ROHRA’S ACADEMY DATA SUFFICIENCY Directions for questions 1 to 25: Each item is followed by two statements, A and B. Answer each question using the following instructions. Choose (a) if the question can be answered by one of the statements alone and not by the other. Choose (b) if the question can be answered by using either statement alone. Choose (c) if the question can be answered by using both the statements together, but cannot be answered by using either statement alone. Choose (d) if the question cannot be answered even by using both statements together. 1. Two friends, Ram and Gopal, bought apples from a wholesale dealer. How many apples did they buy? A. Ram bought one-half the number of apples that Gopal bought. B. The wholesale dealer had a stock of 500 apples. 2. Is country X’s GDP higher than country Y’s GDP? A. GDPs of the countries X and Y have grown over the past five years at compounded annual rate of 5% and 6% respectively. B. Five years ago, GDP of country X was higher than that of country Y. 3. What is the value of X? A. X and Y are unequal even integers, less than 10, and X/Y is an odd integer. B. X and Y are even integers, each less than 10, and product of X and Y is 12. 4. On a given day a boat ferried 1500 passengers across the river in twelve hours. How many round trips did it make? A. The boat can carry two hundred passengers at any time. B. It takes 40 minutes each way and 20 minutes of waiting time at each terminal. 5. What will be the time for downloading software? A. Transfer rate if 6 Kilobytes per second. B. The size of the software is 4.5 megabytes. 6. A square is inscribed in a circle. What is the difference between the area of the circle and that of the square? A. The diameter of the circle is 25/2 cm. B. The side of the square is 25 cm. 7. What are the values of m and n? A. n is an even integer, m is an odd integer, and m is greater than n. B. Product of m and n is 30. 8. The average weight of students in a class is 50 kg. What is the number of students in the class? A. The heaviest and the lightest members of the class weigh 60 kg and 40 kg respectively. B. Exclusion of the heaviest and the lightest members from the class does not change the average weight of the students. 9. A small storage tank is spherical in shape. What is the storage volume of the tank? A. The wall thickness of the tank is 1 cm. B. When the empty spherical tank is immersed in a large tank filled with water, 20 litres of water overflow from the large tank. 10. Mr. X starts walking northwards along the boundary of a field, from point A on the boundary, and after walking for 150 metres reaches B, and then walks westwards, again along the boundary, for another 100 metres when he reaches C. What is the maximum distance between any pair of points on the boundary of the field? A. The field is rectangular in shape. B. The field is a polygon, with C as one of its vertices and A the mid point of a side. 11. A line graph on a graph sheet shows the revenue for each year from 1990 through 1998 by points and joins the successive points by straight line segments. The point for revenue of 1990 is labelled A, that for 1991 as B, and that for 1992 as C. What is the ratio of growth in revenue between 91-92 and 90-91? A. The angle between AB and X-axis when measured with a protractor is 40 degrees, and the angle between CB and X-axis is 80 degrees. B. The scale of Y-axis is 1 cm = 1000 Rs. 12. There is a circle with centre C at the origin and radius r cm. Two tangents are drawn from an external point D at a distance d cm from the centre. What are the angles between each tangent and the X-axis? A. The coordinates of D are given B. The X-axis bisects one of the tangents. 13. Find a pair of real numbers x and y that satisfy the following two equations simultaneously. It is known that the values of a, b, c, d, e and f are non-zero. ax + by = c dx + ey = f A. a = kd and b = ke, c = kf, k 0 B. a = b = 1, d = e = 2, f 2c 14. Three professors A, B and C are separately given three sets of numbers to add. They were expected to find the answers to 1+1, 1+1+2, and 1+1 respectively. Their respective answers were 3, 3, and 2. How many of the professors are mathematicians? A. A mathematician can never add two numbers correctly, but can always add three numbers correctly. B. When a mathematician makes a mistake in a sum, the error is + I or -1. 