • • N(N – 1) / 2 = 36 N (N – 1 ) = 72 N^2 –N – 72 =0 or N^2 -9N + 8N -72 =0 N (N – 9) +8(N – 9) or N = 9 or - 8 Thus N = 9. answer.
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. The letters of the word ADROIT are permuted in all possible ways to form 6! different words. How many words can be formed which neither begin with T nor end in A? • Total possibilities of permutations of ADROIT = 6! = 720. words starting with T = 5! = 120. words ending with A = 5! = 120. there are some words which have T as start and A as end, just remove them: 4! = 24. thus answer = 720 – (120+12024)=504 answer
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If the letters of the word ‗NUMBERS‘ are permuted in all possible ways, then in how many of these permutations, are the vowels never together i.e. vowels are separated?
• There are 7! digits in numbers. So we can make 7! Number of words from this. • Let us consider all the vowels together, there are 2 vowels. Thus we have only 5 + 1 = 6! Options. Thus we can say that there are 5040 – 720 number of permutations. = 4320
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ERROR SPOTTING

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While (A) a strong defend (B) is important to any country it cannot be more important than the livelihood (C) of its (1) citizens.
• Instead of defend, use defence (noun should be used and not the verb).

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It (A) can take hundreds (B) of different experiments to achieve (C) a (D) ultimate solution.

• (d) use an or the instead of a.

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Studying (A) the science of (B) logic is one way to (C) cultivate one‘s reason (D) skills.
• (d) it should be reasoning and not reason.

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Every candidate under (A) considering (B) for a military job must undergo (C) a thorough medical (0) examination.
• (b) it should be consideration and not considering.
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Drug abuse (A) become one of (B) our most (C) serious social problems (D)
• It should be ‗ Drug abuse has become …‖

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Although (A) the advisory commission on Central America has completed its (B) report that examines (C) the political tensions in that area, but, no easing (D) of tensions has resulted.
• (d) remove but. We don‘t use but with although, we may use yet with although.

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Hard work and self-discipline often result (A) in a rise (B) not only in (C) salary but also in your self-esteem
• ( c) put your after in. • Or you may use one‘s with another replacement – instead of your – use one‘s.

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Caffeine (A) in coffee is relative (B) harmless if people drink (C) it moderately (D)
• (b) use relatively and not relative (we should use adverb and not adjective).

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When they have been (A) frightened (B) as for example, by (C) an electrical storm, dairy cows may refuse giving (D) milk.
• (d) it should be refuse to give and not refuse giving.

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An unexpected raise (A) in the cost of living as well as (B) a decline in employment opportunities resulted (C) in the rapid implementation (0) of new Goveinment programmes for the unemployed.
• (a) use rise instead of raise.
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It is (A) imperative that a management student maintains (B) a grade point at (C) ―B‖ in (D) major field.
• (c ) delete at.

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If the ozone gases of the atmosphere did not filter out (A) the ultraviolet rays of the sun, life (B) we know (C) would not have evolved on earth (D).
• ( a) it should be ‗had not filtered out ‗ instead of ‗did not filter out‘

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The baby was left (A) in charge (B) of (C) elderly lady
• (b) instead of ‗in charge‘ use ‗in the charge‘

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More than (A) one scientists (B) have contributed (C) to the success of this venture (D)
• (b) instead of scientists use singular – scientist.

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Smoking (A) is not allowed at petrol pumps because there is (B) too many (C) easily ignited (D) material in the vicinity
• (c) use too much • Or • You may also correct (b) where you may use there are .
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Regardless of (A) your teaching method, the objective of any conversation class should be (B) for the students practice (C) speaking words (D)
• (c ) instead of the students practice, use ‗the students to practise‘.

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Atrophy (A) can affect a cell, organ (B) tissues (C) or(D) limb.
• Instead of tissues, use tissue, because we are using a with them.

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The pleura that cover (A) the exterior(B)of the lungs (C) and the inner walls of the chest cavity is (D) a thin elastic membrane.
• (a) it should be covers.

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Many of us bemoan (A) our lack of foresight by complaining that if we would have (B) bought property twenty years ago, we could have (C) taken advantage of the recent real estate (D) boom.

• (b) with if we cannot use models, so instead of ‗we would have‘ use ‗we had‘
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After the absentee (A) ballots had been counted, the total of the authorised votes cast (B) in the election were (C) one third (D) than what had been predicted.
• (c ) the subject is total, so we should use the was instead of were (total is singular).
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Organised (A) labour has fight (B) for and won protection and benefits (C) for its (D) workers.
• (b ) instead of fight, we should use fought.

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The book is well-printed (A) and attractively bound (B) making altogether (C) an attractive volume (D).

• ( c) it should be making it altogether

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He is one (A) of the shrewdest men (B) that is (C) in the (D) administration.
• (c ) it should be are and not is.

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No sooner had he (A) come from Mumbai when (B) he was asked (C) to proceed to (D) Delhi.

• (b) no sooner is always followed by than and not when.

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Drug abuse (A) become one of (B) our most (C) serious social problems (D)
• (a) it should be drug abuse has become.

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Alexander Calder, who was originally (A) interested j (B) mechanical engineering later (C) became a sculpture (D)
• (d) use sculptor and not sculpture (which is an art).

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ANALYTICAL ABILITY

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Dhawal travels 900 kms. by train at an average speed of 60 km per hour; 3,000 kms. by steamship at an average of 25 kms. per hour; 400 kms. by aeroplane at 350 kms. per hour; and finally 15 kms. by bus at 25 kms. per hour. Calculate his average speed for the entire journey. ( marks)
• Average speed = Total Distance / total time • =(900+3000+400+15) / (15+120+1.14+.6) • =31.55 answer.
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Average monthly income of all the workers of a company is Rs. 6,000. Average monthly income of male and female workers of the company is Rs. 6,200 and Rs 5,200 respectively. Find the percentage of male and female workers in the company.
• Solve it by alligation method..

