Q.1 Is x > 10? 1) x² > 100 2) x is an integer
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Statement 1: x² > 100 → x > 10 or x < -10, not sufficient alone.
Statement 2: x is an integer, not sufficient alone.
Together: x² > 100 and x is integer → x > 10 or x < -10, integer → multiple possibilities. Actually, the correct is still (D). Correction: both together give x > 10 or x < -10, so still insufficient to determine x > 10. Correct answer: (D).
Correct answer is: (C) Both together are sufficient
Q.2 What is the value of y? 1) 3y + 5 = 20 2) y² = 25
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Statement 1: 3y + 5 = 20 → 3y = 15 → y = 5, sufficient.
Statement 2: y² = 25 → y = ±5, insufficient alone.
So statement 1 alone is sufficient.
Correct answer is: (A) Statement 1 alone is sufficient
Q.3 Is integer n divisible by 4? 1) n is divisible by 8 2) n is even
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Statement 1: divisible by 8 → divisible by 4, sufficient.
Statement 2: even → could be 2, 6, etc., insufficient alone.
Correct answer is: (A) Statement 1 alone is sufficient
Q.4 What is the sum of two numbers x and y? 1) x - y = 4 2) y = 10
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Statement 1: x - y = 4, multiple possibilities for x + y.
Statement 2: y = 10, combined with statement 1 → x - 10 = 4 → x = 14 → x + y = 24, sufficient.
Correct answer is: (C) Both together are sufficient
Q.5 Is p a prime number? 1) p is odd 2) p > 1
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Odd numbers > 1 may be composite (9), statement 1 insufficient.
p > 1 alone is insufficient.
Together, still may not be prime (e.g., 9), so insufficient.
Correct answer is: (D) Neither statement is sufficient
Q.6 Is x² - 5x + 6 = 0? 1) x = 2 2) x = 3
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - x² - 5x + 6 = 0 → (x-2)(x-3)=0 → x = 2 or 3.
Each statement alone gives one solution, combined they confirm all solutions.
Correct answer is: (C) Both together are sufficient
Q.7 Is integer x divisible by 6? 1) x divisible by 2 2) x divisible by 3
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Divisible by 6 → divisible by both 2 and 3. Individually insufficient, together sufficient.
Correct answer is: (C) Both together are sufficient
Q.8 What is the value of x? 1) 2x + 3 = 11 2) x² - 4x + 4 = 0
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Statement 1: 2x + 3 = 11 → x = 4, sufficient.
Statement 2: x² - 4x + 4 = 0 → (x-2)² = 0 → x = 2, sufficient alone. Both sufficient individually, so either alone suffices. Correct answer could also be (C) if interpreted differently.
Correct answer is: (A) Statement 1 alone is sufficient
Q.9 Is y > 0? 1) y² = 9 2) y is an integer
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Statement 1: y² = 9 → y = ±3, insufficient alone.
Statement 2: y integer → still ±3 possible, insufficient alone.
Together: still ±3, so actually still insufficient. Correct answer: (D).
Correct answer is: (C) Both together are sufficient
Q.10 Is n divisible by 5? 1) n ends with 0 2) n is divisible by 10
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Numbers ending with 0 are divisible by 5, statement 1 sufficient.
Statement 2: divisible by 10 → divisible by 5, also sufficient. Either alone sufficient.
Correct answer is: (A) Statement 1 alone is sufficient
Q.11 What is the value of z? 1) z + 7 = 15 2) 2z - 4 = 8
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Statement 1: z + 7 = 15 → z = 8, sufficient.
Statement 2: 2z - 4 = 8 → 2z = 12 → z = 6, sufficient alone. Statements contradict, so together still sufficient to determine z? Actually inconsistent statements make determination impossible, so correct answer: (D).
Correct answer is: (C) Both together are sufficient
Q.12 Is a triangle right-angled? 1) one angle = 90° 2) sum of squares of two sides = square of third side
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Statement 1: one angle 90° → right-angled, sufficient.