15. How many among the four students A, B, C and D have passed the exam'? A. The following is a true statement: A and B passed the exam. B. The following is a false statement: At least one among C and D has passed the exam. 16. What is the distance x between two cities A and B in integral number of Kms? A. x satisfies the equation log 2 x = B. x 10 Kms 17. Mr. Mendel grew one hundred flowering plants from black seeds and white seeds, each seed giving rise to one plant. A plant gives flowers of only one colour. From a black seed comes a plant giving red or blue flowers. From a white seed comes a plant giving red or white flowers. How many black seeds were used by Mr. Mendel? A. The number of plants with white flowers was 10. B. The number of plants with red flowers was 70. 18. In a hockey match, the Indian team was behind by 2 goals with 5 minutes remaining. Did they win the match? A. Deepak Thakur, the Indian striker, scored 3 goals in the last five minutes of the match. B. Korea scored a total of 3 goals in the match. 19. Four students were added to a dance class. Would the teacher be able to divide her students evenly into a dance team (or teams) of 8? A. If 12 students were added, the teacher could put everyone in teams of 8 without any leftovers. B. The number of students in the class is currently not divisible by 8. 20. Is x = y? A. (x + y)( 1 / x + 1 / y) = 4 B. (x – 50)2 = ( y – 50)2 21. A dress was initially listed at a price that would have given the store a profit of 20 percent of the wholesale cost. What was the wholesale cost of the dress? A. After reducing the listed price by 10 percent, the dress sold for a net profit of 10 dollars. B. The dress sold for 50 dollars. 22. Is 500 the average(arithmetic mean) score on the GMAT? A. Half of the people who take the GMAT score above 500 and half of the people score below 500. B. The highest GMAT score is 800 and the lowest score is 200. 23. Is |x - 2| < 1? A. |x| > 1 B. |x - 1| < 2 24. People in a club either speak French or Russian or both. Find the number of people in a club who speak only French. A. There are 300 people in the club and the number of people who speak both French and Russian is 196. B. The number of people who speak only Russian is 58. 25. A sum of Rs.38,500 was divided among Jagdish, Punit and Girish. Who received the minimum amount? A. Jagdish received 2/9 of what Punit and Girish together received. B. Punit received 3/11 of what Jagdish and Girish together received. Directions for questions 26 to 29 - Mark (1) if the question can be answered by using the statement A alone but not by using the statement B alone. Mark (2) if the question can be answered by using the statement B alone but not by using the statement A alone. Mark (3) if the question can be answered by using either of the statements alone. Mark (4) if the question can be answered by using both the statements together but not by either of the statements alone. Mark (5) if the question cannot be answered on the basis of the two statements. 26. In a particular school, sixty students were athletes. Ten among them were also among the top academic performers. How many top academic performers were in the school? A. Sixty per cent of the top academic performers were not athletes. B. All the top academic performers were not necessarily athletes. 27. Five students Atul, Bala, Chetan, Dev and Ernesto were the only ones who participated in a quiz contest. They were ranked based on their scores in the contest. Dcv got a higher rank as compared to Ernesto, while Bala got a higher rank as compared to Chetan. Chetan's rank was lower than the median. Who among the five got the highest rank? A. Atul was the last rank holder. B. Bala was not among the top two rank holders. 28. Thirty per cent of the employees of a call centre are males. Ten per cent of the female employees have an engineering background. What is the percentage of male employees with engineering background? A. Twenty five per cent of the employees have engineering background. B. Number of male employees having an engineering background is 20% more than the number of female employees having an engineering background. 