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Solution ..
• Thus we can see the ratio between male and female is 800 : 200 or 4:1. • Thus male workers are 80% and female workers are 20% of total number of workers.
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Mix

6200 6000

5200

800

200

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The salaries paid to the managers of a company had a mean of Rs. 20,000 with a standard deviation of Rs. 3000. What will be the mean and standard deviation if all the salaries are increased by (i) 10%, (ii) 10% of the existing mean?
• If salaries are increased by 10%, new mean and standard deviation both will increase by 10%. If salary is increased by 2000 in each case, only mean will increase, and standard deviation will remain same. Answer.
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Puzzle test
• Tata produces car components. The company has to ensure that it does not supply defective parts. If a buyer receives a defective part, Tata has to pay a penalty of Rs 200 per component. It produces 1000 components at a time in a batch. It wants to test the quality of these before shipping them to its buyers. It can use two tests for quality control. Test 1 costs Rs 8per component but it identifies only 80% of all defective parts. Test 2 costs Rs 12 per component but it can detect all defective parts. Tata can rework defective parts at a cost of Rs 100 per part. Let ‘x’ be number of defective parts per batch. What should be the value of X if both the tests are equal for Tata ?
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Solution..
• Test 2 cost : 12 *1000 = 12000 • Test 1 cost (it is equal to test 2). = 12000 • That means cost can be divided in two parts: 1000*8 = 8000 • Due to defects : 4000 • Differential cost (200 – 100) = 100 • Thus number of defective parts: 4000/100 = 40 • These are only 20%, so number of defective items is 40 *100/20 =200 answer.
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Data sufficiency question…
• • • • c and d are positive integers. Is c even? (I) c^2- 1 is odd (II) ( c-3) (d + 2) is odd. Only (1) can give you correct answer.

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Goti and Jitu are two friends. If Goti tells the truth 40% of the time and Jitu 30% of the time, the probability that they will contradict each other when they are narrating the same incident is
• Goti speaks the truth but Jitu lies : (.4 * .7) = .28 • Goti lies, but Jitu speaks the truth :(.6*.3) =.18 • Thus they will contradict = 46% answer.
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if arithmetic mean of 17 15, 23, x and 19 be 20 then what is the value of x
• There are 5 values so total 5*20 = `100 • Total of 17,15,23,19 = 84. • Thus x is 100 – 84 = 16 answer.
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The average of first 30 natural numbers is
• Let us add all the 30 numbers. The total is (30 *31 )/2 = 465 or (1 + 2+ 3 + …. 30) • Or n/2 (first term + last term) • =30/2 (1 +30) = 30/2 *31 the total is 465. • Thus average is : 465/30 = 15.5 answer.

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What is the average of all prime numbers between 30 and 50
• • • • Let us count all prime numbers : 31,37,41,43,47, Let us add them : 199 Their average is 199/5 = 39.9 approx. answer.

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The average of first five multiples of 3 is
• List down first 5 multiples: • 3,6,9,12,15 • The mid point is 9, therefore average is 9. answer. • Or you may add them = 45 now divide it by 5, we get 9 as answer.

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The number of employees, average wages per employee W of the wage per employee for two factories are given below: Factory A Factory B Number of Employees 100 200 Average Wage per Employee (Rs.) 120 200 Variance of the Wages per Employee 16 25 In which factory is there-greater variation in the distribution of wages per employee?

• Coeffecient of variance = std. dev. / mean *100 • = 4/120 *100 = 3.33%. In factory B, it is 5/200 *100 = 2.5%. Thus there is greater variance in factory A.
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if a, b, C, d, e are five consecutive odd integers, then what is their arithmetic mean
• List down any consecutive odd integers: • 1,3,5,7,9 • Add them up, we get : 25, divide it by 5, we get 5, which is the middle figure. Thus their average is their middle point which is C. answer.

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‗A‘ sells a car to ‗B‘ at 10% profit, ‗B‘ sells it to ‗C at 20% loss If the cost of A is Rs.5000, then find Cost of ‗C‘.
• A sells it for Rs. 5500. B sells it at 80% or 4400. thus cost of C is 4400 answer.

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A man sold 250 chairs and had a gain equal to S P of 50 chairs. What is his profit in %?
• Let us assume selling price of 250 chairs was 2500 (10 per piece). • Thus gain is 10 * 50 = 500 • Thus cost is 2500 – 500 = 2000. • Thus profit in % is 500/2000 *100 = 25% answer.
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What is the loss percent if a man loses Rs. 10 on selling an article for Rs.100?
• • • • Sale price = 100 Loss = 10 Cost = 100 +10 = 110 Loss in % = 10/110 *100 = 9.9% answer.
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2/8/2009

What is the sum of the digits of the number : 10^560 -123456789?
• In this number, we have 551 times 9 and one time all the digits from 1 to 8. • Thus the total of all the digits is : • (551*9) + 36 +1 • =4996 answer.

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Solve it
• 100 liters of a mixture of Boric Acid and water contains 80% Boric Acid. So what amount of water should be added to the mixture to reduce the strength of Boric Acid in the mixture to 50%?

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Solution
• Total liquid = 100 liters • Boric acid = 80 liters • We have to make it 50%, so the total liquid should be 160 (just double of it). That means we have to add 160-100 = 60 liters of water. • Answer.
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Solve it
• If 7 men or 8 women or 10 boys can finish a piece of work in 24.days each of 9 hours, then find how many men with the help of 4 women and 5 boys can finish the work in 18 days each of 6 hours. • Solution : • 4 women = 5 boys, so 10 boys. • 10*24/18*9/6* = 20 boys, we already have 10 boys, we need additional 10 boys to complete the work. 10 boys are equal to 7 men, so we need 7 more men to complete the work. Ans.
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They ought to be here before now.
• Change before to by.

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He is known about charity.

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The man laboured to good results.
• Change to into for • Correct : • The man laboured for good results.

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I was on bed when he telephoned me.
• Instead of on, use in • I was in bed when he telephoned me.

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This work of art is worthy for praise.
• Instead of worthy for praise, use praiseworthy. • OR • This work of art is worthy of praise.

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Which newspaper do you subscribe for?
• Instead of for, use to.

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He scoffed on the idea of revolution.
• Instead of on, use at.

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Where have you been to?
• There is no need of to. • Where have you been?

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He lives at Delhi in India.
• Correct sentence: • He lives in Delhi in India.

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The man died from fever.
• Use of instead of from.

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Sumit rushed at my room, panting for breath.
• Instead of at, use into.

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The poor man is beset by difficulties.
• Correct : • The poor man is beset with difficulties.

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Bitthal is distinguished in the cartoons for his sense of humour
• Instead of in, use for.

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He is a descendant from the Mughal royalty.
• Instead of from, use of.

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The river flows below the bridge.
• Correct : • The river flows under the bridge.

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The weather was not very congenial for him.
• Correct sentence: • The weather was not very congenial to him.

