GMAT Maths Practice Paper

    GMAT PAPER- IV 1. Gauri went to the stationers and bought things worth Rs 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?(1 Rupee = 100 Paise) (a) Rs 15 (b) Rs 15.70 (c) Rs 19.70 (d) Rs 20 (e) Rs 18 (c)Let the amount of taxable purchases be Rs x. 30 100 ⇒ x = 5. Then, 6% of x = Solution. Cost of tax free items = Rs [25 – (5 + 0.30)] = Rs 19.70. 2. A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is : (a) 250 (b) 276 (c) 280 (d) 285 (e) 255 (d) Since the month begins with a Sunday, so there will be five Sundays in the month. ⎛ 510 × 5 + 240 × 25 ⎞ 8550 ⎜ ⎟ = 30 = 285 30 ⎠ Required average = ⎝ . Solution 3. Two pipes A and B can fill a tank in 20 and 30 minutes, respectively. If both the pipes are used together, then how long will it take to fill the tank? (a) 12 min (b) 15 min (c) 25 min (d) 50 min (e) 30 min 1 20 ; (a) Part of the tank filled by A in 1 min = 1 30 . Part of the tank filled by B in 1 min = 1 ⎞ ⎛ 1 1 ⎜ 20 + 30 ⎟ ⎝ ⎠ = 12 . Part of the tank filled by (A + B) in 1 min = Solution. Both the pipes can fill the tank completely in 12 minutes. 4. In an examination, the average marks obtained by students who passed was x%, while the average of those who failed was y%. The average mark of all students taking the examination was z%. Find in terms of x, y and z, the percentage of students taking the exam who failed. (a) (z – x) / (y – x) (b) (x – z) / (y – z) (c) (y – x) / (z – y) (d) (y – z) / (x – z) (e) (z – x) / (y –z) (a) Let the failed candidates be F and the total candidates be 100. Then, (100 – F).x% + F.y% = z%(100). Solving the equation, we get x – Fx + Fy = z; ⇒ F = (z – x) / (y – x). Solution. 5. A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest $6500 for 6 months, B, $8400 for 5 months and C, $10,000 for 3 months. A wants to be the working member for which he was to receive 5% of the profits. The profit earned was $7400. Calculate the share of B in the profit. (a) $ 1900 Solution. (b) $ 2660 (c) $ 2800 (d) $ 2840 (b) For managing, A receives = 5% of $7400 = $370. Balance = $ (7400 – 370) = $7030. Ratio of their investments = (6500 × 6) : (8400 × 5) : (10000 × 3) = 39000 : 42000 : 30000 = 13 : 14 : 10. 14 ⎞ ⎛ ⎜ 7030 × 37 ⎟ ⎝ ⎠ = $ 2660. B's share = $ 6. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. Was China's GDP in 2001 50% higher than that of India ? It is given that FEI for a country in a year is the ratio (expressed as a percentage) of its foreign equity inflows to its GDP. (1) FEI of India in the year 2001 was 0.72 while FEI of China in the year 2001 was 4.80. (2) China's foreign equity inflows in 2001 were 10 times that to India. (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. FEI = foreign equity inflows ×100 GDP of the country = foreign equity inflows ×100 Solution. (c) Given : FEI ⇒ GDP of a country Hence, we need FEI and foreign equity infows of a country to get GDP of that country. Here we have been asked about the comparison of GDPs of China and India. Therefore, ratios of foreign equity inflows in the given two countries are sufficient to lead us towards answer. ∴ Statements (1) and (2) together are necessary to answer the question. 7. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. A tea dealer mixed 60 kg of ordinary tea with 40 kg of one of better quality. What would be the cost price of each kind of tea if the dealer gains 25% on his outlay? (1) Selling price of the mixture per kg is equal to the cost price of sugar per kg and the dealer get 20% profit by selling sugar at $ 25 per kg. The dealer is habituated to count his percent profit on cost price for all the goods except sugar. (2) Difference between the cost prices of each kind of tea is $ 2 per kg. (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. (c) Let the price of ordinary tea = $P per kg and in the mixture, ratio of ordinary tea and better quality tea = 60 : 40 = 3 : 2. (1) ⇒ Selling price of mixture = Cost price of sugar = $. 