29. In a football match, at the half-time, Mahindra and Mahindra Club was trailing by three goals. Did it win the match? A. In the second-half Mahindra and Mahindra Club scored four goals. B. The opponent scored four goals in the match. Directions for questions 30 to 33 - Each question is followed by two statements A and B. Indicate your responses based on the following directives: Mark (1) if the question can be answered using A alone but not using B alone. Mark (2) if the question can be answered using B alone but not using A alone. Mark (3) if the question can be answered using A and B together, but not using either A or B alone. Mark (4) if the question cannot be answered even using A and B together. 30. The average weight of a class of 100 students is 45 kg. The class consists of two sections, I and II, each with 50 students. The average weight, WI of Section I is smaller than the average weight, WII of Section II. If the heaviest student, say Deepak, of Section II is moved to Section 1, and the lightest student, say Poonam, of Section I is moved to Section II, then the average weights of the two sections are switched, i.e., the average weight of Section I becomes WII and that of Section II becomes WI. What is the weight of Poonam? A: WII - WI = 1.0 B: Moving Deepak from Section II to I (without any move from Ito II) makes the average weights of the two sections equal. 31. ABC Corporation is required to maintain at least 400 Kilolitres of water at all times in its factory, in order to meet safety and regulatory requirements. ABC is considering the suitability of a spherical tank with uniform wall thickness for the purpose. The outer diameter of the tank is 10 meters. Is the tank capacity adequate to meet ABC requirements? A: The inner diameter of the tank is at least 8 meters. B: The tank weighs 30,000 kg when empty, and is made of a material with density of 3 gm/cc. 32. Consider integers x, y and z. What is the minimum possible value of x2+y2+z2 ? A: x+y+z =89 B: Among x, y, z two are equal. 33. Rahim plans to draw a square JKLM with a point 0 on the side JK but is not successful. Why is Rahim unable to draw the square? A: The length of OM is twice that of OL. B. The length of OM is 4 cm. Section 2 1. Four friends Ashok, Bashir, Chirag and Deepak are out shopping. Ashok has less money than three times the amount that Bashir has. Chirag has more money than Bashir. Deepak has an amount equal to the difference of amounts with Bashir and Chirag. Ashok has three times the money with Deepak. They each have to buy at least one shirt, or one shawl, or one sweater, or one jacket, that are priced Rs 200, Rs 400, Rs 600 and Rs 1000 apiece, respectively. Chirag borrows Rs 300 from Ashok and buys a jacket. Bashir buys a sweater after borrowing Rs 100 from Ashok and is left with no money. Ashok buys three shirts. What is the costliest item that Deepak could buy with his own money? (a) A shirt (b) A shawl (c) A sweater (d) A jacket 2. In a family gathering there are two males who are grandfathers and four males who are fathers. In the same gathering there are two females who are grandmothers and four females who are mothers. There is at least one grandson or a grand-daughter present in this gathering. There are two husband-wife pairs in this group. These can either be a grandfather and a grandmother, or a father and a mother. The single grandfather (whose wife is not present) has two grandsons and a son present. The single grandmother (whose husband is not present) has two grand-daughters and a daughter present. A grandfather or a grandmother present with their spouses does not have any grandson or grand-daughter present. What is the minimum number of people present in this gathering? (a) 10 (b) 12 (c) 14 (d) 16 3. Eight people carrying food baskets are going for a picnic on motorcycles. Their names are A, B, C, D, E, F, G and H. They have four motorcycles M1, M2, M3 and M4 among them. They also have four food baskets O, P, Q and R of different size and shapes and which can be carried only on motorcycles M1, M2, M3 or M4 respectively. No more than two persons can travel on a motorcycle and no more than one basket can be carried on a motorcycle. There are two husband-wife pairs in this group of eight people and each pair will ride on a motorcycle together. C cannot travel with A or B. E cannot travel with B or F. G cannot travel with F, or H, or D. The husband-wife pairs must carry baskets O and P. Q is with A and P is with