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We are expecting the reply till evening.
• Correct sentence: • We are expecting the reply by evening.

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He has not been cured for his disease.
• Correct sentence: • He has not been cured of his disease.

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We must not carp with the errors of our ancestors.
• Correct sentence: • We must not carp at the errors of our ancestors.

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Patanjali is an authority for Sanskrit grammar.
• Correct sentence: • Patanjali is an authority on Sanskrit grammar.

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The shopkeeper deals with cotton and cloth.
• Correct : • The shopkeeper deals in cotton and cloth.

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SOLVE IT
• A salesman has a 35 hours per week normal schedule. During normal hours he gets Rs.40. per hour and for overtime he gets 1.5 times his normal charges. What is his income if he works for 60 hours in a week? • SOLUTION : • 35*40 + 25*60 =1400+1500 = 2900 ANS.
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What is the cube root of 571787?
• • • • • • • Options : 47 73, 83 93 Answer : 83.
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 81

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3A+2B / 5A-3B =12/15 what is the ratio of A to B?
• 3A + 2B = 12 5A – 3B = 15 • Multiply the first equation with 5 and 2nd equation with 3, we get : • 15A + 10 B = 60 and • 15A -9 B = 45 • 19 B = 15. thus B = 15/19
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Solution …
• • • • • • • • 3A + 2B = 12 B =15/19 Putting this value in the first equation. 3A + 30/19 = 12 3A = 12 -30/19 = 228 -30 / 19 3A = 198/19 A = 198/57 A: B = 198/57 : 15/19 = 22: 5
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if p/q 2/3, what is the value of p+q / p-q
• • • • P=2 Q =3 Answer : (2+3) / (2-3) = - 5 answer.

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Two dice are tossed simultaneously. What is the probability of getting the sum as a prime number?
• Prime number : 2,3,5,7,11, • Total possibilities = 6* 6 = 36 • Answer = 16 out of 36 or 16/36. ans.
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Solution…
Total of 2 3 4 12 5 6 7 8 9 10 11

1

1

2

3

4

5

6 5 4

3

2

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What is the value of * in the given equation….

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Solution
• • • • We know that (A –B)^2 = A^2 – 2AB+ B^2 A = 16/7 B= 9/7, solutoin is 1. (16 -7 = 7,so 7/7) Thus the above equation is just expansion of this equation. Thus the value of * is 2AB, out of which we already have B. thus the remaining number is 2A = 32/7, we already have 7, thus answer is 32.
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There is a circular park of 20 meters diameter. Inside the circular park is a path 1 meter wide. Find the area of the park.
• Area of circle = pi* radius * radius • = pi * 10^2 – 9^2 { A^2 – B^2=(A+B) (A-b)} • = pi * 19*1 = 19 pi. Answer.
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A can do a piece of work in 8 days, B can do it in 9 days and C can do it in 6 days. On the first two days A & B work together and on the third day C joins them. What is the total number of days worked, needed to complete the work?

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Solution
• For the first 2 days – A and B are working together… (2*1/8) + (2* 1/9) = 34/72 • Now A,B,C will work together: • 1/8 +1/9 + 1/6 = 29/72 • They will complete the work in 72/29 • Now multiply this by (1- 34/72) * 72/29 • (because 34/72 work is already complete, the remaining work is 38/72) • =38/72 *72/29 = 38/29. • Thus total time required is 2 +38/29 answer.
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Surface area of a cube is 150 cm^2 . What is the length of its edge?
• • • • •

Surface area of cube : Formula = 6 * Side * side 6 * side * side = 150 Side * side = 25 Side = 5 answer.

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93

A circular cord of 35 cm is drawn into a rhombus. what is the length of its edge?
• Length of cord = 35 Cm • Edge = 35/4 = 8.75 answer.

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94

The age of the father is 4 times the son‘s age. 5 years ago it was 7 times the son‘s age. What is his age now?
• Let us assume father‘s age = X , son‘s age is X /4 . • (X-5) / (X/4 – 5) =7 or (X-5)/ (X – 20)/4 =7 Or 4X- 20 = 7X – 140 • - 3X = -120, or X = 40 Answer.
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 95

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96

What is the difference between a discount of 40% on Rs. 1000 and two successive discounts of 35% and 5% on the same amount?
• =1000*.35*.05 = discount of 350+32.5 • v/s discount of 400. the difference is : 17.5 answer.
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 97

A man sold a horse at a loss of 7%. Had he been able to sell it at a gain of 9%, it would have fetched Rs.64 more than it did. What is the cost price of the horse?
• 64 *100/16 = 400 answer
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 98

Solve it ..
• On an article marked Rs.20000, a customer has a choice between three successive discounts of 20%, 2O% and l0% and three successive discounts of 40%, 5% and 5%. By choosing the better offer, determine the amount he can save. • Solution : • 20000*.8*.8*.9 v/s 20000*.6*.95*.95 • =12000 v/s 10300. thus savings are 1700.
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 99

A manufacturer sells a vehicle to a dealer at a profit of 40%, the dealer sells it to a customer at a profit of 30% and the customer sells it to a friend for Rs.7280 at a loss of 2O%. Find the cost price of the vehicle for the manufacturer?
• 7280*100/80*100/130*100/140 = 5000. ans. 2/8/2009 AFTERSCHO☺OL's MATERIAL
FOR PGPSE PARTICIPANTS 100

What profit percent is made by selling an article at a certain price, if by selling it at two-thirds of that price, there would be a loss of 20%?
• 80 *3/2 = 120 thus there will be profit of 20%. Answer.
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 101

Two articles are sold at Rs.198 each such that a prof1t of 10% is made on the first while a loss of 10% is incurred on the other. What would be the net profit/loss on the two transactions combined?

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Solution
• • • • Sold Profit on first 198 *10/110 =18 Loss on 2nd = 198 * 10/90 =22 There is net loss of Rs. 4

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103

.A person purchases 50 dozen toys at Rs.4 per dozen. Of these, 40 toys were found broken. At what price should he sell the remaining toys in order to make a profit of 5%?

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Solution
• • • • • • • • No. toys : 50 * 12 = 600 Defective = 40 Net = 560 Cost : 4 * 50 = 200 add profit = 5% = 10 Selling price = 210 No. of dozens = 560/12 = 46.66 dozens New sale price per dozen= 4.5 answwer.
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 105

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.A fruit vendor sells apples at cost price but uses false weight of 960 gm instead of 1 kg. Find the gain %.
• • • •
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Profit = 1000 grams – 960 grams = 40 Cost = 960 Profit = 40/960 *100 = 4.16% answer.
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 106

• A engaged 40 labourers on a job. He was paid Rs.1,050 for the work. After retaining 20% of it, he distributed the remaining amount amongst the labourers. If the number of men to women labourers was as 5: 3 and their wages were as 3 : 2, then how much did a man get as wages?

