# 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 ; if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
Mark ; if the question can be answered by using either statement alone.
Mark ; if the question can be answered by using both statements together, but cannot be answered by using either statement alone.
Mark ; 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)}

1. BD \bot AC
2. AB=3 cm and BC = 4 cm

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

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

3. Who saves more A or B?

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

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

1. The roots of the equation are integers.
2. 200 < | α | < 300, where α is one of roots of the given equation.

5. What is the value of α?

1. α and β are the roots of the equation {x}^{2} – 5x – 24 = 0
2. 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?

1. The first painter can completely paint the board in 12 hours.
2. 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?

1. \frac {b}{a}=-40
2. \frac {c}{a}=400

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

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

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

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

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

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

## Read More Questions on Data Sufficiency

11. What is the value of x?

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

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

1. y is divisible by (x+1) and (x+2)
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?

1. The probability of drawing a blue marble is \frac {1}{3}
2. 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?