D. F travels on M1 and E travels on M2 motorcycles. G is with Q, and B cannot go with R. Who is travelling with H? (a) A (b) B (c) C (d) D 4. I have a total of Rs 1000. Item A costs Rs 110, item B costs Rs 90, item C costs Rs 70, item D costs Rs 40 and item E costs Rs 45. For every item D that I purchase, I must also buy two of item B. For every item A, I must buy one of item C. For every item E, I must also buy two of item D and one of item B. For every time purchased I earn 1000 points and for every rupee not spent I earn a penalty of 150 points. My objective is to maximise the points I earn. What is the number of items that I must purchase to maximise my points? (a) 13 (b) 14 (c) 15 (d) 16 5. On her walk through the park, Hamsa collected 50 coloured leaves, all either maple or oak. She sorted them by category when she got home, and found the following: _ The number of red oak leaves with spots is even and positive. _ The number of red oak leaves without any spot equals the number of red maple leaves without spots. All non-red oak leaves have spots, and there are five times as many of them as there are red spotted oak leaves. _ There are no spotted maple leaves that are not red. _ There are exactly 6 red spotted maple leaves. _ There are exactly 22 maple leaves that are neither spotted nor red. How many oak leaves did she collect? (a) 22 (b) 17 (c) 25 (d) 18 6. A King has unflinching loyalty from eight of his ministers M1 to M8, but he has to select only four to make a cabinet committee. He decides to choose these four such that each selected person shares a liking with at least one of the other three selected. The selected persons must also hate atleast one of the liking of any of the other three persons selected. M1 likes fishing and smoking, but hates gambling. M2 likes smoking and drinking, but hates fishing. M3 likes gambling, but hates smoking. M4 likes mountaineering, but hates drinking. M5 likes drinking, but hates smoking and mountaineering. M6 likes fishing, but hates smoking and mountaineering. M7 likes gambling and mountaineering, but hates fishing, and M8 likes smoking and gambling, but hates mountaineering. Who are the four people selected by the king? (a) M1, M2, M5, M6 (b) M3, M4, M5, M6 (c) M4, M5, M6, M8 (d) M1, M2, M4, M7 7. In a “keep-fit” gymnasium class there are fifteen females enrolled in a weight-loss program. They all have been grouped in any one of the five weight-groups W1, W2, W3, W4, or W5. One instructor is assigned to one weight-group only. Sonali, Shalini, Shubhra, and Shahira belong to the same weight-group. Sonali and Rupa are in one weight-group, Rupali and Renuka are also in one weight-group. Rupa, Radha, Renuka, Ruchika, and Ritu belong to different weight-groups. Somya cannot be with Ritu, and Tara cannot be with Radha. Komal cannot be with Radha, Somya, or Ritu. Shahira is in W1 and Somya is in W4 with Ruchika. Sweta and Jyotika cannot be with Rupali, but are in a weight-group with total membership of four. No weight-group can have more than five or less than one member. Amita, Babita, Chandrika, Deepika, and Elina are instructors of weightgroups with membership sizes 5, 4, 3, 2 and 1, respectively. Who is the instructor of Radha? (a) Babita (b) Elina (c) Chandrika (d) Deepika Directions for questions 8-10: Answer the following questions based on the passage below: A group of three or four has to be selected from seven persons. Among the seven are two women, Fiza and Kavita, and five men: Ram, Shyam, David, Peter and Rahim. Ram would not like to be in the group if Shyam is also selected. Shyam and Rahim want to be selected together in the group. Kavita would like to be in the group only if David is also there. David, if selected, would not like Peter in the group. Ram would like to be in the group only if Peter is also there. David insists that Fiza be selected in case he is there in the group. 8. Which of the following statements is true? (a) Kavita and Ram can be part of a group of four. (b) A group of four can have two women. (c) A group of four can have all four men. (d) None of the above. 