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Solution
• • • • • No . Of men = 5/ (5+3) *40 = 25 25 men were working Total payments to men: 5*3 = 15, women : 3*2 = 6 Thus payment received was 15/21 * (1050*.8) • =total payment received = 600 • Payment per man – 600/25 = 24 answer.
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 108

arrange eight of the nine numbers 2,3,4,5, 7,10, 11,12,13 in the vacant squares of 3X4 array shown below so that the arithmetic average of the numbers in each row and column is the same integer. What is their average?

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Solution
• Let us add these numbers:
• • • • Sum( 1,2,3,4,5, 7,9,10, 11,12,13,14,15, - X) X = left out number =106-X Let us assume average = Y

• The average is same, so total of columns should be 4Y. • 3*(4Y) = 106-X • 12Y = 106 – X, by hit and trial, we know that X should be 10. Thus Y = 8. • Thus average is 8 and left out number is 10. • Answer.
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 110

For how many integers N, N/(20—n) is the square of an integer?
• • • • (a) 0 (b) 1 (c) 2 (d) 3 (e) 4 Solution : square cannot be negative, so 20-N must be positive. Therefore N can be upto 19 only. By trial, we can see that when N = 16, this is square, there is no 2/8/2009 AFTERSCHO☺OL's MATERIAL 111 other option, Thus answer is B. FOR PGPSE PARTICIPANTS

Puzzle
• A truck tra veiled from town A to town B over several days. During the first day, it covered 1/p of the total distance, where p is a natural number. During the second day, it travelled 1/q of the remaining distance, where q is a natural number. Duthig the third day, it travelled i/p of the distance remaining after the second day, and during the fourth day, l/q of the distance remaining after third day. By the end of the fourth day the truck had travelled 3/4 of the distance between A and B. • The value of p+q is • (a) 4 0) 5 • (c) 6 (d) 7 • (e) 8
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 112

Solution
• Try from options, it cannot be 5 or 6, it has to be higher value 7 or 8. Let us try for 7. • Let us assume that the number is 144 (we have assumed it because 4*3*4*3 = 144) • First day: 36 is used, left out is 108. 2nd day: 36 is used and left out is 72. 3rd day: 18 is used and left out is 54. 4th day 18 is used and left out is 36. • We know that now 1/4 th is left out, so our condition is fulfilled. Thus this is the answer. •
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 113

In a certain factoiy, each day the expected number of accidents is related to the number of overtime hour by a linear equation. Suppose that on one day there were 1000 overtime hours logged and 8 accidents reported, and on another day there were 400 overtime hours logged and 5 accidents. What are the expected numbers of accidents when no overtime hours are logged?

• (a) 2 • (c) 4

(b) 3 (d) 5

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Solution
• Let us frame 2 equations and use them to solve this question: • 8 = 1000X +Y • 5 = 400 X +Y • Solving these we get : 3 = 600X • X = 1/200; putting this value, we get Y. • Y = 3. • Thus when there is no overtime, the number of accident is 3. Answer.
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 115

In which year did the firm pay maximum tax?

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Solution
• Since all the figures are in %, we cannot calculate the value of taxes paid as absolute value. We are not aware of change in sales also. So answer : cannot be determined.

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Solve it :
• Seven integers A, B, C,D, E, Fand G arc to be arranged in an increasiug order such that • i. First four numbers are in arithmetic progression. • ii. Last four numbers are in geometric progression. • iii. There exists one number between E and G. • iv. There exist no numbers between A and B. • v. D is the smallest number and E is the greatest. • Vi. A / D = G /C = F / A >1 • vii. E= 960 • What is E / A?

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SOLUTION
• F is more than A and A is more than D and G is more than C. • D is smallest :D - - - - - - E (G will come one less than E, A and B are close. C has to be near D. • DC BAGFE • The last four are in GP. • Thus E = A *r^3 (because it is GP) and A = D +3(common difference)
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 119

Continued…
• • • • • • • • • • E = 960 Let us find factors of 960 2*2*2*2*2*2*3*5 Thus A must be 15 and ratio must be 4 The numbers will be : 15,60,240,960. Or A may be 120 and ratio may be 2, the numbers will be 120,240,480 and 960 Thus F/A = 240/15 = 16 or 480/120 = 2. The 2nd option is better. Thus A/D = 2 and D = 60 We can write that A = D + (3*common difference) =120=60 +(3*common difference).
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 120

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Continued…
• • • • • 120=60 +(3*common difference). Common difference is 20 Thus the numbers are : 60,80,100,120,240,480,960 Thus we can find answer to the question: E/A • =960/120 = 8 answer.
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 121

Goti and Nitin could do a piece of work in 12 days. Nitin and Kap together do lt In 15 days. If Goti is twice as good a workman as Kap, find in how many days Goti alone will do it?

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Solution
• • • • • • • G = 2K (now add the two equations) 2K+N+N+K = 1/12+1/15 = 27/180, K+N = 1/15 or 2 (K+N) = 2/15 3K +2N = 3/20 K = 3/20 – 2/15 = 1/60 Thus Kap can do it in 60 days. Goti being twice fast, can do it in 30 days alone. Answer.
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 123

2/8/2009

Goti car paint a fence 100 metres long in 6 days, then how much time will both Goti and his friend Kap take, if Kap is thrice as efficient as Goti?
• Goti‘s one day work = 1/6, Kap=3*1/6 • 1/6 + 3/6 = 4/6 • Thus they will take 6/4 = 1.5 days to 2/8/2009 AFTERSCHO☺OL's MATERIAL complete theFOR PGPSE PARTICIPANTS work.

124

Two pipes A and B can fill a cistern in 10 and 15 minutes respectively. Both pipes are opened together but at the end of 3 minutes, ‗B‘ is turned off. How much time will the cistern take to fill?
• 3/10 +3/15 = 75/150 thus the remaining pipe A will take 5 minutes to fill up the tank. Total time: 2+5 = 7 minutes. Ans.
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 125

Explanation
• 75/150 = is half of the total pip3 thus the pipe is helf illed. Thus A can fill the remaining portion in 5 minutes (it takes 10 minutes to fill completely).

