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03 Apr 2020, 02:46
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
59% (02:24) correct
41%
(02:30)
wrong
based on 274
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Set S contains five distinct positive integers, each of which is greater than 2. Is the mean of S greater than the median of S?
(1) The sum of the elements of S is equal to 20 times the smallest element of S.
(2) The median of S is 8 greater than the smallest element of S.
Are You Up For the Challenge: 700 Level Questions
(1) The sum of the elements of S is equal to 20 times the smallest element of S.
(2) The median of S is 8 greater than the smallest element of S.
Are You Up For the Challenge: 700 Level Questions
03 Apr 2020, 03:40
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Bunuel
Assume smallest term of the set = \(a\)
(1) The sum of the elements of S is equal to 20 times the smallest element of S.
--> Sum = \(20a\) & Mean = \(\frac{20a}{5} = 4a\)
Case 1: Set = {\(3, 4, 5, 6, 42\)}; Sum = \(60\), Mean = \(4a = 12\), Median = \(5\) --> Mean > Median
Case 2: Set = {\(3, 12, 13, 15, 17\)}; Sum = \(60\), Mean = \(4a = 12\), Median = \(13\) --> Mean < Median
--> Insufficient
(2) The median of S is 8 greater than the smallest element of S
Case 1: Set = {\(a, a + 1, a + 8, a + 9, a + 12\)}, Mean = \(a + 6\), Median = \(a + 8\) --> Mean < Median
Case 2: Set = {\(a, a + 3, a + 8, a + 99, a + 100\)}, Mean = \(a + 42\), Median = \(a + 8\) --> Mean > Median
--> Insufficient
Combining (1) & (2),
Mean = \(4a\) & Median = \(a + 8\)
Question: Is Mean > Median ??
Is \(4a > a + 8\) ?
--> Is \(4a - a > 8\) ?
--> Is \(3a > 8\) ?
--> Is \(a > 2.66\) ?
--> Always True (Since all terms are greater than 2 and are integers, Possible values of \(a = 3, 4, 5, . . .\) ) --> Sufficient
Option C
General Discussion
03 Apr 2020, 03:00
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Bunuel
Question: Is mean > median?
Let terms are a, b, c, d, e such that a<b<c<d<e
Statement 1: a+b+c+d+e = 20a
1, 2, 3, 4, 10 mean > Media
2, 5, 10, 11, 12 mean > Media
Mean is always greater than median hence
SUFFICIENT
Statement 2: c = 8+a
For smallest mean terms may be 1, 2, 9, 10, 11 Mean < Median
For Large mean terms may be 1, 2, 9, 100, 200 Mean > Median
NOT SUFFICIENT
Answer: Option A