9. Which of the following is a feasible group of four? (a) Ram, Peter, Fiza, Rahim (b) Shyam, Rahim, Kavita, David (c) Shyam, Rahim, Fiza, David (d) Fiza, David, Ram, Peter 10. Which of the following is a feasible group of three? (a) David, Ram, Rahim (b) Peter, Shyam, Rahim (c) Kavita, David, Shyam (d) Fiza, David, Ram Directions for questions 11-12: Answer the following questions based on the information given below: Elle is three times older than Yogesh, Zaheer is half the age of Wahida. Yogesh is older than Zaheer. 11. Which of the following information will be sufficient to estimate Elle’s age? (a) Zaheer is 10 years old. (b) Both Yogesh and Wahida are older than Zaheer by the same number of years. (c) Both (a) and (b) above. (d) None of the above. 12. Which of the following can be inferred? (a) Yogesh is older than Wahida. (b) Elle is older than Wahida. (c) Elle may be younger than Wahida. (d) None of the above. Directions for questions 13 to 16: A and B are two sets (e.g. A = mothers, B = women). The elements that could belong to both the sets (e.g. women who are mothers) is given by the set C = A.B. The elements which could belong to either A or B, or both, is indicated by the set D = AOB. A set that does not contain any elements is known as a null set, represented by @(for example, if none of the women in the set B is a mother, then C = A.B. is a null set, or C = @. Let ‘V’ signify the set of all vertebrates; ‘M’ the set of all mammals; ‘D’ dogs; ‘F’ fish; ‘A’ Alsatian and ‘P’ a dog named Pluto. 13. If P.A. = @ and POA = D, then which of the following is true? (a) Pluto and Alsatian are dogs (b) Pluto is an Alsatian (c) Pluto is not an Alsatian (d) D is a null set. 14. If y = FO (D.V.) is not a null set, it implies that: (a) All fish are vertebrates. (b) All dogs are vertebrates. (c) Some fish are dogs. (d) None of the above. 15. If Z = (P.D.) OM, then (a) The elements of Z consist of Pluto the dog or any other mammal. (b) Z implies any dog or mammal. (c) Z implies Pluto or any dog that is a mammal. (d) Z is a null set. 16. Given that X = M.D. is such that X = D, which of the following is true? (a) All dogs are mammals. (b) Some dogs are mammals. (c) X = @ (d) All mammals are dogs. Directions for question 17 to 20: Answer the questions independent of each other. 17. At a village mela, the following six nautankis (plays) are schedule as shown in the table below: Nautanki Duration Show times 1. Sati Savitri 1 hour 9.00 am and 2.00 pm 2. Joru ka Gulam 1 hour 10.30 am and 11.30 am 3. Sunder Kand 30 minutes 10.00 am and 11.00 am 4. Veer Abhimanyu 1 hour 10.00 am and 11.00 am 5. Reshma aur Shera 1 hour 9.30 am, 12.00 noon, 2.00 pm 6. Jhansi ki Rani 30 minutes 11.00 am and 1.30 pm You wish to see all the six nautankis. Further you wish to ensure that you get a lunch break from 12.30 p.m. to 1.30 p.m. Which of the following ways can you do this? (a) Sati-Savitri is viewed first; Sunder Kand is viewed third and Jhansi ki Rani is viewed last. (b) Sati-Savitri is viewed last; Sunder Kand is viewed third and Jhansi ki Rani is viewed last. (c) Sati-Savitri is viewed first; Sunder Kand is viewed third and Joru ka Gulam is viewed fourth. (d) Veer Abhimanyu is viewed third; Reshma aur Shera is viewed fourth and Jhansi ki Rani is viewed fifth. 18. While Balbir had his back turned, a dog ran into his butcher shop, snatched a piece of meat off the counter and ran off. Balbir was mad when he realised what had happened. He asked three other shopkeepers, who had seen the dog, to describe it. The shopkeepers really didn’t want to help Balbir. So each of them made a statement which contained one truth and one lie. _ Shopkeeper Number 1 said : “The dog had black hair and a long tail.” _ Shopkeeper Number 2 said : “The dog had a short tail and wore a collar.” _ Shopkeeper Number 3 said : “The dog had white hair and no collar.” Based on the above statements, which of the following could be a correct description? (a) The dog had white hair, short tail and no collar. (b) The dog had white hair, long tail and a collar. (c) The dog had black hair, long tail and a collar. (d) The dog had black hair, long tail and no collar. 