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126

A is twice as good a workman as B; and together they finish a work in 14 days. In how many days can it be done by each separately?
• Let us assume that A takes X and B takes 2X days. 1/2x + 1/x = 1/14 • Let us assume 1/x = Y • Y/2 + Y = 1/14 • 3/2Y = 1/14 or Y = 2/42 or 1/21 • Thus A can do it in 21 days and B in 42 days. Answer. 2/8/2009 AFTERSCHO☺OL's MATERIAL 127
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If 20 men complete one-third of a piece of work in 20 days, how many more men should be employed to finish the rest of the work in 25 days?
• • • • Total work left = 2*20 = 40 days. Total mandays required = 40*20 = 800 Thus no. of persons required = 800/25=32 Additional persons required = 32-20=12 persons. Answer.
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 128

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Goti can copy 75 pages in 25 hours Goti and Kap together can copy 135 pages in 27 hours In what time can Kap copy 42 pages?
• Goti copies 3 pages in one hour. Thus he copies 27*3 = 81 pages. Kap copies (13581) = 54 pages in 27 hours, or 2 pages in one hour. Thus 42/2 = 21 hours will be taken by Kap Sa. Answer.
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 129

goti & Kap can do a piece of work in 4.8 days, Kap and Jitu together can do it in 8 days and the three together in 4 days. How long would Goti & Jitu together take to do it‘

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Solution
• (calculate for 1 day and add them to get the ans.) • G+K +K +J= 1 / (4.8) + 1/8 • GKKJ = 12.8 / 38.4 • GKJ = ¼ • K = 12.8 / 38.4 - ¼ • = (12.8 – 9.6) / 38.4 • = 3.2 / 38.4 = 1/12 • Thus G+J = ¼ - 1/12 = 2/12 = 1/6 • G + J will do it in 6 days. Answer.
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 131

A person works twice as fast as a woman. A woman works twice as fast as a child. If 16 persons can complete a job in 12 days, then how many days would be required for 32 women and 64 children together to complete the same job?
• 32 women = 16 men • 64 children = 16 men. • Thus they will together do it in 6 days. 2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS Ans.

132

3 pipes A, B and C can fill a cistern in 15, 20 and 30 min. respectively. They were all turned on at the same time. After 5 minutes the first two pipes were turned off. In what time will the cistern be filled?

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Solution
• 5/15 + 5/20 5/30 • = (20+15+10) / 60 = 45/60 or ¾ • Thus remaining ¼ of the cistern can be filled by C in 7.5 minutes only. • Thus total time taken is 5 + 7.5 =12.5 minutes

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134

A certain number of men can finish a piece of work in 100 days. If, however, there are 10 men less, it would take 10 days more for the work to finish. How many men were there?
• • • • Let the number of men = X Total work = 100X (X-10) 110 = 100X or 110X -1100 = 100X 10X = 1100 or X = 110.
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 135

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A, B and C can do a piece of work in 20, 20 and 40 days respectively. They began the work together but C left 2 days before the completion of work. In how many days would the work have been completed?

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Solution
• • • • • For 2 days only A and B worked 2/20 + 2/20 = 4/20 or 1/5 Together (all three) : 1/20+1/20+1/40 = (2+2+1) / 40 = 1/8 Thus they take 8 days to complete the work, but they completed only 4/5 work together, so 8*4/5 = 6.4 days were taken by them. Thus total days : 8.4 days. Answer.
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 137

2/8/2009

ERROR SPOTTING Industrial accidents/(1)usually result into /(2) ignorance/(3)or carelessness/(4) No Error (5)
• The correct sentence should be : • Industrial accidents are caused by ignorance or carelessness. • So answer is (2)
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 138

Some people are like (1)to do a lot of social work/(2)even though they are poor(3)and lack resources
• Correct sentence should be : • Some people want / are likely to do a lot of social work, even though they are poor and lack resources. 2/8/2009 AFTERSCHO☺OL's MATERIAL • So answer is (1) FOR PGPSE PARTICIPANTS .

139

ERROR SPOTTING Some men (1)have conveniently believe (2)that women are inferior to(3) men in respect of abilities.(4) No Error (5)
• (2) = it should be : have conveniently believed.

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140

ERROR SPOTTING His qualities include(1)the ability to take/(2)right and/(3)quickly decisions.(4)/ No Error(5)
• ANSWER : (4) • It should be quick decisions.

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141

ERROR SPOTTING If you want to (1)ensure prompt service (2)please be contacted to us (3) at your earlier convenience. (4) No Error (5)

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142

They founded (1)this institution for/(2)the welfare of the poor (3) and the disable people.(4) No Error (5)

• Answer (4) it should be : • For the disable (there is no need to put people with disable).
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 143

He asked me/U) what had my total investrnents(2)during the (3) last five years.(4) No Error. (5)
• Answer : (2) it should be : • What had my total investments been

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144

He takes the(1) prescribed medicine regularly(2) and that is how(3) he has succeed to control his ailment.(4) No Error (5)
• Answer : (3) • It should be : this is how

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145

We should take(1) regular exercises to keep ourself (2) fit and active.(3) No Error (4)
• (2) it should be : regular exercises to keep • (there is no need of ourself).

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146

Each time (1) you reached this spot (2) go back and(3) start your next (4) round again.(4) No Error (5)
• (2) it should be – you reach this spot.

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147

SENTENCE IMPROVEMENT
• The honourable court had taken a leniency view because the accused had no previous criminal record. • (1) had viewed leniency (2) had taken a leniency viewing • (3) had taken a lenient view(4) Noae of these • (5) No correction required • Solution: • (3)
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 148

Sentence improvement
• Maintaining global peace is our self-made commitment to the word. • (1) self-making commitment • (2) self-made committee • (3) made of self-connnitment • (4) None of these • (5) No correction required • Solution (5)
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 149

The dinner party hosted by the President at the club was shifted to an undisclosed location.
• (1) a locality undisciosing • (2) a undisc location • (3) an undisc location • (4) None of these • (5) No correction required • Solution •2/8/2009 (5) AFTERSCHO☺OL's MATERIAL
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150

Sentence improvement
• The government should launch such projects which should reversible the destructive cycle of flood and drought. • (1) should have reversible (2) should be reverse (3) should have been reverse • (4) None of these • (5) No correction required • Solution : • (4) correct answer: should reverse
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 151

