DIRECTIONS for questions 51 and 52: These questions are based on the following data.
Rama went to the market and bought some apples, mangoes and bananas. He bought 42 fruits in all. The number of bananas is less than half the number of apples; the number of mangoes is more than one-third the number of apples and the number of mangoes is less than three-fourths the number of bananas.
51. How many apples did Rama buy?
(1) 20 (2) 23 (3) 26 (4) 28
52. How many bananas did Rama buy?
(1) 8 (2) 9 (3) 10 (4) 11
DIRECTIONS for questions 53 and 54: These questions are based on the information given below.
Car C1 starts at town T1 at 5 a.m. and reaches town T2 at 10 a.m. Car C2 starts at town T2 at 7 a.m. and reaches town T1- at 11 a.m.
53. If the distance between towns T1 and T2 is 320 km, what is the distance between the two cars 15 min after they meet each other?
(1) 36 km (2) 40 km (3) 48 km (4) Cannot be determined
54. One hour after C1 starts, another car C3 – whose speed is 25% more than that of C1 – starts from T1 towards T2. How many of the following statements is/are true?
I. Cars C1 and C3 reach T2 at the same time.
II. C3 meets C2 20 min after C1 meets C2.
III. When C3 meets C2, C2 has to still travel for 1 hr 30 min to reach T1.
(1) Exactly one of the three statements is true. (2) Exactly two of the three statements are true.
(3) All the three statements are true. (4) None of the statements are true.
DIRECTIONS for question 55 to 58: Select the correct alternative from the given choices.
55. Amit found that he needs to multiply a natural number N with at least p to make it a perfect square and with at least q to make it a perfect cube. He also found that he needs to multiply N with at least r to make it a perfect cube as well as a perfect square. If p, q and r are natural numbers, then which of the following expresses the relationship between p, q and r?
(1) p x q = r (2) p x q > r (3) p x q < r (4) Depends on N
56.In the given rectangle ABCD, E and F are points on BC such that AB : BE : EF : FC = 1 : 2 : 1 : 4. Which of the following is true of the values of ΔEAF and ΔACF?
(1) ΔEAF > ΔACF (2) ΔEAF = ΔACF
(3) ΔEAF < ΔACF (4) Cannot be determined
57. There are three equal circles C1, C2 and C3 each of radius 6 cm, where C1 and C3 pass through
the centre of C2. What is the area of the shaded region? (in sq.cm) C1
(1) 36 3 −12π (2) 48 3 −16π
(3) 36π − 54 3 (4) None of these
58. Malini and Shalini play a game in which they first write down the first n natural numbers and
then take turns in inserting plus or minus signs between the numbers. When all such signs
have been placed the resulting expression is evaluated (i.e., the additions and subtractions are
performed) Malini wins if the sum is even and Shalini wins if the sum is odd. Assuming that the concept of even and odd (i.e., even and odd parities) is defined for all integers, which of the following statements is true?
(1) Malini wins if n is a multiple of 4 (2) Shalini wins if n is even
(3) Shalini wins if n is odd (4) Malini loses if n is a multiple of 4
DIRECTIONS for questions 59 and 60: These questions are based on the following data.
A teacher found that the performance of her students in the mid-term exams, comprising 6 subjects – A, B, C, D, E and F, is as follows:
59. If the number of students who passed in all the six subjects is 10, then find the number of students who passed in exactly five subjects.
(1) 10 (2) 15 (3) 20 (4) Cannot be determined.
DIRECTIONS for questions 61 to 63: These questions are based on the data given below.
Everyday, Saddam, the office attender fetches water for the office in container A which has certain rated capacity. However, because of a dent at the bottom of the container, only 80% of the rated capacity of the container can be used to fill water. This water is transferred periodically into a smaller container B - for people in the office to use this water for drinking. There is an outlet (a faucet) in B from which water is let out. Since the faucet is fixed at a level above the base of B, water upto 10% of the rated capacity of B cannot be let out through the faucet. Everyday in the morning, after Saddam fetches water in container A, he cleans B and fills B to the brim by pouring water from A into B. Whenever the water level falls to the faucet level in B, he again fills B to the brim by pouring water from A into B. The questions in this set are independent of each other.
61. On a particular day, Saddam finds that he filled B five times (including the first time) and at the end of the day, A was empty. The water level in B reached the faucet level. What is the ratio of the rated capacities of A and B?
(1) 4.6 : 1 (2) 5 : 1 (3) 5.75 : 1 (4) 6.25 : 1
62. If Saddam gets the dent in container A removed (so that water can be fetched in this container to its rated capacity) how many times can he fill container B (including the first time in the morning) given that the rated capacities of the two containers are in the ratio 10 : 1?
(1) 9 times (2) 10 times (3) 12 times (4) 11 times
63. Saddam gets the dent in container A removed. He also gets the faucet in container B refixed so that all the water filled into B can be used. He keeps filling B from A everytime B gets emptied. After he pours out water from A into B the last time (i.e., A gets emptied), what percentage of B is empty? The ratio of the rated capacities of A and B is 7.5 : 1?
