TANCET Data Sufficiency Questions and Answers for Entrance Test

Directions: Each of the questions below consists of a question and two statements numbered I and II 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
(1) if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question;
(2) if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question
(3) if the data either in statement I alone or in statement II alone are sufficient to answer the question;
(4) if the data given in both the statements I and II together are not sufficient to answer the question
(5) If the data in both the statements I and II together are necessary to answer the question.

1. What is the maximum value of a/b?
I. a, a + b and a + 2b are three sides of a triangle.
II. a and b both are positive.

2. ABC is a triangle with <B = 90°. What is the length of the side AC?
I. D is the midpoint of BC and E is the midpoint of AB.
II. AD=7 and CE=5

3. Five integers A, B, C, D and E are arranged in such a way that there are two integers between B and C and B is not the greatest. There exists one integer between D and E and D is smaller than E. A is not the smallest integer. Which one is the smallest?
I. E is the greatest
II. There exists no integer between B and E.
4. The base of a triangle is 60 cms, and one of the base angles is 60°. What is length of the shortest side of the triangle?
I. The sum of lengths of other two sides is 80 cms
II. The other base angle is 45°.

5. A, B, C, D, E and F are six integers such that E < F, B > A, A < D < B. C is the greatest integer. Is A the smallest integer?
I. E + B < A+ D
II. D < F

6. Let PQRS be a quadrilateral. Two circles 01 and 02 are inscribed in triangles PQR and PSR respectively. Circle 01 touches PR at M and circle O2 touches PR at N. Find the length of MN.
I. A circle is inscribed in the quadrilateral PQRS.
II. The radii of the circles 01 and 02 are 5 and 6 units respectively.

7. A group of six friends noticed that the sum of their ages is the square of a prime number. What is the average age of the group?
I. All members are between 50 and 85 years of age.
II. The standard deviation of their ages is 4.6.

8. Harry and Sunny have randomly picked 5 cards each from a pack of 10 cards, numbered from 1 to 10. Who has randomly picked the card with number 2 written on it?
I. Sum of the numbers on the cards picked by Harry is 5 more than that of Sunny.
II. One has exactly four even numbered cards while the other has exactly four odd numbered cards.

9. We have two unknown positive integers m and n, whose product is less than 100. There are two additional statement of facts available:
I. mn is divisible by six consecutive integers {j, j+1, …, j+ 5}
II. m + n is a perfect square.

10. The average weight of students in 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.
II. Exclusion of the heaviest and the lightest members from the class does not change the average weight of the students.

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11. A small storage tank is spherical tank in shape. What is the storage volume of the tank?
I. The wall thickness of the tank is 1 cm.
II. When the empty spherical tank is immersed in a large tank filled with water, 20 litres of water over flow from the large tank.

12. 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?
I. The field is rectangular in shape.
II. The field is a polygon, with C as one of its vertices and A the midpoint of a side.

13. 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 l99l as B, and that for 1992 as C. What is the ratio of growth in revenue between 91 -92 and 90-91?
I. 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.
II. The scale of Y-axis is 1cm = Rs1000.

14. 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
II. The X-axis bisects one of the tangents.

15. 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
II. a=b=1, d=e=2, f≠2c

16. 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.
II. When a mathematician makes a mistake in a sum, the error is +1 or -(1)

17. How many among the four students A, B, C and D have passed the exam?
I. The following is a true statement: A and B passed the exam.
II. The following is a false statement. At least one among C and D has passed the exam.

18. What is the distance x between two cities A and B in integral number of Kms?
I. x satisfies the equation log2x = √x;
II. x < 10 Kms

19. 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?
I. The number of plants with white flowers was 10.
II. The number of plants with red flowers was 70.

20. Consider three real numbers, X, Y and Z. Is Z the smallest of these numbers?
I. X is greater than at least one of Y and Z.
II. Y is greater than at least one of X and Z.