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11 Dec 2023, 07:00
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D
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12 Days of Christmas 🎅 GMAT Competition with Lots of Questions & Fun
If the data set P consists of 5 different prime numbers and has a median of 13, is the average (arithmetic mean) of the data set P greater than 11?
(1) The product of any three numbers of the data set P is odd.
(2) The range of the data set P is even.
If the data set P consists of 5 different prime numbers and has a median of 13, is the average (arithmetic mean) of the data set P greater than 11?
(1) The product of any three numbers of the data set P is odd.
(2) The range of the data set P is even.
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13 Dec 2023, 11:14
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GMAT Club Official Explanation:
If the data set P consists of 5 different prime numbers and has a median of 13, is the average (arithmetic mean) of the data set P greater than 11?
The median of a set with an odd number count, like 5, is the middle term when the numbers are arranged in order. Thus, a median of 13 implies that 13 is the middle term: {_, _, 13, _, _}.
The question asks whether the average of the data set is greater than 11, i.e., whether the sum is greater than 5*11 = 55.
Since the set consists of 5 different prime numbers, the smallest sum for the set is 54, which occurs with the set {2, 3, 13, 17, 19}. Note that the next larger set, {3, 5, 13, 17, 19}, has a sum of 57. Thus, there would be a NO answer for the set {2, 3, 13, 17, 19}, but a YES answer for all other possible sets.
(1) The product of any three numbers of the data set P is odd.
The above implies that the set consists only of odd primes, as the inclusion of 2 would make the statement false. Consequently, our set cannot be {2, 3, 13, 17, 19}, meaning the sum is greater than 55. Sufficient.
(2) The range of the data set P is even.
The range is the difference between the largest and the smallest terms of the set. For the range to be odd, either both of those terms must be even or both of those terms must be odd. However, the first case is not possible since the largest term, being a prime greater than 13 must be odd, thus we have the second case. This means that the smallest term cannot be 2, and again our set is not {2, 3, 13, 17, 19}, and thus the sum is greater than 55. Sufficient.
Answer: D.
General Discussion
11 Dec 2023, 07:18
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Bunuel
(1) The product of any three numbers of the data set P is odd.
The set doesn't contain two.
_ _ 13 17 19
The average will be lowest when the first two places have lowest values
3 5 13 17 19
The sum of the set is (3+5+13+17+19) = 57
As the sum is greater than 55, the average is greater than 11. The statement is sufficient.
(2) The range of the data set P is even
All prime numbers are odd, hence if the range of the prime number is even, the set doesn't contain any even prime.
The statement conveys the same information as statement 1.
If we take the lowest prime numbers 3, 5, 13, 17, and 19, the average is greater than 11.
Hence this statement is also sufficient.
IMO D
