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# Given the ascending set of positive integers {a, b, c, d, e,

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

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19 Jun 2011, 14:36
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Given the ascending set of positive integers {a, b, c, d, e, f}, is the median greater than the mean?

(1) a + e = (3/4)(c + d)

(2) b + f = (4/3)(c + d)
[Reveal] Spoiler: OA

Last edited by siddhans on 20 Jun 2011, 22:32, edited 1 time in total.

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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, 16:32
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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.

Not a good question.
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Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

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12 Feb 2013, 14:29
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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.

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

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09 Mar 2014, 20:55
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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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10 Dec 2016, 16:44
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Below is the best reply that I have found on another forum. It's quite understandable.

Median = (c+d)/2
Average = (a+b+c+d+e+f)/6

Median > Average
(c+d)/2 > (a+b+c+d+e+f)/6
3c + 3d > a+b+c+d+e+f
2c + 2d > a+b+e+f
2(c+d) > a+b+e+f

Thus, the question can be rephrased:

Is 2(c+d) > a+b+e+f?

Statement 1: a + e = (3/4)(c + d)
Insufficient.

Statement 2: b + f = (4/3)(c + d)
Insufficient.

Statement 1 and 2 together:
a+b+e+f = (3/4)(c+d) + (4/3)(c+d)
a+b+e+f = (3/4 + 4/3)(c+d)
a+b+e+f = (25/12)(c+d)
Sufficient.

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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, 18:37
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.

Not a good question.

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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, 18:40
venmic wrote:
Bunuel Is this not a GMAT type question ?

It's a GMAT type question, but from my point of view not a very good one.
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Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

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13 Feb 2013, 01:17
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.
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Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

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22 May 2017, 07:53
siddhans wrote:
Given the ascending set of positive integers {a, b, c, d, e, f}, is the median greater than the mean?

(1) a + e = (3/4)(c + d)

(2) b + f = (4/3)(c + d)

The problem asks if (C+D)/2 > (A+B+C+D+E+F)/6?

In other words, is 2C + 2D > A+B+E+F?

Statement 1: A+E = 3/4*(C+D)

We can quickly realize that B and F are unknown, so we cannot answer the question provided (is 2C+2D>A+B+E+F?). Insufficient.

Statement 2: Here we are given B+F = 4/3(C+D). Similarly, we do not know the values of A or E, so this statement is insufficient.

Statements 1+2: When combined, we know that B+F and A+E can be expressed in terms of C and D, so via substitution we can do algebra to arrive at this answer:

2C + 2D > 25/12C + 25/12D? No, because 25/12 > 2.

Sufficient.

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Re: Given the ascending set of positive integers {a, b, c, d, e,   [#permalink] 22 May 2017, 07:53
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