Q.1 1. What is the value of x? Statement 1: 2x + 3 = 11 Statement 2: x - 1 = 4
x = 5
x = 4
x = 6
Cannot be determined
Explanation - Statement 1: 2x + 3 = 11 => 2x = 8 => x = 4. Statement 2: x - 1 = 4 => x = 5. Since both statements give different values, the answer cannot be determined from the combination. Hence, correct is B. Actually, in data sufficiency terms, each statement alone is sufficient, but combination is inconsistent.
Correct answer is: x = 4
Q.2 2. Is y > 10? Statement 1: y + 5 = 15 Statement 2: 2y = 22
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1: y + 5 = 15 => y = 10. Statement 2: 2y = 22 => y = 11. Individually, statements give different information. Combined, y could be 10 or 11, so we can determine if y > 10? Only Statement 2 confirms y > 10. Hence, statements together are sufficient.
Correct answer is: Both statements together are sufficient
Q.3 3. What is the value of z? Statement 1: 3z - 9 = 0 Statement 2: z^2 = 9
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1: 3z - 9 = 0 => z = 3. Statement 2: z^2 = 9 => z = 3 or -3. Combining both statements, z = 3. Hence, both statements together are sufficient.
Correct answer is: Both statements together are sufficient
Q.4 4. Is number n even? Statement 1: n is divisible by 4 Statement 2: n is divisible by 2
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1: If n divisible by 4, n is even. Statement 2: If n divisible by 2, n is even. Hence, each statement alone is sufficient. Statement 2 alone suffices.
Correct answer is: Statement 2 alone is sufficient
Q.5 5. What is the sum of two numbers, a and b? Statement 1: a = 7 Statement 2: b = 5
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1 alone gives only a. Statement 2 alone gives only b. Combining both, sum = 7 + 5 = 12. Hence both statements together are sufficient.
Correct answer is: Both statements together are sufficient
Q.6 6. Is x > y? Statement 1: x - y = 2 Statement 2: y - x = -2
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1: x - y = 2 => x = y + 2 => x > y. Statement 2: y - x = -2 => x - y = 2 => x > y. Each statement alone suffices to determine x > y.
Correct answer is: Statement 1 alone is sufficient
Q.7 7. What is the value of p? Statement 1: 2p + q = 10 Statement 2: q = 4
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1 alone has two variables, cannot determine p. Statement 2 alone gives q only. Combining: 2p + 4 = 10 => 2p = 6 => p = 3. Hence both statements together are sufficient.
Correct answer is: Both statements together are sufficient
Q.8 8. Is x a prime number? Statement 1: x is odd Statement 2: x < 10
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1 alone: x odd => could be 1, 3, 5, 7, 9, etc., not sufficient. Statement 2 alone: x < 10 => 1-9, not sufficient. Combined: x < 10 and odd => 1, 3, 5, 7, 9, still not sufficient to determine if prime. Hence cannot be determined.
Correct answer is: Cannot be determined
Q.9 9. What is the value of x + y? Statement 1: x = 2 Statement 2: y = 5
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1 gives x only, statement 2 gives y only. Combining: x + y = 2 + 5 = 7. Hence sufficient together.
Correct answer is: Both statements together are sufficient
Q.10 10. Is z divisible by 3? Statement 1: z = 15 Statement 2: z is odd
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1: z = 15 => divisible by 3. Statement 2: z is odd => could be 1, 3, 5, 7, etc., insufficient. Hence statement 1 alone is sufficient.
Correct answer is: Statement 1 alone is sufficient
Q.11 11. What is the value of a? Statement 1: 5a = 25 Statement 2: a + b = 10
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1: 5a = 25 => a = 5. Statement 2 alone cannot determine a. Hence statement 1 alone is sufficient.
Correct answer is: Statement 1 alone is sufficient
Q.12 12. Is x^2 = 16? Statement 1: x = 4 Statement 2: x is positive
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1: x = 4 => x^2 = 16, sufficient alone. Statement 2: x positive => x could be any positive number, not sufficient. Hence statement 1 alone sufficient. But combining both: still x = 4. Correct answer is A actually.
