24 questions. Each is marked with the exam level it suits. Answer, then open the step-by-step solution.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x and y are positive integers, each at most 20. Is x greater than y?
I. x > y.
II. x − y = 7.
I alone allows (2, 1), (3, 1), (3, 2), (4, 1), (4, 2), …: the answer is always Yes.
II alone allows (8, 1), (9, 2), (10, 3), (11, 4), (12, 5), …: the answer is always Yes.
Answer: Each statement alone is sufficient.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x is a positive integer less than 50. Is x divisible by 3?
I. x leaves remainder 1 when divided by 3.
II. x has exactly 2 positive factors.
From I alone, x can be 1, 4, 7, 10, 13, 16, 19, 22, …: the answer is always No.
From II alone, x can be 2, 3, 5, 7, 11, 13, 17, 19, …: the answer is not fixed.
Answer: Statement I alone is sufficient, but statement II alone is not.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x and y are positive integers, each at most 20. Is x greater than y?
I. x > y.
II. x is even and y is odd.
I alone allows (2, 1), (3, 1), (3, 2), (4, 1), (4, 2), …: the answer is always Yes.
II alone allows (2, 1), (2, 3), (2, 5), (2, 7), (2, 9), …: 100 pairs fit and the answer varies.
Answer: Statement I alone is sufficient, but statement II alone is not.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x is a positive integer less than 30. Is x divisible by 4?
I. x is a perfect square.
II. x is a multiple of 8.
From I alone, x can be 1, 4, 9, 16, 25: the answer is not fixed.
From II alone, x can be 8, 16, 24: the answer is always Yes.
Answer: Statement II alone is sufficient, but statement I alone is not.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x and y are positive integers, each at most 20. What is the value of xy?
I. x = 3y.
II. x + y = 24.
I alone allows (3, 1), (6, 2), (9, 3), (12, 4), (15, 5), …: 6 pairs fit and the answer varies.
II alone allows (4, 20), (5, 19), (6, 18), (7, 17), (8, 16), …: 17 pairs fit and the answer varies.
Together they allow (18, 6): the answer is always 108.
Answer: Both statements together are sufficient, but neither alone is.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x and y are positive integers, each at most 20. Is x greater than y?
I. x = 3y.
II. x > y.
I alone allows (3, 1), (6, 2), (9, 3), (12, 4), (15, 5), …: the answer is always Yes.
II alone allows (2, 1), (3, 1), (3, 2), (4, 1), (4, 2), …: the answer is always Yes.
Answer: Each statement alone is sufficient.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x is a positive integer less than 40. Is x greater than 17?
I. x leaves remainder 3 when divided by 5.
II. x is a perfect cube.
From I alone, x can be 3, 8, 13, 18, 23, 28, 33, 38: the answer is not fixed.
From II alone, x can be 1, 8, 27: the answer is not fixed.
Using both, x can be 8: the answer is always No.
Answer: Both statements together are sufficient, but neither alone is.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x and y are positive integers, each at most 20. What is the value of xy?
I. y = 11.
II. x + 2y = 27.
I alone allows (1, 11), (2, 11), (3, 11), (4, 11), (5, 11), …: 20 pairs fit and the answer varies.
II alone allows (1, 13), (3, 12), (5, 11), (7, 10), (9, 9), …: 10 pairs fit and the answer varies.
Together they allow (5, 11): the answer is always 55.
Answer: Both statements together are sufficient, but neither alone is.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x is a positive integer less than 50. Is x greater than 13?
I. The digits of x add up to 4.
II. x has exactly 3 positive factors.
From I alone, x can be 4, 13, 22, 31, 40: the answer is not fixed.
From II alone, x can be 4, 9, 25, 49: the answer is not fixed.
Using both, x can be 4: the answer is always No.
Answer: Both statements together are sufficient, but neither alone is.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x is a positive integer less than 30. Is x divisible by 5?
I. x leaves remainder 4 when divided by 5.
II. The digits of x add up to 11.
From I alone, x can be 4, 9, 14, 19, 24, 29: the answer is always No.
From II alone, x can be 29: the answer is always No.
Answer: Each statement alone is sufficient.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x is a positive integer less than 50. Is x greater than 19?
I. x is a multiple of 3.
II. x has exactly 2 positive factors.
From I alone, x can be 3, 6, 9, 12, 15, 18, 21, 24, …: the answer is not fixed.
From II alone, x can be 2, 3, 5, 7, 11, 13, 17, 19, …: the answer is not fixed.
Using both, x can be 3: the answer is always No.
Answer: Both statements together are sufficient, but neither alone is.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x is a positive integer less than 40. Is x divisible by 5?
I. x is a multiple of 7.
II. x is even.
From I alone, x can be 7, 14, 21, 28, 35: the answer is not fixed.
From II alone, x can be 2, 4, 6, 8, 10, 12, 14, 16, …: the answer is not fixed.
Using both, x can be 14, 28: the answer is always No.
Answer: Both statements together are sufficient, but neither alone is.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x is a positive integer less than 30. What is the value of x?
I. x is a multiple of 4.
II. x < 25.
From I alone, x can be 4, 8, 12, 16, 20, 24, 28: the answer is not fixed.