A comnilttee comprising eminent experts from various fields were setting up. (1) was setup (2) was setting up (3) were being set up (4) None of these (5) No correction required
• Solution : (1)
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 152

Our foreign exchange reserves have been increased substantial. (1) have been increased substantially (2) have increased substantially (3) have substantially increasing (4) None of these (5) No correction required
• Solution : (2)
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 153

The key to a competitive economy is its investment regime.
• • • • • • • (1) competition economy is (2) competing economist lays (3) economy competition was (4) None of these (5) No correction required Solution (5)
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 154

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Driving a car in jammed traffic require extraordinary patience especially when other drivers are not disciplined. (1) required extraordinary patient (2) requires extraordinary patience (3) requiring extraordinary patience (4) None of these (5) No correction required
• Solution (2)
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 155

Chinese army possesses highly sophisticated simulotors on which their soldiers are training.
• • • • • • (1) which their soldiers training on (2) on which their soldiers have trains (3) which their soldiers do train (4) None of these (5) No correction required Solution : last part : soldiers are getting training. 2/8/2009 AFTERSCHO☺OL's MATERIAL 156 (so answer is (4)) PGPSE PARTICIPANTS FOR

Every novel activity will be likely to face resistance from vested interests.
• • • • • • (1) is likely to face (2) would be like facing (3) No correction required (4) will be likely facing (5) None of these Solution : (1)
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 157

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We observed that traders were not primarily dedicated with art of selling.
• • • • • (1) dedicated to the art of(2) None (3) dedicated in the art by (4) dedicated by the art of (5) No correction required Solution (1) preposition error .
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 158

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161

If expenses per participant during the meeting is Rs.200 in 1995, which keeps on increasing at the rate of 10% per year, then what are the total expenses (in Rs.thousand) in 1996. The graph below shows the number of participants coming from different regions?

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Solution
• 200*1.1*360 = 79200 answer.

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163

The following graph shows profits of 5 companies. What was the average profit in 1979?

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164

Solution :
• • • • • • • A =130 B = 40 C = 110 D = 60 E = 90 Let us add them and divide by 5: =430/5 = 86 answer.
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 165

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Solve it
• A cube with edges equal to 8cm is painted on all the six faces and is subsequently cut into 64 identical cubes. The number ct smaller cubes painted on atleast two faces is • (1) 24 (2) 16 • (3) 36 • (4) 32
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 166

Solution
• There are four on the top right side. There are 4 on the opposite side also (4*4*4 = 64).

• Thus we have 4+4+2+2 cubes in front, same 12 in the back side also. We have 8 in sides also. Thus we have 32 cubes. • Ans.
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 167

Solve it
• The perimeter of a regular hexagon is 36cm. The area of the hexagon is • (1) 54*sqrt(3) sq cm (2) 108*3 sq cm • (3) 27*3 sq cm (4) 18*3 sq cm • Solution: • One side of hexagon = 6 • One triagle = ((sqrt(3)/4 * side )^2 =1.7/4* 36 • Hexagon = 6* equilateral triangle = 6*sqrt(3)/4*36 • =54* sqrt(3) ans
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 168

Solve it …
• How many patient does the doctor examine in a day, if he treats 5 patients in 3 hours with breaks of 10 minutes between two consecutive patients and works for 10 hours per day? • (1) 16 (2) 15 • (3) 12 (4) 20

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Solution
• • • • • • • 3 hours = 180 minutes Break = 4*10 = 40 Time per patient = 140 / 5 = 28 minutes Total time : 10 hours *60 = 600 minutes 600 – 28 = 572 Now dividing 572 / (28+10) = 15 Thus the doctor checks 15+1 = 16 patients.
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 170

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If the interior angle of a regular polygon is twice its exterior angle then the polygon is a (1) rhombus (2) pentagon (3) hexagon (4) heptagon
Interior angle = 2X and exterior angle = X 3X = 180 or X = 60 Thus one exterior angle is 60 Thus 360/60 = 6 Thus the shape is hexagon. Answer.
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 171

DATA SUFFICIENCY QUESTION. 40 pens were distributed equally amon all the participants, then how many participants were there? (A) The number of participants was a prime number greater than 10. (B) The leftover pen was kept by the Chairman.
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 172

Solution
• If we combine both the statements, we can get the answer. One pen was left (given to the chairman), so 39 pen were distributed. • 39 = 3*13 • Thus the number of participants must be either 3 or 13. since it had to be above 10, therefore the answer is 13. (so answer can be drawn with the help of both the students together). Ans.
2/8/2009 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 173

WHAT IS THE VALUE OF X

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174

WHAT IS THE VALUE OF X

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175

Data sufficiency question.
• • • • • • • Is the series a GP? (A)If the third term is twice the second. (B)The fourth term is eight times the first. Solution Let us start from 1 1,2,4,8 = yes it is GP Thus the answer can be drawn with the help of both the statements. Ans.
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS 176

2/8/2009

The number of common terms in the two-seç 17, 21, 25,.. ., 417 and 16, 21, 26,. . ., 466
• Let us start from 21. In the first term the gap is of 4 and in second series the gap is of 5. their LCM is 20 so we have to find the gaps of 20 each. • Last term is 417. let us deduct 21 from 417, we get 396. now let us divide it by 20. We get : 19. Thus we have 19+1 = 20 common terms. Answer. 2/8/2009 AFTERSCHO☺OL's MATERIAL 177
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Solution continued. .. .
• The final series is : • 21,41,61,81,101,121,141,161,181,201,221 ,241,261,281,301,321,341,361,381,401,

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178

What is the total production of machine no. 3?

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Solution
• Production accepted : 100 – 27 = 73%. • Thus total production • 100/73 * 438 = 600 units answer.

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• The integers 1, 2,..., 40 are written on a blackboard. The following operation is then repeated 39 times: In each repetition, any two numbers, say a and b, currently on the blackboard are erased and a new number a + b —1 is written. What will be the number left on the board at the end? • Options: (1) 820 (2) 821 (3) 781 (4) 819 (5) 780
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Solution ….
• In the first round, we add up 1 and 2 and get 2. now we take up 2 and 3, we get 4, now we take up 4 and 4 and get 7. now we take up 7 and 5 and get 11. Now we take up 11 and 6 and get 16. We can find that we have an increasing series : • 2,4,7,11,16 …. … • Let us add 1 to 39. =39*40/2 = 780 • Let us add 780 + 1= 781 answer.
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What is the total sale (in no. of units) in the year 1991?

