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10 Jun 2015, 04:13
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
70% (02:33) correct
30%
(03:09)
wrong
based on 1186
sessions
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Date
Time
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A set of 5 numbers has an average of 50. The largest element in the set is 5 greater than 3 times the smallest element in the set. If the median of the set equals the mean, what is the largest possible value in the set?
(A) 85
(B) 86
(C) 88
(D) 91
(E) 92
(A) 85
(B) 86
(C) 88
(D) 91
(E) 92
15 Jun 2015, 04:29
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Bunuel
MANHATTAN GMAT OFFICIAL SOLUTION:
Two techniques will help us efficiently interpret the information given in the question. First, we draw a number line with 5 dots representing the 5 numbers in the set. Second, we label these numbers A, B, C, D, and E, with the understanding that A ≤ B ≤ C ≤ D ≤ E.
Attachment:
2015-06-15_1526.png [ 7.99 KiB | Viewed 24837 times ]
We are told that:
A + B + C + D + E = 250 (The set of 5 numbers has an average of 50.)
E = 5 + 3A (The largest element is 5 greater than 3 times the smallest element in the set.)
C = 50 (The median of the set equals the mean.)
We want to maximize E. We should arrange our dots on the number line such that we obey the constraints, yet also note where we have some flexibility.
Attachment:
2015-06-15_1526_001.png [ 8.7 KiB | Viewed 24661 times ]
Similarly, Point B can be anywhere on the line from Point A to Point C. We maximize E by minimizing B, so B = A.
Attachment:
2015-06-15_1527.png [ 6.4 KiB | Viewed 24363 times ]
A + (A) + 50 + 50 + (5 + 3A) = 250
105 + 5A = 250
5A = 145
A = 29
E = 5 + 3A = 5 + 3(29) = 5 + 87 = 92.
Attachment:
2015-06-15_1528.png [ 7.35 KiB | Viewed 24199 times ]
The correct answer is E.
10 Jun 2015, 05:59
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Since GMAT typically doesn't require difficult arithmetic, I figured there was at least 1 option that when you subtracted 5, was easily divisible by 3 (Biggest -5 = 3 x smallest).
There were 2 options:
86 and 92.
I quickly calculated what the smallest would have to be in these cases:
86, the smallest would have to be 27
92, the smallest would have to be 29
Using logic, we can see the data set, in order, looking like this:
Smallest, Smallest, 50 (this is the median), 50 (this is the lowest possible after the median to get the biggest remaining value), Biggest
I subbed in the 2 options and 92 was correct:
29, 29, 50, 50, 92-> mean of 50.
There were 2 options:
86 and 92.
I quickly calculated what the smallest would have to be in these cases:
86, the smallest would have to be 27
92, the smallest would have to be 29
Using logic, we can see the data set, in order, looking like this:
Smallest, Smallest, 50 (this is the median), 50 (this is the lowest possible after the median to get the biggest remaining value), Biggest
I subbed in the 2 options and 92 was correct:
29, 29, 50, 50, 92-> mean of 50.
