Data Sufficiency Questions and Answers

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Q1
What is the value of x? Statement 1: x is a prime number. Statement 2: x is between 10 and 20.
  • A Statement 1 alone is sufficient
  • B Statement 2 alone is sufficient
  • C Both statements together are sufficient
  • D Each statement alone is sufficient
Answer: Option C
Explanation: Both statements together are necessary to determine that x could be 11, 13, 17, or 19, but not a unique value.
Q2
Is y divisible by 5? Statement 1: y ends with 0 or 5. Statement 2: y is a multiple of 10.
  • A Statement 1 alone is sufficient
  • B Statement 2 alone is sufficient
  • C Both statements together are sufficient
  • D Each statement alone is sufficient
Answer: Option A
Explanation: Statement 1 alone is sufficient as numbers ending with 0 or 5 are divisible by 5.
Q3
What is the area of the rectangle? Statement 1: Length is 10 cm. Statement 2: Perimeter is 34 cm.
  • A Statement 1 alone is sufficient
  • B Statement 2 alone is sufficient
  • C Both statements together are sufficient
  • D Each statement alone is sufficient
Answer: Option C
Explanation: Both statements are needed to find width (7 cm) and calculate area (70 cm²).
Q4
Is triangle ABC equilateral? Statement 1: AB = BC. Statement 2: ∠A = ∠B = ∠C.
  • A Statement 1 alone is sufficient
  • B Statement 2 alone is sufficient
  • C Both statements together are sufficient
  • D Each statement alone is sufficient
Answer: Option B
Explanation: Statement 2 alone is sufficient as equal angles (60° each) confirm equilateral triangle.
Q5
What is the average of a, b, and c? Statement 1: a + b = 15. Statement 2: b + c = 20.
  • A Statement 1 alone is sufficient
  • B Statement 2 alone is sufficient
  • C Both statements together are sufficient
  • D Neither statement is sufficient
Answer: Option D
Explanation: Neither statement alone nor together gives a + b + c, so average cannot be determined.
Q6
Is m > n? Statement 1: m² > n². Statement 2: m - n > 0.
  • A Statement 1 alone is sufficient
  • B Statement 2 alone is sufficient
  • C Both statements together are sufficient
  • D Each statement alone is sufficient
Answer: Option B
Explanation: Statement 2 directly states m > n. Statement 1 is insufficient as it could mean m > n or m < n for negative numbers.
Q7
What is the value of 2x + 3y? Statement 1: x = 5. Statement 2: y = 3.
  • A Statement 1 alone is sufficient
  • B Statement 2 alone is sufficient
  • C Both statements together are sufficient
  • D Each statement alone is sufficient
Answer: Option C
Explanation: Both statements are needed to calculate 2(5) + 3(3) = 10 + 9 = 19.
Q8
Is the integer k divisible by 3? Statement 1: k is divisible by 6. Statement 2: k is divisible by 9.
  • A Statement 1 alone is sufficient
  • B Statement 2 alone is sufficient
  • C Both statements together are sufficient
  • D Each statement alone is sufficient
Answer: Option D
Explanation: Both statements individually confirm divisibility by 3 since 6 and 9 are multiples of 3.
Q9
What is the ratio of boys to girls in the class? Statement 1: There are 15 boys. Statement 2: The total students are 40.
  • A Statement 1 alone is sufficient
  • B Statement 2 alone is sufficient
  • C Both statements together are sufficient
  • D Neither statement is sufficient
Answer: Option C
Explanation: Both statements needed: Girls = 40 - 15 = 25, Ratio = 15:25 = 3:5.
Q10
Is p a positive number? Statement 1: p > -1. Statement 2: p² = 16.
  • A Statement 1 alone is sufficient
  • B Statement 2 alone is sufficient
  • C Both statements together are sufficient
  • D Neither statement is sufficient
Answer: Option D
Explanation: Statement 1: p could be negative (e.g., -0.5) or positive. Statement 2: p could be 4 or -4. Neither alone is sufficient.

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