Data Sufficiency Sample Questions

Data Sufficiency Sample Questions | 8 Questions

1. What is the average (arithmetic mean) of a, b, and c ?
 
(1) a + 2b + 3c = 10 
(2) 3a + 2b + c = 14

Answer Choices: 
A. Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.  
B. Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.  
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.  
D. EACH statement ALONE is sufficient.  
E. Statements (1) and (2) TOGETHER are not sufficient.

Answer: C

Answer Explanation: The average of a, b, and c is a+b+c/3. Statement (1) says that a+2b+3c = 10, but there is not enough information to determine the value of a+b+c. Thus, statement (1) alone is not sufficient. Similarly, the equation statement (2) also fails to give enough information, so statement (2) alone is not sufficient. If the equations in statements (1) and (2) are added together, term by term, the result is 4a+4b+4c=24, which means that a+b+c = 6. The average is therefore 6/3 = 2. Thus, BOTH statements TOGETHER are sufficient to answer the question. The best answer is C.


2. By what percent was the price of a certain candy bar increased?

(1)The price of the candy bar was increased by 5 cents. 
(2)The price of the candy bar after the increase was 45 cents.

Answer Choices:
A. Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are not sufficient.

Answer: C

Answer Explanation: In (1), only the increase in price is given, and both the original and final prices are unknown. Thus, the percent increase cannot be determined from (1) alone, and the answer must be B, C, or E. In (2), only the final price is given, so the percent increase cannot be determined from (2) alone, and the answer must be C or E. From (1) and (2) together, the amount of the increase is known and the price before the increase can be computed. Therefore, the percent increase can be determined, and the best answer is C.


3. Is the integer n odd?
 
(1) n is divisible by 3. 
(2) n is divisible by 5.

Answer Choices:
A. Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are not sufficient.

Answer: E

Answer Explanation: In statement (1), n is divisible by 3, but n may be even or odd as the examples n = 6 and n = 9 show. Similarly, in statement (2), n is divisible by 5, but it may be even or odd as the examples n = 10 and n = 15 show. Since neither statement alone is sufficient, the answer must be C or E. From (1) and (2) together, n must be divisible by 15, and the examples n = 30 and n = 45 show that n may be even or odd. Thus, the best answer is E.

4. A shirt and a pair of gloves cost a total of $41.70. How much does the pair of gloves cost?
 
(1)The shirt costs twice as much as the gloves. 
(2)The shirt costs $27.80.

Answer Choices:
A. Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are not sufficient

Answer: D

Answer Explanation: From (1) it can be determined that the total cost of the shirt and gloves is three times the cost of the gloves alone; in other words, the gloves cost one third as much as the shirt and gloves together. Thus, (1) alone is sufficient, and the answer must be A or D. Since the cost of the gloves is the difference between the total cost, $41.70, and the cost of the shirt, statement (2) alone is also sufficient. The best answer is therefore D.

5. If on a fishing trip Jim and Tom each caught some fish, which one caught more fish?

(1) Jim caught 2/3 as many fish as Tom.
(2) After Tom stopped fishing, Jim continued to fish until he caught 12 fish.

Answer Choices:
A. Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.  
B. Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.  
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.  
D. EACH statement ALONE is sufficient.  
E. Statements (1) and (2) TOGETHER are not sufficient.

Answer: A

Answer Explanation: Statement (1) indicates that Jim caught fewer fish than Tom. Therefore, (1) alone is sufficient to answer the question, and the answer must be A or D. Statement (2) gives no information about the number of fish Tom caught. Therefore, (2) alone is not sufficient. And the best answer is A.

6. From May 1, 1960 to May 1, 1975 the closing price of a share of stock X doubled. What was the closing price of a share of stock X on May 1, 1960? 

(1) From May 1, 1975, to May 1, 1984, the closing price of a share of stock X doubled. 
(2) From May 1, 1975, to May 1, 1984, the closing price of a share of stock X increased by $4.50.

Answer Choices:

A. Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are not sufficient.

Answer: C

Answer Explanation: Neither statement (1) alone nor statement (2) alone gives any information about the price from 1960 to 1975. Thus, the answer must be C or E. From statements (1) and (2) together, the closing price of a share of the stock on May 1, 1975, can be determined ($4.50) and the closing price on May 1, 1960, can be determined (half of $4.50). Therefore, (1) and (2) together are sufficient, and the best answer is C.

7. If r and s are integers, is r divisible by 7?
 
(1) The product rs is divisible by 7. 
(2) s is not divisible by 7.

Answer Choices:
A. Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are not sufficient.

Answer: C

Answer Explanation: If a product rs is divisible by the prime number 7, then either r is divisible by 7 or s is divisible by 7. Hence, statement (1) alone implies that either r or s is divisible by 7, but it is not sufficient to determine that r is divisible by 7. Therefore, the answer must be B, C, or E. Statement (2) alone is clearly not sufficient, since no information is given about r. Hence, the answer must be C or E. The two statements together are sufficient: If rs is divisible by 7 and s is not divisible by 7, then r is divisible by 7. Thus, the best answer is C.


8. Buckets X and Y contained only water and bucket Y was 1/2 full. If all of the water in bucket X was then poured into bucket Y, what fraction of the capacity of Y was then filled with water?

(1) Before the water from X was poured, X was 1/3 full.
(2) X and Y have the same capacity.

Answer Choices:
A. Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are not sufficient.

Answer: C

Answer Explanation: Statement (1) alone is not sufficient since it gives no information about the relative capacities of the two buckets. Thus, the answer must be B, C, or E. Statement (2) alone is not sufficient since it gives no information about the amount of water in bucket X. Thus, the answer must be C or E. If (1) and (2) are considered together, it can be determined that bucket Y is filled to (1/2 + 1/3) of its capacity. Therefore, the best answer is C.