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• = 82016 answer.

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What is the % increase in the sale of VCR in 1993 against 1992?
• • • • • Sale in 1993 =6151 Sale in 1992 = 3006 Difference = 3145 Increase in % = 3145/3006 *100 = 105% answer.

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This graph shows price of 4 shares, what is the average price of these 4 shares?

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Solution
• Let us add them: • (150+40+120+90)/4 = 100 answer

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what is the production of food grains in 1991, expressed as a percentage of its production in 1989?

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Solution
• 15/20 *100 = 75 % answer.

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Which is the most logical idea?
• If an ant were as big as a horse, could it move mountains? • No. A giant ant . . . . . (select from a,b,c,d) • (a) Would be a structural failure. • (b) Would never be able to move mountains. • (c) Would be a mere curiosity. • (d) Would never be able to hunt for food.
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Solution
• A giant Ant would not be able to move mountains because it is just a curoisity (we are not sure about what could it do). Other options are not logical – as logically we cannot say that it is structural failure or it cannot hunt for food or it cannot move mountains.

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Puzzle test…
• Nine cricket fans are watching a match in a stadium. Seated in one row, they are J, K, L, M, N, 0, P, Q and R. L is at the right of M and at third place at the right of N. K is at one end of the row. Q is immediately next to 0 and P. 0 is at the third place at the left of K. J is right next to left of 0. • Who is sitting in the centre of the row? • (a)L (b)O • (c)J (d)Q
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Solution …
• NRMLJOPQK • J IS IN THE CENTRE

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A and B start walking in opposite directions. A covers 3 km and B covers 4 km. Then A turns right and walks 4 km while B turns left and walks 3 km. How far is each from the starting point?
• A is 3 KM in one direction and 4 KM in right. Applying pythogorus, we find that A is 5 KM from the starting point. Similarly B is also 5 KM from the starting point. Ans.
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Ram walks 10 m south from his house, turns left and walks 25 m, again turns left and walks 40 m, then turns right and. walks 5 m to reach to school. In which direction the school is from his house?
• Draw a map and get the answer = northeast.
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In a class of 35 students Kiran is placed 7th from the bottom whereas Sohan is placed 9th from the top. Mohan is placed exactly in between the two. What is Kiran‘s position from Mohan?
• 10th • From 9th to the top and 7th to the bottom, we have 21 candidates (35-(6+8) ). Mohan is just in the centre. So from Mohan, Kiran th place. Answer. is 2/8/2009 at 10 AFTERSCHO☺OL's MATERIAL 196
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A watch reads 4 If the minute hand points towards the East, in which direction does the hour hand point?
• The hour hand is towards South West.

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Puzzle
• Goti and I started walking towards each other from two places lOO m apart. After walking 30m, Goti turns left and goes lO m, then he turns right and goes 20m then turns right again and comes back to the road and starts walking. If we walk with the same speed, what is the distance between us at this point of time
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Solution
• (Goti walks 70 meters in all), so I walk 70 meters towards Goti‘s starting point and now I am 30 meters from that. Goti takes only 30+20 meters on the road. Thus Goti is 50 meters from my starting point. Thus there is a gap of 20 meters between me and Goti. Answer.

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Sum of 1st to 30th terms of a series in arithmetic progèssion is 150. if the first term is A, what is 30th term of the series?
• • • • Sum = 30/2 (2a + (29)D) = 150 2a + 29d =150*2/30 = or 29 D = 10 – 2A 30th term = A + 29D 29 D = 10 – 2A, putting the value, we get the answer = 10 – A answer
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Question on number system
• Convert 252 into binary system • 252 / 2 = 126 / 2 = 63/2 = 31/2 = 15/2 = 7/2 = 3/2 =1 (starting from last remainder to the first) • 11111100 answer. • Convert it again to decimal system: • 1*2^7+1*2^6+1*2^5+1*2^4+1*2^3+1*2^2+ 0*2^1+0*2^0 = 128+64+32+16+8+4 = 252
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Multiply 12 to 13 ( note - both are octal numbers, your outcomes must also be in octal numbers)?
• Let us first convert them into decimal numbers: 12= 1*8^1 + 2*8^0 =10 • 13 = 1*8^1 + 3*8^0 =11 • Now multiply 10 to 11 = 110 • Now convert it into octal number: • 110/8 = 13 / 8 • =156 • Test = now convert 156 to decimal number 2/8/2009 AFTERSCHO☺OL's MATERIAL 202
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Convert 156 (octal) to decimal number …..
• 1*8^2 + 5*8^1 + 6*8^0 • =64+40+6 • =110 answer.

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Multiply 5 (base 16) to 12 (base 7) and get the outcome in binary?
• • • • (5*16^0 ) * (1*7^1 +2*7^0) 5 *9 = 45 45/2 = 22/2 = 11/2 = 5/2 =2/2 1 =101101 answer.

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78.8% of a common medicine for stomach-upsets is absolute alcohol; 3.3% of it is mentha oil; 0.07% spear mint oil; and 0.177% chloroform. How much of each of these compounds is there in a pack of 30 ml? solution alchol = 23.6 ml, 1 ml of menthol oil and so. On.
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What is the sum of cubes of the first 5 natural numbers?
• • • • Formula = [N (N+1)/2 ]^2 = [5*6 / 2 ]^2 =225 answer.

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What is the sum of squares of the first 13 natural numbers?
• • • • Formula =[n(n+1)(2n+1) ] /6 =(13*14*27)/6 =819 answer.

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In a Class of 80 pupils, the number of boys is three-fifths the number of girls. Determine the number of girls in the class.
• • • • • Let the number of girls be X X + 3/5X = 80 8/5 X = 80 X = 80 *5/8 X = 50 (the number of girls is 50, boys are 30) answer.
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The difference between two numbers is 30. On dividing the greater by the smller the quotient is 3. Find the numbers.
• • • • Let the smaller number be X. 3X – X = 30 2X =30; X = 15, Thus 2 numbers are 15 and 45 answer.

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Gunpowder contains 75% nitre and 10% sulphur. The rest of it is charcoal. What is the amount of charcoal in 9 kg of gunpowder.
• • • • Charcoal is (100 – 75 – 10) = 15% 9 KG = 9000 Grams 9000*15/100 =1350 grams answer.
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Question on profit
• At what percentage alove the Cost price must an article be marked so as to gain 33% after allowing the customer a discount of 5%? • (a) 48% (b) 43% • (c) 40% (d) 38% • (e) None of the above
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Solution …
• Let the cost be 100 • Final price being realised 133 • It is after discount, so price before discount (marked price) is : • 133*100/95 =140 , so 40 is the answer.

