Data Sufficiency Practice Questions
Data sufficiency questions test your ability to determine whether you have enough information to answer a question. Each question is followed by two statements. You must decide whether the information provided in the statements is sufficient to answer the question.
Answer choices:
- 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 statement ALONE is sufficient
- EACH statement ALONE is sufficient
- Statements (1) and (2) TOGETHER are NOT sufficient
Questions 1-10: Arithmetic
1. What is the value of x?
Answer: A
Statement (1) alone is sufficient because we can solve for x directly: x = 10 - 3 = 7.
Statement (2) alone is not sufficient because many numbers are prime (2, 3, 5, 7, etc.).
2. Is y positive?
Answer: B
Statement (1) is not sufficient because y could be positive or negative (both square to positive numbers).
Statement (2) is sufficient because if y³ > 0, then y must be positive (negative numbers have negative cubes).
3. What is the average of a, b, and c?
Answer: E
Neither statement alone is sufficient. Together, we know a + 2b + c = 25, but we don't know the individual values or a + b + c specifically.
We need a + b + c to find the average, which we cannot determine from the given information.
4. How much does a car cost?
Answer: C
Statement (1) alone is not sufficient because we don't know the bicycle's price.
Statement (2) alone is not sufficient because we don't know the relationship between car and bicycle prices.
Together, we can determine the car costs 2 × $200 = $400.
5. Is integer n divisible by 3?
Answer: A
Statement (1) is sufficient. If n² is divisible by 9, then n must be divisible by 3.
Statement (2) is not sufficient. Being even tells us nothing about divisibility by 3 (e.g., 2 is not divisible by 3, but 6 is).
6. What is the value of z?
Answer: D
Each statement alone is sufficient.
From (1): z = 10 - 5 = 5
From (2): z = 2 + 3 = 5
7. How many books are on the shelf?
Answer: D
Each statement alone is sufficient.
From (1): books = 10 + 5 = 15
From (2): books = 18 - 3 = 15
8. What is the ratio of x to y?
Answer: A
Statement (1) is sufficient: 2x = 3y ⇒ x/y = 3/2
Statement (2) is not sufficient: x + y = 10 gives many possible ratios (e.g., 1:9, 2:8, 3:7, etc.)
9. Is m an integer?
Answer: B
Statement (1) is not sufficient. For example, √2 is not integer but (√2)² = 2 is integer.
Statement (2) is sufficient. If 2m is an integer, then m must be either an integer or a half-integer. But since 2m is integer, m = k/2 where k is integer. If k is even, m is integer; if k is odd, m is half-integer. Wait, this seems to suggest it's not sufficient either.
Correction: Actually, statement (2) alone is not sufficient. For example, if 2m = 1 (integer), then m = 0.5 (not integer). If 2m = 2 (integer), then m = 1 (integer). So we cannot determine.
Neither statement alone is sufficient. Together: if m² is integer and 2m is integer, then m must be integer. For example, if m = 0.5, then m² = 0.25 (not integer). So if both conditions hold, m must be integer. Answer should be C.
Correction: Answer is C
10. What is the value of p + q?
Answer: B
Statement (1) is not sufficient. Many pairs of numbers have difference of 7 (e.g., 10 and 3, 8 and 1).
Statement (2): p² - q² = (p - q)(p + q) = 63. This alone is not sufficient.
Together: We know p - q = 7, so 7(p + q) = 63 ⇒ p + q = 9. So both together are sufficient.
Wait, but the question is asking for p + q, and statement (2) alone doesn't give us that value without statement (1).
Actually, the answer should be C.
Correction: Answer is C
Questions 11-12: Algebra
11. What is the value of x?
Answer: D
Each statement alone is sufficient.
From (1): 2x = 8 ⇒ x = 4
From (2): 3x = 12 ⇒ x = 4
12. Is y > 0?
Answer: B
Statement (1): y² = 4 ⇒ y = 2 or y = -2. Not sufficient to determine if y > 0.
Statement (2): y³ = -8 ⇒ y = -2. This is definitely not greater than 0. Sufficient to answer the question (the answer is "no").
Data Sufficiency Questions - Quiz
Q1. Who is the tallest among the brothers A, B, C, and D?
Statements:
1. C is shorter than only B.
2. D is taller than only A.
Options:
I) Statement 1 alone is sufficient
II) Statement 2 alone is sufficient
III) Both Statement 1 and 2 together are sufficient
IV) Both Statement 1 and 2 even together are not sufficient
Answer: I) Statement 1 alone is sufficient
Explanation: Statement 1 implies B is taller than everyone else, so B is the tallest. Statement 2 does not give enough info. Hence Statement 1 alone is sufficient.
Q2. What is the value of 'x'?
Statements:
1. x² + x - 6 = 0
2. x ≥ 0
Options:
I) Statement 1 alone is sufficient
II) Statement 2 alone is sufficient
III) Both together are sufficient
IV) Both together are not sufficient
Answer: III) Both statements together are sufficient
Explanation: From (1): roots are -3 and 2. From (2): x ≥ 0. Combining → x = 2.
Q3. What is the sum of the ages of John and Peter?
Statements:
1. John is 5 years older than Peter.
2. The average of their ages is 25.
Answer: II) Statement 2 alone is sufficient
Explanation: Average is 25 → total = 50. Enough to find the sum.
Q4. What is the value of x in the equation x² + 6x + 9 = 0?
Statements:
1. x = -3
2. Discriminant is zero
Answer: III) Both statements together are sufficient
Explanation: Discriminant=0 → one root. Statement 1 gives that root = -3. Together they are sufficient.
Q5. Is triangle ABC an equilateral triangle?
Statements:
1. AB = AC
2. BC = 2 × AB
Answer: II) Statement 2 alone is sufficient
Explanation: If BC = 2AB, triangle cannot be equilateral. Statement 2 alone answers.
Q6. What is the value of x in 2x + 5 = 11?
Statements:
1. x = 3
2. x is a prime number
Answer: I) Statement 1 alone is sufficient
Explanation: Statement 1 directly gives x. Statement 2 is vague.
Q7. How much did Mr. Smith spend on his vacation?
Statements:
1. He spent $500 on flight.
2. He spent $800 on hotel stay.
Answer: III) Both statements together are sufficient
Explanation: Total = 500 + 800 = 1300.
Q8. Is the given rectangle a square?
Statements:
1. Each side = 8 cm
2. Diagonals are equal
Answer: I) Statement 1 alone is sufficient
Explanation: Equal sides imply it's a square. Statement 2 is true for all rectangles.
Q9. What is the sum of the angles of a triangle?
Statements:
1. One angle is 60°
2. Triangle is equilateral
Answer: II) Statement 2 alone is sufficient
Explanation: Equilateral triangle → sum is 180° always.
Q10. What is the total number of students in a class?
Statements:
1. 20 boys in class
2. Girls : Boys = 2:5
Answer: III) Both statements together are sufficient
Explanation: Boys = 20, Girls = (2/5)×20 = 8. Total = 28.