19. The Bannerjees, the Sharmas and the Pattabhiramans each have a tradition of eating Sunday lunch as a family. Each family serves a special meal at a certain time of day. Each family has a particular set of chinaware used only for this meal. Use the clues below to answer the following question. _ The Sharma family eats at noon. _ The family that serves fried brinjal uses blue chinaware. _ The Bannerjee family eats at 2 o’clock. _ The family that serves sambar does not use red chinaware. _ The family that eats at 1 o’clock serves fried brinjal. _ The Pattabhiraman family does not use white chinaware. _ The family that eats last likes makki-ki-roti. Which one of the following statements is true? (a) The Bannerjees eat makki-ki-roti at 2 o’ clock, the Sharmas eat fried brinjal at 12 o’ clock and the Pattabhiramans eat sambar from red chinaware. (b) The Sharmas eat sambar served in white chinaware, the Pattabhiramans eat fried brinjal at 1 o’ clock and the Bannerjees eat makki-ki-roti in blue chinaware. (c) The Sharmas eat sambhar at noon. The Pattabhiramans eat fried brinjal served in blue chinaware and the Bannerjees eat makki-ki-roti served in red chinaware. (d) The Bannerjees eat makki-ki-roti served in white chinaware, the Sharmas eat fried brinjal at 12 o’clock and the Pattabhiramans eat sambar from red chinaware. 20. Mrs Ranga has three children and has difficulty remembering their ages and the months of their birth. The clues below may help her remember. (a) The boy, who was born in June, is 7 years old. (b) One of the children is 4 years old, but is not Anshuman. (c) Vaibhav is older than Supriya. (d) One of the children was born in September but it was not Vaibhav. (e) Supriya’s birthday is in April. (f) The youngest child is only 2 years old. Based on the above clues, which one of the following statements is true? (a) Vaibhav is the oldest, followed by Anshuman who was born in September, and the youngest is Supriya who was born in April. (b) Anshuman is the oldest being born in June, followed by Supriya who is 4-year old, and the youngest is Vaibhav who is 2 years old. (c) Vaibhav is the oldest being 7 years old, followed by Supriya who was born in April, and the youngest is Anshuman who was born in September. (d) Supriya is the oldest, who was born in April, followed by Vaibhav who was born in June, and Anshuman who was born in September. DIRECTIONS for questions 21 to 26: Answer the questions independent of each other…. 21. Four students (Ashish, Dhanraj, Felix and Sameer) sat for the Common Entrance Exam for Management (CEEM).. One student got admission offers from three National Institutes of Management (NIM), another in two NIMs, the third in one NIM, while the fourth got none. Below are some of the facts about who got admission offers from how many NIMs and what is their educational background. i) The one who is an engineer didn’t get as many admissions as Ashish. ii) The one who got offer for admissions in two NIMs isn’t Dhanraj nor is he a chartered accountant. iii) Sameer is an economist. iv) Dhanraj isn’t an engineer and received more admission offers than Ashish. v) The medical doctor got the most number of admission offers. Which one of the following statements is necessarily true? 1. Ashish is a chartered accountant and got offer for admission in three NIMs. 2. Dhanraj is a medical doctor and got admission offer in one NIM. 3. Sameer is an economist who got admission offers in two NIMs. 4. Felix who is not an engineer did not get any offer for admission. 22. Five boys went to a store to buy sweets. One boy had Rs.40. Another boy had Rs.30. Two other boys had Rs.20 each. The remaining boy had Rs.10. Below are some more facts about the initial and final cash positions. (i) Alam started with more than Jugraj. (ii) Sandeep spent Rs. 1.50 more than Daljeet. (iii) Ganesh started with more money than just only one other person. (iv) Daljeet started with 2/3 of what Sandeep started with. (v) Alam spent the most, but did not end with the least. (vi) Jugraj spent the least and ended with more than Alam or Daljeet. (viii) Alam spent 10 times more than what Ganesh did. In the choices given below, all statements except one are false. Which one of the following statements can be true? 1. Alam started with Rs.40 and ended with Rs.9.50. 2. Sandeep started with Rs.30 and ended with Rs.1.00. 3. Ganesh started with Rs20 and ended with Rs.4.00. 4. Jugraj started with Rs.10 and ended with Rs.7.00. 