Correct answer is: Both statements together are sufficient
Q.13 13. What is the difference between x and y? Statement 1: x + y = 10 Statement 2: x - y = 4
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1 alone: sum known, difference unknown. Statement 2 alone: difference known, sum unknown. Together: x + y = 10, x - y = 4 => x = 7, y = 3 => difference = 4. Hence sufficient together.
Correct answer is: Both statements together are sufficient
Q.14 14. Is number n divisible by 5? Statement 1: n ends with 0 Statement 2: n is even
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1: Ends with 0 => divisible by 5. Statement 2: Even number could be 2, 4, 6, etc., insufficient. Hence statement 1 alone sufficient.
Correct answer is: Statement 1 alone is sufficient
Q.15 15. What is the value of x? Statement 1: x + 2 = 7 Statement 2: x - 3 = 2
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1: x + 2 = 7 => x = 5. Statement 2: x - 3 = 2 => x = 5. Both statements individually sufficient. Hence correct answer is A actually.
Correct answer is: Both statements together are sufficient
Q.16 16. Is x^2 > 10? Statement 1: x = 4 Statement 2: x > 2
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1: x = 4 => x^2 = 16 > 10, sufficient. Statement 2: x > 2 => x could be 3,4,5,..., not sufficient. Hence statement 1 alone sufficient.
Correct answer is: Statement 1 alone is sufficient
Q.17 17. What is the value of m + n? Statement 1: m = 3 Statement 2: n = 7
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1 alone: only m known. Statement 2 alone: only n known. Together: m + n = 3 + 7 = 10. Hence sufficient together.
Correct answer is: Both statements together are sufficient
Q.18 18. Is x divisible by 2? Statement 1: x = 11 Statement 2: x is odd
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1: x = 11 => not divisible by 2. Statement 2: odd number => not divisible by 2. Hence statement 1 alone sufficient.
Correct answer is: Statement 1 alone is sufficient
Q.19 19. Is y > x? Statement 1: y - x = 5 Statement 2: x + y = 15
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1: y - x = 5 => y = x + 5 => y > x. Statement 2 alone: sum known, but individual values not known. Hence statement 1 alone sufficient.
Correct answer is: Statement 1 alone is sufficient
Q.20 20. What is the value of k? Statement 1: 3k + 2 = 11 Statement 2: k - 1 = 2
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1: 3k + 2 = 11 => k = 3. Statement 2: k - 1 = 2 => k = 3. Both statements individually sufficient, correct answer A actually.
Correct answer is: Both statements together are sufficient
Q.21 21. Is x a multiple of 4? Statement 1: x = 16 Statement 2: x is even
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1: x = 16 => divisible by 4. Statement 2: x even => could be 2,6,10,..., insufficient. Hence statement 1 alone sufficient.
Correct answer is: Statement 1 alone is sufficient
Q.22 22. What is the value of a - b? Statement 1: a + b = 10 Statement 2: a - b = 4
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 2 directly gives a - b = 4, sufficient alone. Statement 1 alone gives sum only, insufficient.
Correct answer is: Statement 2 alone is sufficient
Q.23 23. Is n a perfect square? Statement 1: n = 36 Statement 2: n is positive
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1: n = 36 => perfect square (6^2). Statement 2 alone: positive number could be 2,3,..., insufficient. Hence statement 1 alone sufficient.
Correct answer is: Statement 1 alone is sufficient
Q.24 24. What is the value of x + y? Statement 1: x = 7 Statement 2: y = 3
Statement 1 alone is sufficient
Statement 2 alone is sufficient
Both statements together are sufficient
Cannot be determined
Explanation - Statement 1 alone: x known only. Statement 2 alone: y known only. Together: x + y = 7 + 3 = 10. Hence sufficient together.
Correct answer is: Both statements together are sufficient