Below are some data sufficiency problems with a higher difficulty level, along with their answers and explanations.
GMAT Data Sufficiency Question 6
Directions for Questions 6 and 7: Each question is followed by two statements, A and B. Use the following instructions to answer each question:
(a) If the question can be answered using statement A alone but not statement B alone.
(b) If the question can be answered using statement B alone but not statement A alone.
(c) If the question can be answered using either statement alone.
(d) If the question can be answered using both statements together but not by either statement alone.
The "Player of the Match" award goes to the player scoring the most points in a tennis tournament. If there is a tie, the player with more aces wins. If it is still a tie, the player with fewer double faults wins. Players A, B, and C are tied in points. B has two more aces than A. C has the same number of double faults as A. Who is the Player of the Match?
A. C scored 10 points fewer than both A and B.
B. The double faults made by B are one fewer than the aces made by A.
Answer: (d)
Explanation:
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Statement A tells us that C scored fewer points than A and B but doesn't distinguish between A and B.
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Statement B provides information about double faults and aces but not the total points. Together, they allow comparison and determination of the winner by giving us enough to compare aces and double faults along with points.
GMAT Data Sufficiency Question 7
Four students – P, Q, R, and S secured the top four positions in an exam, but P did not get first, Q did not get second, R did not get third, and S did not get fourth. Who ranked where?
A. Neither P nor S were in the top 2.
B. Neither Q nor R was in the bottom 2.
Answer: (c)
Explanation:
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Statement A excludes P and S from the top 2, providing partial information.
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Statement B excludes Q and R from the bottom 2, offering additional partial information.
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Together, they help determine the exact ranks of P, Q, R, and S by elimination.
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GMAT Data Sufficiency Question 8
The following question is followed by two statements, A and B. Use the instructions to determine the answer:
(a) If the question can be answered using statement A alone but not statement B alone.
(b) If the question can be answered using statement B alone but not statement A alone.
(c) If the question cannot be answered using both statements together.
(d) If the question can be answered using both statements together but not by either statement alone.
Mr. Sharma distributes 45 candies among five children such that each child receives at least one candy, and no two children receive the same candies. What number of candies is received by the child who gets the most?
A. Each child receives more than 4 candies.
B. The sum of candies received by the child who gets the most and the child who gets the least is 23.
Answer: (b)
Explanation:
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Statement A provides information on the minimum number of candies each child receives but will not determine the distribution.
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Statement B allows us to deduce the distribution since the total candies and the sum of the maximum and minimum candies provide enough constraints to solve the problem.
GMAT Data Sufficiency Question 9
The following question is followed by two statements, A and B. Use the instructions to determine the answer:
(a) If the question can be answered using statement A alone but not statement B alone.
(b) If the question can be answered using statement B alone but not statement A alone.
(c) If the question cannot be answered using both statements together.
(d) If the question can be answered using both statements together but not by either statement alone.
In a line of students facing East, there are 12 students to the left of Ramesh and 18 students to the right of Suresh. How many students are in the line?
A. There are 6 students between Ramesh and Suresh.
B. The total number of students is a prime number less than 31.
Answer: (c)
Explanation:
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Statement A gives partial information about the students between Ramesh and Suresh but not the total.
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Statement B provides a constraint on the total number of students but without knowing the positions of Ramesh and Suresh.
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Combined, they allow us to determine the total number of students considering the prime number constraint.
GMAT Data Sufficiency Question 10
The following question is followed by two statements, A and B. Use the instructions to determine the answer:
(a) If the question can be answered using one of the statements alone but not the other.
(b) If the question can be answered using either statement alone.
(c) If the question can be answered using both statements together but not by either statement alone.
(d) If the question cannot be answered even using both statements together.
The houses of Arun, Varun, Mohit, and Suresh are of different sizes. Arun lives in the second largest house, which has the same number of rooms as Varun's house. The largest house does not have the maximum number of rooms. Suresh does not live in the smallest house. The total number of rooms in Mohit's and Varun's houses is even. Who lives in the second smallest house, and how many rooms does it have?
A. One house has three rooms, and the others have one, two, and four rooms.
B. The houses have two, three, three, and five rooms, in no particular order.
Answer: (a)
Explanation:
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Statement A provides a specific distribution of rooms allowing us to deduce the number of rooms in the second smallest house.
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Statement B gives a broader range, making it more difficult to pinpoint the exact number of rooms.
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Statement A alone provides enough detail to answer the question.
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