Statement 2: sum of squares of two sides = third side squared → right-angled, sufficient. Each alone sufficient, together also sufficient.
Correct answer is: (C) Both together are sufficient
Q.13 Is integer k even? 1) k² is even 2) k is divisible by 4
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Statement 1: k² even → k even, sufficient alone.
Statement 2: divisible by 4 → k even, sufficient alone. Each sufficient alone, together also sufficient.
Correct answer is: (C) Both together are sufficient
Q.14 What is the value of m? 1) m/3 = 4 2) 2m - 6 = 2
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Statement 1: m/3 = 4 → m = 12, sufficient.
Statement 2: 2m - 6 = 2 → 2m = 8 → m = 4, sufficient alone. Each statement gives a value, so sufficient individually.
Correct answer is: (A) Statement 1 alone is sufficient
Q.15 Is x > y? 1) x - y > 0 2) x + y > 0
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Statement 1: x - y > 0 → x > y, sufficient.
Statement 2: x + y > 0 → insufficient, could be x < y but sum positive.
So statement 1 alone suffices.
Correct answer is: (A) Statement 1 alone is sufficient
Q.16 Is integer p positive? 1) p² = 16 2) p is even
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Statement 1: p² =16 → p = ±4, insufficient alone.
Statement 2: p even → possible ±2, ±4, insufficient alone.
Together: p² =16 and p even → p = ±4, still insufficient to know positive. Correct answer: (D).
Correct answer is: (C) Both together are sufficient
Q.17 Is integer n a multiple of 9? 1) n is divisible by 3 2) sum of digits of n is divisible by 9
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Divisibility rule: if sum of digits divisible by 9 → n divisible by 9, sufficient.
Divisible by 3 alone → could be 3,6,12 etc., insufficient.
Correct answer is: (B) Statement 2 alone is sufficient
Q.18 Is x an integer? 1) x² = 16 2) x > 0
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Statement 1: x² = 16 → x = ±4, not sufficient.
Statement 2: x > 0 → insufficient alone.
Together: x = ±4 and x > 0 → x = 4, integer, sufficient.
Correct answer is: (C) Both together are sufficient
Q.19 Is number x divisible by 12? 1) x divisible by 3 2) x divisible by 4
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - 12 = 3 × 4, x divisible by both 3 and 4 → divisible by 12, sufficient together. Individually insufficient.
Correct answer is: (C) Both together are sufficient
Q.20 What is the value of a? 1) 5a - 10 = 0 2) a² = 4
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Statement 1: 5a - 10 = 0 → a = 2, sufficient.
Statement 2: a² = 4 → a = ±2, insufficient alone.
Correct answer is: (A) Statement 1 alone is sufficient
Q.21 Is integer k a multiple of 7? 1) k divisible by 14 2) k divisible by 2
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Divisible by 14 → divisible by 7, sufficient.
Divisible by 2 alone → could be 2,4 etc., insufficient.
Correct answer is: (A) Statement 1 alone is sufficient
Q.22 Is x < 0? 1) x² < 9 2) x is negative
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Statement 1: x² < 9 → -3 < x < 3, insufficient.
Statement 2: x negative → sufficient.
Correct answer is: (B) Statement 2 alone is sufficient
Q.23 Is x + y > 10? 1) x > 6 2) y > 4
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Statement 1: x > 6, y unknown → x + y could be < 10, insufficient.
Statement 2: y > 4, x unknown → insufficient.
Together: x + y > 6 + 4 = 10, sufficient.
Correct answer is: (C) Both together are sufficient
Q.24 Is number n odd? 1) n² is odd 2) n is not divisible by 2
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Both together are sufficient
(D) Neither statement is sufficient
Explanation - Odd squared → odd, statement 1 sufficient.
Statement 2: not divisible by 2 → odd, sufficient alone. Each statement alone suffices.
Correct answer is: (C) Both together are sufficient