## Riya Agarwal is teaching live on Unacademy Plus

2 DATA SUFFICIENCY g0 Ou 45

About Me . I hold a B.E degree in Electronics and Communication Engineering. . CAT, 18: DI & LR-99.59 %ile. You can follow me on Unacademy for complete preparation guide on DILR section for CAT and OMETs S.

2 DATA SUFFICIENCY g0 Ou 45

CAT 1999

Direction for questions 1 to 10: Each question is followed by two statements I and II. Mark: a. if the question can be answered by any one of the statements alone, but cannot be answered by using the other statement alone. b. if the question can be answered by using either statement alone. c. if the question can be answered by using both the statements together, but cannot be answered by using either statement alone. d. if the question cannot be answered even by using both the statements together.

Questions 1 to 10: 1. The average weight of students in a class is 50 kg. What is the number of students in the class? I. The heaviest and the lightest members of the class weigh 60 kg and 40 kg respectively. Il. Exclusion of the heaviest and the lightest members from the class does not change the average weight of the students. 2. A small storage tank is spherical in shape. What is the storage volume of the tank? I. The wall thickness of the tank is 1 cm. Il. When an empty spherical tank is immersed in a large tank filled with water, 20 I of water overflow from the large tank. 3. Mr X starts walking northwards along the boundary of a field from point A on the boundary, and after walking for 150 m reaches B, and then walks westwards, again along the boundary, for another 100 m when he reaches C. What is the maximum distance between any pair of points on the boundary of the field? I. The field is rectangular in shape. Il. The field is a polygon, with C as one of its vertices and A as the mid-point of a side.

4. 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 1991-92 and 1990-91? I. The angle between AB and X-axis when measured with a protractor is 40 , and the angle between CB and X-axis is 80 . The scale of Y-axis is 1 cm = Rs. 100 ll. 5. 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. I. The coordinates of D are given. Il. The X-axis bisects one of the tangents. 6. 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 I. a kd and b ke, c kf, k 0

7. 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? I. A mathematician can never add two numbers correctly, but can always add 3 numbers correctly. Il. When a mathematician makes a mistake in a sum, the error is +1 or-1. 8. How many students among A, B, C and D have passed the examination? I. The following is a true statement: A and B passed the examination. Il. The following is a false statement: At least one among C and D has passed the examination. 9. What is the distance x between two cities A and B in integral number of kilometres? I. x satisfies the equation 2log x x Il. xs 10 km 10. Mr Mendel grew 100 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? I. The number of plants with white flowers was 10. Il. The number of plants with red flowers was 70.

7. 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? I. A mathematician can never add two numbers correctly, but can always add three numbers correctly When a mathematician makes a mistake in a sum, the error is +1 or -1. Il. a. if the question can be answered with the help of any one statement alone but not by the other statement. b. if the question can be answered with the help of either of the statements taken individually. c. if the question can be answered with the help of both statements together. d. if the question cannot be answered even with the help of both statements together. Solution: Statement II tells us that mathematicians can make mistakes which are always errors of +1 and - 1. Also statement I tells us that mathematicians can never add 2 numbers correctly but we know he can make mistakes also. Again he can always add 3 numbers correctly. Therefore, as mistakes can be made here too, we cannot decide as to who is a mathematician. Answer: Option (d)

8. How many students among A, B, C and D have passed the examination? I. The following is a true statement: A and B passed the examination. Il. The following is a false statement: At least one among C and D has passed the examination. if the question can be answered with the help of any one statement alone but not by the other statement. if the question can be answered with the help of either of the statements taken individually. if the question can be answered with the help of both statements together. if the question cannot be answered even with the help of both statements together. a. b. c. d. Solution: From I, we know A and B passed the examination. From ll, we know the condition that among C and D at least one passed (or both passed) is false. Therefore, it is obvious that both C and D have failed. Thus, both statements are necessary to find the answer Answer: Option (c)