20 per kg ( % profit is counted on Selling price for sugar) ⎛ 100 ⎞ Rs ⎜ ⎟20 ∴ Cost price of mixture = ⎝ 100 + 25 ⎠ = $ 16 per kg 7. (2) ⇒ Price of better quality tea = $. (P + 2) per kg. Now, we use Alligation method P 16 3 P+2 2 ⇒ P + 2 − 16 3 = 16 − P 2 Hence, Cost price of each kind of tea can be calculated using both statements together. 8. An express train travelled at an average speed of 100 km/hr, stopping for 3 minutes after every 75 km. How long did it take to reach its destination 600 km from the starting point? (a) 6 hrs 21 min (b) 6 hrs 24 min (c) 6 hrs 27 min (d) 6 hrs 30 min (e) 6 hrs 32 min ⎛ 600 ⎞ ⎜ ⎟ (a) Time taken to cover 600 km = ⎝ 100 ⎠ hrs. = 6 hrs. 600 −1 Number of stoppages = 75 =7 Solution. Total time of stoppage = (3 × 7) min = 21 min. Hence, total time taken = 6 hrs 21 min. 9. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. A starts a business with $60,000. After 6 months B joins him. What is the profit of B at the end of the year? (1) The share of the profit is in the ratio 4 : 3 (2) B's capital is $90,000. (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. (e) By using both statements, we can't be determined the profit of B. ∴ Both statements together are insufficient to answer the question. Solution. 10. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. In the diagram shown, is Δ ABC isosceles? A D B C (1) BC = BD = DA (2) BD bisects ∠ABC (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. Solution. (c) (1) ⇒ ∠ABD = ∠BAD = θ (let) (2) ⇒ ∠ABD = ∠CBD = θ A θ °– 180 α D α θ θ B α C  Since BC = BD ⇒ ∠BDC = ∠BCD = α (let) ∴ In ΔABD, θ + θ + (180 – α) = 180º ⇒ α = 2θ ⇒ ∠ACB = ∠ABC ⇒ ∠AB = ∠AC ⇒ ΔABC is isosceles. Hence, both statements together are necessary to answer the question. 11. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. Is ababab divisible by 222 where a and b are two digits? (1) a + b = 5. (2) b is an even number (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. ababab = a × 105 + b × 104 + a × 103 + b × 102 + a × 10 + b = a (101010) + b (10101) = 10101 (10a + b) Since 10101 is divisible by 111, ababab is always divisible by 111. ⇒ ababab is divisible by 222 only when b is even. Therefore statement (2) alone is sufficient to answer the question. (b) Solution. 12. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. Who among the three friends A, B and C reached the school first? (1) A reached the school at 7.15 am five minutes before the bell rang. (2) B reached before C, who reached the school before the bell rang. (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. (e) (1) ⇒ Bell range at 7.15 + 5 = 7.20 am Solution. (2) ⇒ Both B and C reached the school before 7.20am (using 1). But exact time of reaching can't be determined. Hence, comparison is not possible. 13. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. What is the percentage of families in the city have telephones? (1) 50 % of the families of the city have televisions. (2) 30% of the television owners of the city have telephones. (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. (c) Let total families in city = x = x 2 Solution (1) ⇒ Families having television x 3x = (2) ⇒ Families having telephoes = 30% of 2 20 3x / 20 = × 100 x ∴ Required % Hence, both statements together are necessary to answer the question. 14. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. A sequence of numbers a1, a2 .......... is given by the rule = a n + 1. Does 3 appear in the sequence? (1) a1 = 2 (2) a3 = 16 (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. (d) Here a1, a2, a3, a4, ....... are a02, a12, a22, a32.......... respectively. (1) ⇒ a1 = 2 ⇒ a2 = 4, a3 = 16 and so on. ∴ Statement (1) alone is sufficient to answer the question. (2) ⇒ a3 = 16 ⇒ a2 = 4, a1 = 2, a0 = 2 ∴ Statement (2) alone is sufficient to answer the question. 15. An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metres of cloth? (a) 178 (b) 195 (c) 204 (d) 488 (b) Let the required time be x seconds. Then, for weaving more metres, more time is required (Direct Proportion) 0.128 : 25 : : 1 : x 25 25 × 1000 Solution. Solution. or 0.128 × x = 25 × 1 or x = 0.128 = 128 or x = 195.31. Required time = 195 seconds (approximately). 16. In a circular lawn there is a 16m long path in the form of a chord. If path is 6m away from the centre of the lawn, then find the radius of the circular lawn. (a) 16 m (b) 6 m (c) 10 m (d) 8 m (e) 12.5 m B 8 r O 6 A C Solution. (c) 2 2 As OC ⊥ AB, we get a right angled triangle with sides 6 and 8. Hence r = OB = 6 + 8 = 10 m 17. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. If x (1) (2) (a) (b) (c) (d) (e) 0, – 1 then is greater than x<1 x>1 Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. EACH statement ALONE is sufficient Statements (1) and (2) TOGETHER are NOT sufficient. (b) (1) ⇒ x < 1 ⇒ x may be positive or negative. 1 1 1 x 1 x +1 ? Solution. ∴ We can't be determined whether x is greater than x + 1 . (2) ⇒ x > 1 ⇒ x is positive ⇒ x < x + 1 ⇒ x x +1 = x ( x + 1) x ( x + 1) [dividing both sides by x (x + 1)] 1 1 ⇒ < x +1 x ∴ Statement (2) alone is sufficient to answer the question. 18. Of the 1000 inhabitants of a town, 60% are males of whom 20% are literate. If, of all the inhabitants, 25% are literate, then what percent of the females of the town are literate ? (a) 22.5 (b) 27.5 (c) 32.5 (d) 37.5 (e) 30% (c) Number of males = 60% of 1000 = 600. Number of females = (1000 – 600) = 400. Number of literates = 25% of 1000 = 250. Number of literate males = 20% of 600 = 120. Number of literate females = (250 – 120) = 130. ⎛ 130 ⎞ ⎜ 400 × 100 ⎟ % ⎝ ⎠ = 32.5%. Required percentage = Solution. 19. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. Which city has the lowest population? (1) Bareilly has 20 lakh population, which is less than the population of Banaras. (2) Patna has population equal to that of Banaras and more than that of Allahabad. (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. Solution. (e) (1) ⇒ Bareilly < Banaras (2) ⇒ Allahabad < Patna = Banaras ∴ No conclusion can be drawn. 20. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. Is x = 11? (1) Square of 11 is not equal to x. (2) (a) (b) (c) (d) (e) Square of x is not equal to the square of 11. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. EACH statement ALONE is sufficient Statements (1) and (2) TOGETHER are NOT sufficient. 2 (d) (1) ⇒ x ≠ 11 ⇒ x ≠ 11 Solution. (2) ⇒ x ≠ 11 ⇒ x ≠ 11 Hence, each statement alone is sufficient to answer the question. 2 ( )2 21. The value of 112 × 54 is : (a) 6700 (b) 70000 (e) None of these 4 (c) 76500 4 (d) 77200 1120000 Solution. (b) 110 × 10 ⎛ 5× 2 ⎞ = 112 × ⎜ ⎟ = ⎝ 4 ⎠ 24 4) (112 × 5 = 2 4 1120000 = 16 = 70000. 22. 22. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. A group of 49 consumers were offered a chance to subscribe to 3 magazines: A, B and C. Thirty-eight of the consumers subscribed to at least one of the magazines. How many consumers subscribed to exactly two of the magazines? (1) Twelve of the 49 consumers subscribed to all three of the magazines. (2) Twenty of the 49 consumers subscribed to magazine A. (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. (e) The number of consumers who subscribed to at least one magazine is the sum of the number of consumers who subscribed to exactly one, two and three magazines. So 38 = N1 + N2 + N3, where N1, N2 and N3 are the number who subscribed to 1, 2 and 3 magazines, respectively. We have to find N2. (1) ⇒ Value of N3. (2) ⇒ Number of subscribers of magazine A. ∴ Both statements together are not sufficient to answer the question. 23. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. How much cardboard will it take to make an open cubical box with no top ? (1) The area of the bottom of the box is 4 square metres. (2) The volume of the box is 8 cubic metres. (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. (d)(1) ⇒ Area of the open cubical box with no top = 4 × 5 = 20 sq m (2) ⇒ Edge of box = 2m. Therefore required area = 5 × (2)2 = 20 sq. m. Hence we can get answer with statement (1) alone and statement (2) alone. Solution. 24. Three men, four women and six children can complete a work in seven days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days? (a) 7 (b) 8 (c) 12 (d) Cannot be determined (e) None of these (a) Let 1 woman's 1 day's work = x. x x Solution. Then, 1 man's 1 day's work = 2 and 1 child's 1 day's work = 4 6x ⎞ 1 ⎛ 3x ⎜ 2 + 4x + 4 ⎟ ⎠= 7 Now, ⎝ = 1 woman alone can complete the work in 49 days. 28x 4 ⇒ ⎛1 4 ⎞ 1 ⎜ × ⎟ x = ⎝ 7 28 ⎠ = 49 . ⎛ 49 ⎞ ⎜ ⎟ So, to complete the work in 7 days, number of women required = ⎝ 7 ⎠ = 7. 25. How many numbers are there between 500 and 600 in which 9 occurs only once? (a) 17 (b) 19 (c) 20 (d) 21 (e) 22 (a) From 500 to 590, the total no. of such numbers = 9 From 591 to 600, the total no. of such numbers = 8 ⇒ Required answer = 9 + 8 = 17 Solution. 26. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. In a row of boys facing north who is on the immediate right of Nishikant? (1) Nishikant is third to the left of Shashikant and third to the right of Ravikant. (2) Dinanath and Premnath are also in the row but Dinanath is the nearest to Shashikant. (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. Solution. (c) By using (1) and (2), we get the following order of their positons. RPNDS 27. A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hours. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at : (a) 7.42 a.m. (b) 7.48 a.m. (c) 8.10 a.m. (d) 8.30 a.m. (e) 8.50 a.m. (a) Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two. Relative speed of A and B = (6 – 1) = 5 rounds per hours. Time taken to complete one round at this speed = hr = 12 min. Hence, they will meet at 7.30 a.m. + 12 min. = 7.42 a.m. Solution. 28. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. A car, originally, was sold for $2,00,000. After a month, the car was discounted x%, and a month later, the car's price was discounted y%. Is the car's price after the discounts less than $1,75,000? (1) y = 10 (2) x = 15 (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. (b) (2) ⇒ The price of the car after the 1st month = $170000. Hence only statement (2) is sufficient to answer the question. A car travels the first one-third of a certain distance with a speed of 10 km/hr, the next one-third distance with a speed of 20 km/hr, and the last one-third distance with a speed of 60 km/hr. The average speed of the car for the whole journey is: (a) 18 km/hr (b) 24 km/hr (c) 30 km/hr (d) 36 km/hr (e) 32 km/hr (a) Let the total distance travelled be x km and the average speed of the car for the whole journey be y km/hr. (x / 3) (x / 3) (x / 3) + + 20 60 Then, = 10 x x x x + + ⇒ 30 60 180 = y ⇒ = 1 ⇒ y = 18 km/hr. 28. 29. Solution. 30. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. A bag contains coins of one-rupee, 50-paise and 25-paise denominations. The total amount in the bag is Rs 500. To find the total number of 50-paise coins, which of the following information is sufficient? (1 Rupee = 100 Paise) (1) The number of the coin is in the ratio 3 : 4 : 5. (2) The number of one rupee-coins is one-fourth the total number of coins in the bag. (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. Solution. (1) ⇒ 3x + 4x (0.50) + 5x (0.25) = 500 ⇒ 6.25x = 500 ⇒ x = 80 ∴ The total number of 50-paise coins = 4x = 320 But we can't be solved the question using statement (2). Hence statement (1) alone is sufficient to answer the question. (a) 31. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee. In how many ways can it be done? (a) 564 (b) 645 (c) 735 (d) 756 (e) None of these (d) A committee of five persons can be made as follows under the given restrictions: (i) 3 men and 2 women (ii) 4 men and 1 woman (iii) 5 men only Required number of ways = Solution. ( 7 C3 ×6 C2 + 7 C4 ×6 C1 + 7 C5 ) ( ) ( ) = 525 + = (525 + 210 + 21) = 756. ⎛ 7× 6×5 6×5 ⎞ × ⎜ ⎟ = ⎝ 3 × 2 ×1 2 ×1 ⎠ + ⎛ 7× 6×5 ⎞ ⎜ 3 × 2 ×1 × 6 ⎟ ⎝ ⎠ ( 7 C3 ×6 C1 ) +( C) 7 5 ⎛ 7×6 ⎞ ⎜ ⎟ + ⎝ 2 ×1 ⎠ 32. 2 If $510 be divided among A, B, C in such a way that A gets 3 rd of what B gets and B gets th of what C gets, 1 4 then their shares are, respectively (a) $ 120, $ 240, $ 150 (c) $ 150, $ 300, $ 60 (e) None of these (b) (d) $ 60, $ 90, $ 360 $ 100, $ 160, $ 250 Solution. 2 1 ⎞ A 2 B 1 ⎛ ⎜ A = 3 B and B = 4 C ⎟ ⇒ B = 3 and C = 4 ⎝ ⎠ (b) A : B = 2 : 3 and B : C = 1 : 4 = 3 : 12 A : B : C = 2 : 3 : 12. 2⎞ ⎛ ⎜ 510 × ⎟ 17 ⎠ ⎝ A's share = $ = $ 60 and 3⎞ ⎛ ⎜ 510 × ⎟ 17 ⎠ ⎝ B's share = $ = $ 90; 12 ⎞ ⎛ ⎜ 510 × ⎟ 17 ⎠ ⎝ C's share = $ = $ 360. 33. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. Is nx – n divisible by x? It is given that x and n are natural numbers. (1) Value of n is known. (2) Value of x is known. (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. Solution. (b) Remember that nx – n is divisible by x if x is a prime number and the divisibility does not depend on the value of n. ∴ Only statement (2) alone is sufficient to answer the question. 34. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. Are x, y and z in A. P. ? (1) x is greater than y but less than z. x= (2) (a) (b) (c) (d) (e) Solution. y+z 2 Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. EACH statement ALONE is sufficient Statements (1) and (2) TOGETHER are NOT sufficient. (b) (1) ⇒ y < x < z. ∴ Statement (1) is not sufficient to answer the question. (2) ⇒ x – y = z – x ⇒ y, x, z are in A.P. ∴ Only statement (2) is sufficient to answer the question. 35. A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank? (a) 20 hrs. (b) 25 hrs. (c) 35 hrs. (d) Cannot be determined (e) None of these (c) Suppose pipe A alone takes x hours to fill the tank. x 2 Solution. Then, B and C will take Now, 36. 1 x and 7 x x 4 hours, respectively, to fill the tank. + 2 x + 4 x 1 =5 ⇒ 1 = 5 ⇒ x = 35 hrs. A company bought a total of 60 computers and 20 printers to modernize its billing operations. If the price of each computer was three times the price of each printer, what percent of the total cost of the purchase was the total cost of the printers? (a) 10% (b) 11% (c) 15% (d) 20% (e) 24% (a) Let the cost of each printer = $ x Cost of each computer = $ 3x Total cost = 60 × 3x + 20x = 200x 20x Solution. Required % = 200x 37. × 100 = 10% A motor cyclist travels for 10 hours, the first half at 21 km/h and the other half at 24 km/h. Find the distance travelled. (a) 225 km (b) 224 km (c) 200 km (d) 234 km (e) 350 km Solution. (b) Let the total distance travelled be x km. x Now, 2 × 21 2 × 24 + x = 10 ⎡1 1⎤ x ⎢ + ⎥ = 60 or ⎣ 7 8 ⎦ 60 × 7 × 8 or x = = 4 × 8 × 7 = 224 km 15