# Mathematics Data Sufficiency Questions and Answers for Mock Test

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## Model Questions on Data Sufficiency in Mathematics

DIRECTIONS: Each question is followed by two statements, I and II. Answer each question using the following instructions:

Mark [1]; if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.

Mark [2]; if the question can be answered by using either statement alone.

Mark [3]; if the question can be answered by using both statements together, but cannot be answered by using either statement alone.

Mark [4]; if the question cannot be answered even by using both statements together.

1. Consider a right angle ΔABC, right angled at B, D is a point on side AC. Find \frac {A(ΔABD)}{A(ΔBDC)}

- BD \bot AC
- AB=3 cm and BC = 4 cm

2. What is the cost of 1 pen, 1 pencil and 1 eraser?

- The cost of 3 pens, 4 pencils and 5 erasers is Rs 15.
- The cost of 7 pens, 9 pencils and 11 erasers is Rs 40.

3. Who saves more A or B?

- The ratio of incomes of A and B is 4:5.
- The ratio of expenditures of A and B is 5:4.

4. Consider the equation {x}^{2} + kx + 2518 = 0. Find k

- The roots of the equation are integers.
- 200 < | α | < 300, where α is one of roots of the given equation.

5. What is the value of α?

- α and β are the roots of the equation {x}^{2} – 5x – 24 = 0
- 3α – 6β = 42

6. Two painters are painting an advertising board. At 12Oclock, they had painted half the board. At what time will the board be fully painted?

- The first painter can completely paint the board in 12 hours.
- The second painter can completely paint the board in 8 hours.

7. What are the roots of the equation a{x}^{2} + bx + c = 0?

- \frac {b}{a}=-40
- \frac {c}{a}=400

8. In the expression \frac {x}{10}-33\frac {x}{5}+c, find the value of c.

- If x=1, the value of expression become 0.
- The expression has got only 5 unique real factors.

9. What are the value of x, y and z?

- x, y and z are two digit consecutive prime numbers.
- z is the largest two digit prime number.

10. What is the sum of all internal angles of a polygon?

- One of the internal angles is 108°
- The polygon is a regular polygon.

## Read More Questions on Data Sufficiency

11. What is the value of x?

- {x}^{2} + x – 12 ≤ 0
- {x}^{4} – 41{x}^{2} + 400 ≤ 0

12. Is y a perfect square, where x and y are natural numbers?

- y is divisible by (x+1) and (x+2)
- y < 200

13. There are less than 40 red, blue and black marbles in a bag. What is the probability of picking a black marble?

- The probability of drawing a blue marble is \frac {1}{3}
- The probability of drawing a red marble is \frac {1}{24}

14. ABC is a right circular cone. This cone has been cut into two parts A (cone) and B (frustum) by a plane parallel to the base. What is the ratio of the volume A to the volume of B?

- Radius of ABC=1.4 times radius of A
- The cone has been cut off at the middle of its height.

15. What is the 25the term of a given sequence?

- The first two terms sequence are \frac {1}{3} and –\frac {3}{4}
- The sum of all the terms of the sequence is 21.

16. A, B and C together completed a project. What proportion of the work was done by A?

- It took 3 people to complete the work
- B did 18% of the work which was \frac {2}{3}rd of the work done by C