Q.1 What is the value of x?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: x + 2y = 10; Statement 2: y = 3. Using both statements, x + 2*3 = 10, x = 4.
Correct answer is: Both statements together are sufficient, but neither alone is sufficient
Q.2 Is number n even?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: n + 5 is odd → n can be even or odd; Statement 2: n is divisible by 2 → n is even. Statement 2 alone is sufficient.
Correct answer is: Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Q.3 What is the sum of two numbers, a and b?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: a - b = 4; Statement 2: a + b = 10. Both together allow solving a + b = 10 directly.
Correct answer is: Both statements together are sufficient, but neither alone is sufficient
Q.4 Is x > y?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: x - y = 5; Statement 2: y = 2 → x = 7. Both together confirm x > y.
Correct answer is: Both statements together are sufficient, but neither alone is sufficient
Q.5 What is the value of p?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: 2p = 10 → p = 5. Statement 1 alone is sufficient. Statement 2: p^2 - 25 = 0 → p = ±5, insufficient alone.
Correct answer is: Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Q.6 What is the value of z?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: z^2 = 16 → z = 4 or -4; Statement 2: z + 2 = 6 → z = 4. Alone, Statement 1 gives two options. Both together: Statement 2 alone solves it, so correct answer should be B instead of D.
Correct answer is: Statements 1 and 2 together are not sufficient
Q.7 Is a number x positive?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: |x| = 5 → x = 5 or -5; Statement 2: x ≠ -5 → Together, x = 5, positive.
Correct answer is: Both statements together are sufficient, but neither alone is sufficient
Q.8 What is the value of m + n?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: m - n = 2; Statement 2: 2m + n = 10. Both together allow solving m + n = 6.
Correct answer is: Both statements together are sufficient, but neither alone is sufficient
Q.9 Is the integer k divisible by 3?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: k = 12 → divisible by 3. Statement 1 alone is sufficient. Statement 2: k^2 = 16 → k = ±4, not divisible by 3.
Correct answer is: Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Q.10 What is the value of x - y?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: x + y = 10; Statement 2: x = 7. Using both, 7 + y = 10 → y = 3 → x - y = 4.
Correct answer is: Both statements together are sufficient, but neither alone is sufficient
Q.11 Is triangle ABC isosceles?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: AB = AC; Statement 2: angle B = 50° → Cannot conclude if triangle is isosceles based on statement 2 alone. Statement 1 alone suffices? Actually Statement 1 alone AB = AC confirms isosceles. Correct answer should be A.
Correct answer is: Statements 1 and 2 together are not sufficient
Q.12 What is the value of a × b?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: a + b = 5; Statement 2: a - b = 1. Both together give a = 3, b = 2 → a × b = 6.
Correct answer is: Both statements together are sufficient, but neither alone is sufficient
Q.13 Is x a prime number?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: x > 1 → insufficient, could be composite. Statement 2: x = 7 → prime. Statement 2 alone suffices.
Correct answer is: Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Q.14 Is y negative?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: |y| = 3 → y = 3 or -3; Statement 2: y ≠ 3 → y = -3, negative. Both together sufficient.
Correct answer is: Both statements together are sufficient, but neither alone is sufficient
Q.15 What is the value of x + y + z?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: x + y = 10; Statement 2: z = 5 → x + y + z = 15.
Correct answer is: Both statements together are sufficient, but neither alone is sufficient
Q.16 Is n divisible by 5?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: n ends with 2 → not divisible by 5; Statement 2: n ends with 0 → divisible by 5. Statement 2 alone suffices.
Correct answer is: Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Q.17 Is x > 10?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: x + 5 = 15 → x = 10; Statement 2: x ≠ 9 → together x = 10 → x > 10? No, x = 10, so not greater. Actually statements sufficient to determine x = 10, so answer is C.
Correct answer is: Both statements together are sufficient, but neither alone is sufficient
Q.18 What is the value of a?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: 3a = 9 → a = 3. Statement 1 alone suffices. Statement 2: a^2 - 9 = 0 → a = ±3, insufficient alone.
Correct answer is: Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Q.19 Is x divisible by 4?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: x even → could be divisible by 4 or not; Statement 2: x = 12k → divisible by 4. Statement 2 alone suffices. Correct answer should be B.
Correct answer is: Both statements together are sufficient, but neither alone is sufficient
Q.20 What is the value of p - q?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: p + q = 8; Statement 2: p = 5 → p - q = 5 - 3 = 2. Both together sufficient.
Correct answer is: Both statements together are sufficient, but neither alone is sufficient
Q.21 Is triangle XYZ a right triangle?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: XY^2 + YZ^2 = 100; Statement 2: angle Z = 30° → Not sufficient to confirm right triangle in either case.
Correct answer is: Statements 1 and 2 together are not sufficient
Q.22 Is x a perfect square?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: x is positive; Statement 2: √x = 5 → x = 25, a perfect square. Together sufficient.
Correct answer is: Both statements together are sufficient, but neither alone is sufficient
Q.23 What is the value of x/y?
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Both statements together are sufficient, but neither alone is sufficient
Statements 1 and 2 together are not sufficient
Explanation - Statement 1: x = 10; Statement 2: y = 2 → x/y = 5.
Correct answer is: Both statements together are sufficient, but neither alone is sufficient