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A vertical pole PO is standing at the centre 0 of a square ABCD. If AC subtends an angle 90° at point P of the pole then the angle subtended by a side of the square at Pis (a) 35° (b) 45° (c) 30° (d) 60° (e) None of the above
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Solution
• When diagonal (in a square) makes angle of 90 degree in a pyrimidical shape, then sides make angles of 60 degree. (rule). • So answer is 60 degrees.

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Find the per cent of pure gold in 22 carat gold, if 24 carat gold is cent per cent pure gold.
• 22/24 *100 • =91.67 % answer.

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In the diagram the two circles pass through each other‘s centre. If the radius of each circle is 2, what is the perimeter of the region marked B?

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Solution
• Permieter of one circle is 2/3 now because, it is being cut by other circle. • Thus 2/3 + 2/3 of perimeters added : • 2 * 2/3 * (formula of perimeter = 2pi *r) • =(8 * pi * r) /3 answer.

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What is angle C?

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Solution
• Angle O is double the angle A. Thus it is 100 degree. Thus C is (180 -100)/2 = 40 degrees answer.

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What is angle a?

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Solution
• • • • • • • • Angles from D and C are equal . 180 – 60 – 37 – x =83 – x Let us sum up for two angles: (180+180 ) = 360 83-x + 83 – x + 180+2X = 360 2Y +2X = 180 let us assume Y = 53 2X = 72 or X = 36 answer (solve by options, so angle A = 53 ) answer.
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Afterschoool conducts three year integrated PGPSE (after class 12th along with IAS / CA / CS) and 18 month PGPSE (Post Graduate Programme in Social Entrepreneurship) along with preparation for CS / CFP / CFA /CMA / FRM. This course is also available online also. It also conducts workshops on social entrepreneurship in schools and colleges all over India – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society.

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Why such a programme?
• To promote people to take up entrepreneurship and help develop the society • To enable people to take up franchising and other such options to start a business / social development project • To enable people to take up social development as their mission • To enable people to promote spirituality and positive thinking in the world
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Who are our supporters?
• Afterschoolians, our past beneficiaries, entrepreneurs and social entrepreneurs are supporting us. • You can also support us – not necessarily by money – but by being promotor of our concept and our ideas.

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About AFTERSCHO☺OL PGPSE – the best programme for developing great entrepreneurs
• • • • • Most flexible, adaptive but rigorous programme Available in distance learning mode Case study focused- latest cases Industry oriented practical curriculum Designed to make you entrepreneurs – not just an employee • Option to take up part time job – so earn while you learn • The only absolutely free course on internet
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Workshops from AFTERSCHO☺OL
• • • • • • • • • IIF, Delhi CIPS, Jaipur ICSI Hyderabad Branch Gyan Vihar, Jaipur Apex Institute of Management, Jaipur Aravali Institute of Management, Jodhpur Xavier Institute of Management, Bhubaneshwar Pacific Institute, Udaipur Engineering College, Hyderabad

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Flexible Specialisations:
• • • • • • • • • • Spiritualising business and society Rural development and transformation HRD and Education, Social Development NGO and voluntary work Investment analysis,microfinance and inclusion Retail sector, BPO, KPO Accounting & Information system (with CA / CS /CMA) Hospital management and Health care Hospitality sector and culture and heritage Other sectors of high growth, high technology and social relevance

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Salient features:
• The only programme of its kind (in the whole world) • No publicity and low profile course • For those who want to achieve success in life – not just a degree • Flexible – you may stay for a month and continue the rest of the education by distance mode. / you may attend weekend classes • Scholarships for those from poor economic background • Latest and constantly changing curriculum – keeping pace with the time • Placement for those who are interested • Admissions open throughout the year • Latest and most advanced technologies, books and study material
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Components
• • • • • • • • • • • • • • Pedagogy curriculum and approach based on IIM Ahmedabad and ISB Hyderabad (the founder is alumnus from IIMA & ISB Hyderabad) Meditation, spiritualisation, and self development EsGotitial softwares for business Business plan, Research projects Participation in conferences / seminars Workshops on leadership, team building etc. Written submissions of research projects/articles / papers Interview of entrepreneurs, writing biographies of entrepreneurs Editing of journals / newsletters Consultancy / research projects Assignments, communication skill workshops Participation in conferences and seminars Group discussions, mock interviews, self development diaryng Mind Power Training & writing workshop (by Dr. T.K.Jain)

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Pedagogy
• • • • • • • • • Case analysis, Articles from Harvard Business Review Quiz, seminars, workshops, games, Visits to entrepreneurs and industrial visits PreGotitations, Latest audio-visuals Group discussions and group projects Periodic self assessment Mentoring and counselling Study exchange programme (with institutions out of India) • Rural development / Social welfare projects
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Branches
• AFTERSCHO☺OL will shortly open its branches in important cities in India including Delhi, Kota, Mumbai, Gurgaon and other important cities. Afterschooolians will be responsible for managing and developing these branches – and for promoting social entrepreneurs.

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Case Studies
• We want to write case studies on social entrepreneurs, first generation entrepreneurs, ethical entrepreneurs. Please help us in this process. Help us to be in touch with entrepreneurs, so that we may develop entrepreneurs.

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Basic values at AFTERSCHO☺OL
• • • • • • Share to learn more Interact to develop yourself Fear is your worst enemy Make mistakes to learn Study & discuss in a group Criticism is the healthy route to mutual support and help • Ask fundamental questions : why, when, how & where? • Embrace change – and compete with yourself only
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www.afterschoool.tk social entrepreneurship for better society

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Description: Join AFTERSCHOOOL. Become social entrepreneur. Promote education, training, development and social change life long. Form voluntary groups for social development. This material is a part of our PGPSE programe. Our programme is available for any student after class 12th / graduation. AFTERSCHO☺OL conducts PGPSE, which is available free to all online students. There are no charges. PGPSE is a very rigorous programme, designed to give a comprehensive training in social entrepreneurship / spiritual entrepreneurship. This programme is aimed at those persons, who want to ultimately set up their own business enterprises which can benefit society substantially. PGPSE is a unique programme, as it combines industry consultancy, business solutions and case studies in addition to spirituality and social concerns. You can read the details at www.afterschoool.tk or at www.afterschool.tk