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16 Jun 2021, 02:00
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C
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Difficulty:
45%
(medium)
Question Stats:
69% (02:04) correct
31%
(02:01)
wrong
based on 186
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Sets S and T contain an equal number of elements, all of which are positive integers. x is the median of S and y is the average (arithmetic mean) of T. Is x > y ?
(1) The sum of S is greater than the sum of T
(2) S consists of consecutive even numbers and T consists of consecutive odd numbers
(1) The sum of S is greater than the sum of T
(2) S consists of consecutive even numbers and T consists of consecutive odd numbers
19 Jun 2021, 02:00
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Sets S and T contain an equal number of elements, all of which are positive integers. x is the median of S and y is the average (arithmetic mean) of T. Is x > y ?
(1) The sum of S is greater than the sum of T.
If S = {2} (median = x = 2) and T = {1} (average = y = 1), then x > y;
If S = {1, 1, 10} (median = x = 1) and T = {1, 2, 3} (average = y = 2), then x < y.
Not sufficient.
(2) S consists of consecutive even numbers and T consists of consecutive odd numbers.
If S = {2, 4} (median = x = 3) and T = {1, 3} (average = y = 2), then x > y;
If S = {2, 4} (median = x = 3) and T = {3, 5} (average = y = 4), then x < y.
Not sufficient.
(1)+(2) In an evenly spaced set (for example, in a set of consecutive even or odd integers, or in a set of any other arithmetic progression) mean = median. So, the mean of S equals to the median of S. So, we need to compare the mean of S to the mean of T. Now, {mean} = {sum of the elements}/{number of elements}.
We also know that sets S and T contain an equal number of elements and the sum of S is greater than the sum of T, hence {sum of the elements in S}/{number of elements} > {sum of the elements in T}/{number of elements}. Sufficient.
Answer: C.
(1) The sum of S is greater than the sum of T.
If S = {2} (median = x = 2) and T = {1} (average = y = 1), then x > y;
If S = {1, 1, 10} (median = x = 1) and T = {1, 2, 3} (average = y = 2), then x < y.
Not sufficient.
(2) S consists of consecutive even numbers and T consists of consecutive odd numbers.
If S = {2, 4} (median = x = 3) and T = {1, 3} (average = y = 2), then x > y;
If S = {2, 4} (median = x = 3) and T = {3, 5} (average = y = 4), then x < y.
Not sufficient.
(1)+(2) In an evenly spaced set (for example, in a set of consecutive even or odd integers, or in a set of any other arithmetic progression) mean = median. So, the mean of S equals to the median of S. So, we need to compare the mean of S to the mean of T. Now, {mean} = {sum of the elements}/{number of elements}.
We also know that sets S and T contain an equal number of elements and the sum of S is greater than the sum of T, hence {sum of the elements in S}/{number of elements} > {sum of the elements in T}/{number of elements}. Sufficient.
Answer: C.
20 Jun 2021, 08:27
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Since S and T have the same number of values, Statement 1 tells us the mean of S is greater than the mean of T. That doesn't answer the question, because the median of S can be very different from the mean of S.
Statement 2 tells us S and T are both equally spaced, and in any equally spaced set, the mean and median are equal. We don't know anything about how big the mean or median of S and T are though, so Statement 2 is not sufficient.
Together, we know from Statement 1 that the mean of S is greater than the mean of T, and we know from Statement 2 that the median of S equals the mean of S, so combined, the median of S is greater than the mean of T, and that's what we wanted to know, so C is the answer.
Statement 2 tells us S and T are both equally spaced, and in any equally spaced set, the mean and median are equal. We don't know anything about how big the mean or median of S and T are though, so Statement 2 is not sufficient.
Together, we know from Statement 1 that the mean of S is greater than the mean of T, and we know from Statement 2 that the median of S equals the mean of S, so combined, the median of S is greater than the mean of T, and that's what we wanted to know, so C is the answer.
