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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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19 Jun 2011, 15:03
bong1993 wrote:
C it is

Please give detailed steps...Dont just give A,B, c...I already know its C
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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, 15:59
Anyone can provide the logic behind this please..
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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, 16:00
Bunuel If you can provide your inputs pls that vvill help
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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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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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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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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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07 Mar 2014, 11:00
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.
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Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

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08 Mar 2014, 07:36
speedilly wrote:
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.

What mistake are you talking about?
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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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11 May 2015, 16:40
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Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

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