(1) 0% (2) 331/3% (3) 25% (4) 50%
DIRECTIONS for questions 64 and 65: These questions are based on the following data.
Amar, Akbar and Anthony sold their three cycles manufactured in different years to Mr.Kishanlal. Mr.Kishanlal gave a total of Rs.1700 to the three and said that Amar should get about one-half of the total amount as his cycle was used less. Akbar’s cycle being used more than Amar’s, he should get about one-third of the total amount and the last one gets about one-ninth. Each individual gets his amount only in denominations of Rs.100.
64. What is the difference between the amounts received by Amar and Anthony?
(1) Rs.900 (2) Rs.700 (3) Rs.800 (4) Rs.600
65. The amount that Amar has is how much more than what Akbar and Anthony together have?
(1) Rs.200 (2) Rs.300 (3) Rs.100 (4) Rs.400
Directions for questions 66 to70: Select the correct alternative from the given choices.
66. A, B and C start running simultaneously from the points P, Q and R respectively on a circular track. The distance (when measured along the track) between any two of the three points P, Q and R is L and the ratio of the speeds of A, B and C is 1 : 2 : 3. If A and B run in opposite directions while B and C run in the same direction, what is the distance run by C before A , B and C meet for the first time?
(1) 310L (2) 311L (3) All three of them will never meet. (4) Cannot be determined
67. A circle of radius 1cm circumscribes a square. A dart is thrown such that it falls within the circle. What is the probability that it falls outside the square?
(1) 1/2π (2) (2π - 1) /2π (3) (π - 1) /π (4) (π - 2) /π
68. Fifteen boys went to collect berries and returned with a total of 80 berries among themselves. What is the minimum number of pairs of boys that must have collected the same number of berries?
(1) 0 (2) 1 (3) 2 (4) 3
69. A cube of edge 12 ft is placed on the floor with one of its faces touching a wall. A ladder of length 35 ft is resting against that wall and is touching an edge of the cube. Find the height at which the top end of the ladder touches the wall, given that it is more than the distance of the foot of the ladder from the wall?
(1) 11 ft (2) 23 ft (3) 21 ft (4) 28 ft
70. Two circles touch each other externally. One of the circles is 300% more in area than the other. If A is the centre of the larger circle and BC is the diameter of the smaller circle and either AB or AC is a tangent to the smaller circle, then find the ratio of the area of the triangle ABC to that of the smaller circle?
(1) 2 : π (2) 3 : π (3) 2 2 : π (4) π : 4 2
DIRECTIONS for questions 71 and 72: Select the correct alternative from the given choices.
71. a1, a2, a3, a4 and a5 are five natural numbers. Find the number of ordered sets (a1, a2, a3, a4, a5) possible such that a1 + a2 + a3 + a4 + a5 = 64.
(1) 64C5 (2) 63C4 (3) 65C4 (4) None of these
72. In the above question if a1, a2, a3, a4 and a5 are non-negative integers then find the number of ordered sets (a1, a2, a3,a4 and a5) that are possible.
(1) 64C5 (2) 63C4 (3) 68C4 (4) None of these
DIRECTIONS for questions 73 to 75: Each question gives certain information followed by two quantities A and B.Compare A and B, and then
Mark 1 if A > B
Mark 2 if B > A
Mark 3 if A = B
Mark 4 if the relationship cannot be determined from the given data.
73. A baker had a certain number of boxes and a certain number of cakes with him. Initially he distributed all the cakes equally among all the boxes and found that there was no cake left without a box. He later found that he had one more box with him and so he redistributed all the cakes equally among all the boxes and found that there was one cake less per box than initially and one cake was left without a box with the baker.
A. The number of cakes per box in the first case.
B. The total number of boxes with the baker.
74. A trader gives a discount of r% and still makes a profit of r%. A second trader marks up his goods by r% and gives a discount of r%.
A. The cost price of the first trader.
B. The cost price of the second trader.
75. A piece of work is carried out by a group of men, all of equal capacity, in such a way that on the first day one man works and on every subsequent day one additional man joins the work. A group of women, all of equal capacity is engaged to carry out a second piece of work with ten women starting the work on the first day and one woman leaving the work at the end of everyday. The second piece of work is thrice as time consuming as the first piece of work while each man is thrice as efficient as each woman. It is known that one man working alone can complete the first piece of work in 6 days.
A. Number of days in which the first piece of work is completed.
B. Number of days in which the second piece of work is completed.
DIRECTIONS for questions 76 and 77: Select the correct alternative from the given choices.
76. A number when divided by a certain divisor, left a remainder of 8. When the same number was multiplied by 12 and then divided by the same divisor, the remainder is 12. How many such divisors are possible?
(1) 1 (2) 2 (3) 4 (4) 5
77. Consider the equation x² + y² + z² = 1. Let (x1, y1, z1) and (x2, y2, z2) be two sets of values of (x, y, z) satisfying the given equation and let A = (x1 – x2)² + (y1 – y2) ² + (z1 – z2)². What is the maximum possible value that A can assume? (assume that all the quantities involved are real numbers)
(1) 1 (2) 2 (3) 4 (4) 6
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