From II alone, x can be 1, 2, 3, 4, 5, 6, 7, 8, …: the answer is not fixed.
Using both, x can be 4, 8, 12, 16, 20, 24: the answer is not fixed.
Answer: The two statements together are not sufficient.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x is a positive integer less than 40. What is the value of x?
I. x is even.
II. x is a prime number.
From I alone, x can be 2, 4, 6, 8, 10, 12, 14, 16, …: the answer is not fixed.
From II alone, x can be 2, 3, 5, 7, 11, 13, 17, 19, …: the answer is not fixed.
Using both, x can be 2: the answer is always 2.
Answer: Both statements together are sufficient, but neither alone is.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x is a positive integer less than 40. Is x divisible by 2?
I. x > 30.
II. x is a multiple of 6.
From I alone, x can be 31, 32, 33, 34, 35, 36, 37, 38, …: the answer is not fixed.
From II alone, x can be 6, 12, 18, 24, 30, 36: the answer is always Yes.
Answer: Statement II alone is sufficient, but statement I alone is not.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x and y are positive integers, each at most 20. Is x greater than y?
I. x > y.
II. xy = 48.
I alone allows (2, 1), (3, 1), (3, 2), (4, 1), (4, 2), …: the answer is always Yes.
II alone allows (3, 16), (4, 12), (6, 8), (8, 6), (12, 4), …: 6 pairs fit and the answer varies.
Answer: Statement I alone is sufficient, but statement II alone is not.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x is a positive integer less than 30. Is x divisible by 5?
I. x is a multiple of 3.
II. x is a perfect square.
From I alone, x can be 3, 6, 9, 12, 15, 18, 21, 24, …: the answer is not fixed.
From II alone, x can be 1, 4, 9, 16, 25: the answer is not fixed.
Using both, x can be 9: the answer is always No.
Answer: Both statements together are sufficient, but neither alone is.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x and y are positive integers, each at most 20. Is x greater than y?
I. x > y.
II. x = 4y.
I alone allows (2, 1), (3, 1), (3, 2), (4, 1), (4, 2), …: the answer is always Yes.
II alone allows (4, 1), (8, 2), (12, 3), (16, 4), (20, 5): the answer is always Yes.
Answer: Each statement alone is sufficient.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x is a positive integer less than 30. Is x greater than 17?
I. x is a multiple of 3.
II. x is a multiple of 9.
From I alone, x can be 3, 6, 9, 12, 15, 18, 21, 24, …: the answer is not fixed.
From II alone, x can be 9, 18, 27: the answer is not fixed.
Using both, x can be 9, 18, 27: the answer is not fixed.
Answer: The two statements together are not sufficient.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x and y are positive integers, each at most 20. What is the value of x?
I. x + 2y = 25.
II. x + y = 13.
I alone allows (1, 12), (3, 11), (5, 10), (7, 9), (9, 8), …: 10 pairs fit and the answer varies.
II alone allows (1, 12), (2, 11), (3, 10), (4, 9), (5, 8), …: 12 pairs fit and the answer varies.
Together they allow (1, 12): the answer is always 1.
Answer: Both statements together are sufficient, but neither alone is.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x and y are positive integers, each at most 20. Is x greater than y?
I. x > y.
II. x = 3y.
I alone allows (2, 1), (3, 1), (3, 2), (4, 1), (4, 2), …: the answer is always Yes.
II alone allows (3, 1), (6, 2), (9, 3), (12, 4), (15, 5), …: the answer is always Yes.
Answer: Each statement alone is sufficient.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x and y are positive integers, each at most 20. What is the value of x?
I. xy = 24.
II. x is even and y is odd.
I alone allows (2, 12), (3, 8), (4, 6), (6, 4), (8, 3), …: 6 pairs fit and the answer varies.
II alone allows (2, 1), (2, 3), (2, 5), (2, 7), (2, 9), …: 100 pairs fit and the answer varies.
Together they allow (8, 3): the answer is always 8.
Answer: Both statements together are sufficient, but neither alone is.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x and y are positive integers, each at most 20. What is the value of xy?
I. y = 7.
II. x + 2y = 25.
I alone allows (1, 7), (2, 7), (3, 7), (4, 7), (5, 7), …: 20 pairs fit and the answer varies.
II alone allows (1, 12), (3, 11), (5, 10), (7, 9), (9, 8), …: 10 pairs fit and the answer varies.
Together they allow (11, 7): the answer is always 77.
Answer: Both statements together are sufficient, but neither alone is.
Each question is followed by two statements. Decide whether the data in the statements are sufficient to answer it.
x and y are positive integers, each at most 20. What is the value of xy?
I. x − y = 4.
II. x + y = 22.
I alone allows (5, 1), (6, 2), (7, 3), (8, 4), (9, 5), …: 16 pairs fit and the answer varies.
II alone allows (2, 20), (3, 19), (4, 18), (5, 17), (6, 16), …: 19 pairs fit and the answer varies.
Together they allow (13, 9): the answer is always 117.
Answer: Both statements together are sufficient, but neither alone is.
These are original practice questions written by Target Campus in the pattern, syllabus and difficulty of IPMAT Indore, IPMAT Rohtak, JIPMAT, NPAT and SET. They are not previous-year papers.
IPMPrep