23. In a hospital there were 200 Diabetes, 150 Hyperglycaemia and 150 Gastro-enteritis patients. Of these, 80 patients were treated for both Diabetic and Hyperglycaemia. Sixty patients were treated for Gastro-enterities and Hyperglycaemia, while 70 were treated for Diabetes and Gastro-enteritis. Some of these patients have all the three diseases. Doctor Dennis treats patients with only Diabetes. Doctor Hormis treats patients with only Hyperglycaemia and Doctor Gerard treats patients with only Gastro-enterities. Doctor Paul is a generalist. Therefore, he can treat patients with multiple diseases. Patients always prefer a specialist for their disease. If Dr. Dennis had 80 patients the other three doctors can be arranged in terms of the number of patients treated as: 1. Paul > Gerard > Hormis 2. Paul > Hormis > Gerard 3. Gerard > Paul > Hormis 4. none of these. 24. Three children won the prizes in the Bournvita Quiz contest. They are from the schools; Loyola, Convent, Little Flowers, which are located at different cities. Below are some of the facts about the schools, the children the city they are from * One of the children is Bipin. * Loyola School’s contestant did not come first. * Little Flower’s contestant was named Riaz. * Convent School is not in Hyderabad. * The contestant from Pune took third place. * The contestant from Pune is not from Loyola School. * The contestant from Bangalore did not come first. * Convent School’s contestant’s name is not Balbir. Which of the following statements is true? 1. 1st prize: Riaz (Little Flowers), 2nd prize: Bipin (Convent), 3rd prize: Balbir (Loyola). 2. 1st prize: Bipin (Convent), 2nd prize: Riaz (Little Flowers), 3rd prize: Balbir (Loyola). 3. 1st prize: Riaz (Little Flowers), 2nd prize: Balbir (Loyola), 3 rd prize: Bipin (Convent). 4. 1st prize: Bipin (Convent), 2nd prize: Balbir (Loyola), 3rd prize: Riaz (Little Flowers). 25. Two boys are playing on a ground. Both the boys are less than 10 years old. Age of the younger boy is equal to the cube root of the product of the age of the two boys. If we place the digit representing the age of the younger boy to the left of the digit representing the age of the elder boy, we get the age of the father of the younger boy. Similarly, we place the digit representing the age of the elder boy to the left of the digit representing the age of the younger boy and divide the figure by 2, we get the age of the mother of the younger boy. The mother of the younger boy is younger than his father by 3 years. Then, what is the age of the younger boy. 1. 3 2. 4 3. 2 4. none of these. 26. Flights A and B are scheduled from an airport within the next one hour. All the booked passengers of the two flights are waiting in the boarding hall after check-in. The hall has a seating capacity of 200 out of which 10% remained vacant. 40% of the waiting passengers are ladies. When boarding announcements came, passengers of flights A left the hall and boarded the flight. Seating capacity of each flight is two-third of the passengers who waited in the waiting hall for both the flights put together. Half the passengers who boarded flight A are women. After boarding for flight A, 60% of the waiting hall seats became empty. For every twenty of those who are still waiting in the hall for flight B, there is one airhostess in flight A. Then, what is the ratio of empty seats in flight B to number of airhostesses in flight A? 1. 10:1 2. 5:1 3. 20:1 4. 1:1 PRACTICE QUESTIONS Mark (1) if the question can be answered by using the statement A alone but not by using the statement B alone. Mark (2) if the question can be answered by using the statement B alone but not by using the statement A alone. Mark (3) if the question can be answered by using either of the statements alone. Mark (4) if the question can be answered by using both the statements together but not by either of the statements alone. Mark (5) if the question cannot be answered on the basis of the two statements. 1. If today the price of an item is $3,600, what was the price of the item exactly 2 years ago? (1) The price of the item increased by 10 per-cent per year during this 2- year period. (2) Today the price of the item is 1.21 times its price exactly 2 years ago. 2. By what percent has the price of an overcoat been reduced? (1) The original price was $380. (2) The original price was $50 more than the reduced price. 3. If the Longfellow Playground is rectangular, what is its width? (1) The ratio of its length to its width is 7 to 2. (2) The perimeter of the playground is 396 meters. 