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Given the ascending set of positive integers {a, b, c, d, e, f}, is the median greater than the mean?

The median of a set with even number of elements is the average of two middle elements when arranged in ascending/descending order. Thus, the median of {a, b, c, d, e, f} is \(\frac{c+d}{2}\).

So, the question asks: is \(\frac{c+d}{2}>\frac{a+b+c+d+e+f}{6}\)? --> is \(3c+3d>a+b+c+d+e+f\)? --> is \(2(c+d)>a+b+e+f\)?

(1) a + e = (3/4)(c + d) --> the question becomes: is \(2(c+d)>b+f+\frac{3}{4}(c + d)\)? --> is \(\frac{5}{4}(c + d)>b+f\)? Not sufficient.

(2) b + f = (4/3)(c + d). The same way as above you can derive that this statement is not sufficient.

(1)+(2) The question in (1) became: is \(\frac{5}{4}(c + d)>b+f\)? Since (2) says that \(b + f = \frac{4}{3}(c + d)\), then the question becomes: is \(\frac{5}{4}(c + d)>\frac{4}{3}(c + d)\)? --> is \(\frac{1}{12}(c+d)<0\)? --> is \(c+d<0\)? As given that \(c\) and \(d\) are positive numbers, then the answer to this question is definite NO. Sufficient.

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

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12 Feb 2013, 13:29

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if all of the integers are positive, then how come c+d<o ? question system contradicts with the solution... You are right Bunuel.. not an air tight question.

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

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09 Mar 2014, 19:55

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We don't have to do any calculations here. For mean, we have to have the sum of the all the numbers in the set while for for the median c and d are sufficient. Since both the options together can give us the mean in terms of c+d, we can compare that against the mean which is also in terms of c+d. So C should be the right choice.
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Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

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04 Aug 2012, 17:37

Bunuel Is this not a GMAT type question ?

Bunuel wrote:

Given the ascending set of positive integers {a, b, c, d, e, f}, is the median greater than the mean?

The median of a set with even number of elements is the average of two middle elements when arranged in ascending/descending order. Thus, the median of {a, b, c, d, e, f} is \(\frac{c+d}{2}\).

So, the question asks: is \(\frac{c+d}{2}>\frac{a+b+c+d+e+f}{6}\)? --> is \(3c+3d>a+b+c+d+e+f\)? --> is \(2(c+d)>a+b+e+f\)?

(1) a + e = (3/4)(c + d) --> the question becomes: is \(2(c+d)>b+f+\frac{3}{4}(c + d)\)? --> is \(\frac{5}{4}(c + d)>b+f\)? Not sufficient.

(2) b + f = (4/3)(c + d). The same way as above you can derive that this statement is not sufficient.

(1)+(2) The question in (1) became: is \(\frac{5}{4}(c + d)>b+f\)? Since (2) says that \(b + f = \frac{4}{3}(c + d)\), then the question becomes: is \(\frac{5}{4}(c + d)>\frac{4}{3}(c + d)\)? --> is \(\frac{1}{12}(c+d)<0\)? --> is \(c+d<0\)? As given that \(c\) and \(d\) are positive numbers, then the answer to this question is definite NO. Sufficient.

if all of the integers are positive, then how come c+d<o ? question system contradicts with the solution... You are right Bunuel.. not an air tight question.

The question is fine in that respect.

After some manipulations the question became "is c+d<0?" So, c+d<0 is not a statement, it's a question and since we know that c and d are positive numbers, then the answer to this question is NO.

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

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07 Mar 2014, 10:00

Bunuel wrote:

mbhussain wrote:

if all of the integers are positive, then how come c+d<o ? question system contradicts with the solution... You are right Bunuel.. not an air tight question.

The question is fine in that respect.

After some manipulations the question became "is c+d<0?" So, c+d<0 is not a statement, it's a question and since we know that c and d are positive numbers, then the answer to this question is NO.

Hope it's clear.

Bunuel, you have an algebra mistake in your solution, as the statements 1) and 2) combined boil down to:

\(1/2 (c+d) > 37/72 (c+d)\).

This seems like a perfectly reasonable GMAT question.

if all of the integers are positive, then how come c+d<o ? question system contradicts with the solution... You are right Bunuel.. not an air tight question.

The question is fine in that respect.

After some manipulations the question became "is c+d<0?" So, c+d<0 is not a statement, it's a question and since we know that c and d are positive numbers, then the answer to this question is NO.

Hope it's clear.

Bunuel, you have an algebra mistake in your solution, as the statements 1) and 2) combined boil down to:

1/2 (c+d) > 37/72 (c+d)

This seems like a perfectly reasonable GMAT question.

What mistake are you talking about?
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11 May 2015, 15:40

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