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Difficulty:
55%
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Question Stats:
67% (02:25) correct
33%
(02:28)
wrong
based on 798
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S = {1, 2, 5, 7, x}
If x is a positive integer, is the mean of set S greater than 4?
(1) The median of set S is greater than 2
(2) The median of set S is equal to the mean of set S
If x is a positive integer, is the mean of set S greater than 4?
(1) The median of set S is greater than 2
(2) The median of set S is equal to the mean of set S
05 Apr 2014, 02:28
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S = {1, 2, 5, 7, x}
If x is a positive integer, is the mean of set S greater than 4?
The mean = (1 + 2 + 5 + 7 + x)/5 = (15 + x)/5. The question asks whether (15 + x)/5 > 4 --> is x > 5.
(1) The median of set S is greater than 2:
The median of a set with odd number of elements is the middle element when arranged in ascending/descending order. Hence the median of set S can be:
2, when \(x\leq{2}\), {x, 1, 2, 5, 7}
x, when \(2\leq{x}\leq{5}\), {1, 2, x, 5, 7};
5, when \(x\geq{5}\), {1, 2, 5, 7, x}.
So, the median of the set will be greater than 2, when x > 2. Hence this statement is not sufficient to say whether x > 5. Not sufficient.
(2) The median of set S is equal to the mean of set S:
The mean = (15 + x)/5 = 3 + x/5.
Since we know that the median of set S must be an integer (2, x, or 5), then the mean, which is 3 + x/5 must also be an integer --> x must be a multiple of 5. The least positive multiple of 5 is 5 itself. If x=5, then S={1, 2, 5, 5, 7} --> mean=4 and the median=5. So, x is not 5, which implies that it must be 10 (the next multiple of 5) or greater. Sufficient.
Answer: B.
Hope it's clear.
If x is a positive integer, is the mean of set S greater than 4?
The mean = (1 + 2 + 5 + 7 + x)/5 = (15 + x)/5. The question asks whether (15 + x)/5 > 4 --> is x > 5.
(1) The median of set S is greater than 2:
The median of a set with odd number of elements is the middle element when arranged in ascending/descending order. Hence the median of set S can be:
2, when \(x\leq{2}\), {x, 1, 2, 5, 7}
x, when \(2\leq{x}\leq{5}\), {1, 2, x, 5, 7};
5, when \(x\geq{5}\), {1, 2, 5, 7, x}.
So, the median of the set will be greater than 2, when x > 2. Hence this statement is not sufficient to say whether x > 5. Not sufficient.
(2) The median of set S is equal to the mean of set S:
The mean = (15 + x)/5 = 3 + x/5.
Since we know that the median of set S must be an integer (2, x, or 5), then the mean, which is 3 + x/5 must also be an integer --> x must be a multiple of 5. The least positive multiple of 5 is 5 itself. If x=5, then S={1, 2, 5, 5, 7} --> mean=4 and the median=5. So, x is not 5, which implies that it must be 10 (the next multiple of 5) or greater. Sufficient.
Answer: B.
Hope it's clear.
General Discussion
18 Oct 2015, 21:20
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ANS is b clearly ;
Quick question Bunnel :- if number are in AP mean = median ; so according to this q the vic-versa doesnt hold true i should believe that ???
Quick question Bunnel :- if number are in AP mean = median ; so according to this q the vic-versa doesnt hold true i should believe that ???
