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06 Oct 2020, 00:15
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E
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Difficulty:
65%
(hard)
Question Stats:
56% (02:13) correct
44%
(02:36)
wrong
based on 183
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Two sets, A and B, include only positive integers. If set A and set B have the same number of terms, is the median of set A greater than the average (arithmetic mean) of set B?
(1) The terms in set A are even and the terms in set B are odd
(2) The sum of the terms of set A is equal to the sum of the terms of set B
(1) The terms in set A are even and the terms in set B are odd
(2) The sum of the terms of set A is equal to the sum of the terms of set B
There are two set A and B which only includes positive integer. A and B have the same number of positive integers. Is the median of A greater than the average of B?
(1)the items in A are even, the items in B is odd
(2)the sum of A is equal to sum of B
(1)the items in A are even, the items in B is odd
(2)the sum of A is equal to sum of B
Updated on: 06 Oct 2020, 09:50
Originally posted by QuantMadeEasy on 06 Oct 2020, 06:16.
Last edited by QuantMadeEasy on 06 Oct 2020, 09:50, edited 1 time in total.
Last edited by QuantMadeEasy on 06 Oct 2020, 09:50, edited 1 time in total.
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Quote:
Step 1: Understanding statement 1 alone
(1) The terms in set A are even and the terms in set B are odd
Lets use values for Set A and Set B to understand:
When Set A = {2, 4, 6} and Set B = { 1, 3, 5}
Median of set A = 4 and average of set B = 3; Median of set A > average of set B
When Set A = {2, 4, 6} and Set B = { 3, 5, 7}
Median of set A = 4 and average of set B = 5; Median of set A < average of set B
Insufficient
Step 2: Understanding statement 2 alone
(2) The sum of the terms of set A is equal to the sum of the terms of set B
When Set A = {1, 2, 6} and Set B = { 1, 3, 5}
Median of set A = 2 and average of set B = 3; Median of set A < average of set B
When Set A = {1, 5, 6} and Set B = { 2, 4, 6}
Median of set A = 5 and average of set B = 4; Median of set A > average of set B
Insufficient
Step 3: Combining statement 1 and 2
When Set A = {4, 8, 12, 14} and Set B = {1, 3, 5, 29}
Median of set A = 10 and average of set B = 9.5; Median of set A > average of set B
When Set A = { 2, 4, 6, 12} and Set B = {1, 3, 5, 15}
Median of set A = 5 and average of set B = 6; Median of set A < average of set B
Insufficient
IMO E
06 Oct 2020, 09:30
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Bunuel
Since the sets have an equal number of terms, Statement 2 tells us they have the same average, so we just want to know if A's median is bigger than A's average. But we have no information about that anywhere in the question - the fact from Statement 1 that A contains even terms is irrelevant. If A is symmetric, its mean and median will be equal; if its elements are skewed so they are mostly small, its median will be smaller than its mean, and if it is skewed so most of its elements are large, its median will exceed its mean. So the answer is E.
If one wanted examples here, one where A's median exceeds B's mean (and thus of A's mean), and one where A's median is less than B's mean, we could have, with a sum of 300 for each set (so a mean of 75 for each) :
A = 0, 98, 100, 102
B = -1, 1, 149, 151
where A has a larger median than mean, or we could have
A = 0, 2, 4, 294
B = -1, 1, 149, 151
where A has a smaller median than mean.
A "set" in math does not contain repeated elements, so the solution posted above mine is technically incorrect.