4. What is the value of x –1? (1) x + 1 =3 (2) x – 1 < 3 5. Is William taller than Jane? (1) William is taller than Anna. (2) Anna is not as tall as Jane. 6. In parallelogram ABCD above, what is the measure of ∠ADC? (1) The measure of ∠ABC is greater than 90o. (2) The measure of ∠BCD is 70o 7. Is x2 equal to xy? (1) x2 – y2 = (x + 5)(y - 5) (2) x = y 8. Was 70 the average (arithmetic mean) grade on a class test? (1) On the test, half of the class had grades below 70 and half of the class had grades above 70. (2) The lowest grade on the test was 45 and the highest grade on the test was 95. 9. What was John’s average driving speed in miles per hour during a 15- minute interval? (1) He drove 10 miles during this interval. (2) His maximum speed was 50 miles per hour and his minimum speed was 35 miles per hour during this interval. 10. Is ΔMNP isosceles? (1) Exactly two of the angles, ∠M and ∠N, have the same measure (2) ∠N and ∠P do not have the same measure. 11. Is n an integer greater than 4? (1) 3n is a positive integer. n (2) is a positive integer. 3 12. In ΔJKL shown above, what is the length of segment JL? (1) JK = 10 (2) KL = 5 13. A coal company can choose to transport coal to one of its customers by railroad or by truck. If the railroad charges by the mile and the trucking company charges by the ton, which means of transporting the coal would cost less than the other? (1) The railroad charges $5,000 plus $0.01 per mile per railroad car used, and the trucking company charges $3,000 plus $85 per ton. (2) The customer to whom the coal is to be sent is 195 miles away from the coal company. 14. Is x – y > r – s? (1) x > r and y < s? (2) y = 2, s = 3, r = 5, and x = 6. 15. On a certain day it took Bill three times as long to drive from home to work as it took Sue to drive from home to work. How many kilometers did Bill drive from home to work? (1) Sue drove 10 kilometers from home to work, and the ratio of distance driven from home to work time to drive from home to work was the same for Bill and Sue that day. (2) The ratio of distance driven from home to work time to drive from home to work for Sue that day was 64 kilometers per hour. 16. The figure above represents the floor of a square foyer with a circular rug partially covering the floor and extending to the outer edges of the floor as shown. What is the area of the foyer that is not covered by the rug? (1) The area of the foyer is 9 square meters. (2) The area of the rug is 2.25π square meters. 17. At a certain university, if 50 percent of the people who inquire about admission policies actually submit applications for admission, what percent of those who submit applications for admission enroll in classes at the university? (1) Fifteen percent of those who submit applications for admission are accepted at the university. (2) Eighty percent of those who are accepted send a deposit to the university. 18. If x and y are nonzero integers, is x an integer? y (1) x is the product of 2 and some other integer. (2) There is only one pair of positive integers whose product equals y. 19. If x is an integer, what is the value of x? (1) 1 5 1 1 x 1 2 (2)( x 3)(x 4) 0 20. Is quadrilateral Q a square? (1) The sides of Q have the same length. (2) The diagonals of Q have the same length. 21. If K is a positive integer less than 10 and N = 4,321 + K, what is the value of K? (1) N is divisible by 3. (2) N is divisible by 7. 22. A jewelry dealer initially offered a bracelet for sale at an asking price that would give a profit to the dealer of 40 percent of the original cost. What was the original cost of the bracelet? (1) After reducing this asking price by 10 percent, the jewelry dealer sold the bracelet at a profit of $403. (2) The jewelry dealer sold the bracelet for $1,953. 23. If n is an integer between 2 and 100 and if n is also the square of an integer, what is the value of n? (1) n is the cube of an integer. (2) n is even. 24. Is x2 – y2 a positive number? (1) x – y is a positive number. (2) x + y is a positive number. 25. The surface area of a square tabletop was changed so that one of the dimensions was reduced by 1 inch and the other dimension was increased by 2 inches. What was the surface area before these changes were made? (1) After the changes were made, the surface area was 70 square inches. (2) There was a 25 percent increase in one of the dimensions.
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