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# M28-43

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Math Expert
Joined: 02 Sep 2009
Posts: 50009

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16 Sep 2014, 01:31
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Difficulty:

45% (medium)

Question Stats:

59% (01:09) correct 41% (00:45) wrong based on 34 sessions

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There are two schools in the village. The average age of pupils in the first school is 12.2 years and the average age of pupils in the second school is 13.1 years. What is the average age of all school pupils in the village?

(1) There are 40 more pupils in the second school than there are in the first.

(2) There are three times as many pupils in the second school as there are in the first.

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Joined: 02 Sep 2009
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16 Sep 2014, 01:31
1
Official Solution:

This is a weighted average question. Say $$x$$ and $$y$$ are the number of pupils in the first and the second schools in the village, respectively: $$\text{average}=\frac{12.2x+13.1y}{x+y}$$.

(1) There are 40 more pupils in the second school than there are in the first. Given: $$x+40=y$$. Not sufficient to find the average.

(2) There are three times as many pupils in the second school as there are in the first. Given: $$3x=y$$. Hence, $$\text{average}=\frac{12.2x+13.1*3x}{x+3x}=\frac{12.2+13.1*3}{4} \approx 12.9$$. Sufficient.

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Joined: 13 Oct 2017
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08 Feb 2018, 02:17
Hi Bunuel,

Why ist't statement 1 sufficient? Is it because x doesn't cancel out once it's plugged in, in place of x?

Thanks as per usual...I'd also be grateful if you can give me a tip on studying...I've tried jeff sackmann's math bible and also tried his additional sets of questions...I thought I was half decent as quants by the time I finished it...then did the real test and found myself scoring a 29...I then did the economist gmat and it was helpful in terms of a few tricks like reverse plugging in etc...but I've now found that I've forgotten a few things I've learned via Sackmann...would you suggest a targeted approach on mathclub like subject by subject sets of 10 questions on the quizzes? I'd really appreciate your advice. Best wishes,

Tosin
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Joined: 02 Sep 2009
Posts: 50009

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08 Feb 2018, 02:35
ttaiwo wrote:
Hi Bunuel,

Why ist't statement 1 sufficient? Is it because x doesn't cancel out once it's plugged in, in place of x?

Thanks as per usual...I'd also be grateful if you can give me a tip on studying...I've tried jeff sackmann's math bible and also tried his additional sets of questions...I thought I was half decent as quants by the time I finished it...then did the real test and found myself scoring a 29...I then did the economist gmat and it was helpful in terms of a few tricks like reverse plugging in etc...but I've now found that I've forgotten a few things I've learned via Sackmann...would you suggest a targeted approach on mathclub like subject by subject sets of 10 questions on the quizzes? I'd really appreciate your advice. Best wishes,

Tosin

For (1): if we substitute $$x+40=y$$ into $$\text{average}=\frac{12.2x+13.1y}{x+y}$$ we'd get $$\text{average}=\frac{25.3 x + 524}{2x+40}$$. Without knowing x or y, we cannot get the single numerical value of this expression, so cannot answer the question.

Check Study Plans for Novice and Advanced GMAT Takers.

For all other QUANT subjects:
ALL YOU NEED FOR QUANT ! ! !

Hope it helps.
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08 Feb 2018, 03:33
Bunuel wrote:
ttaiwo wrote:
Hi Bunuel,

Why ist't statement 1 sufficient? Is it because x doesn't cancel out once it's plugged in, in place of x?

Thanks as per usual...I'd also be grateful if you can give me a tip on studying...I've tried jeff sackmann's math bible and also tried his additional sets of questions...I thought I was half decent as quants by the time I finished it...then did the real test and found myself scoring a 29...I then did the economist gmat and it was helpful in terms of a few tricks like reverse plugging in etc...but I've now found that I've forgotten a few things I've learned via Sackmann...would you suggest a targeted approach on mathclub like subject by subject sets of 10 questions on the quizzes? I'd really appreciate your advice. Best wishes,

Tosin

For (1): if we substitute $$x+40=y$$ into $$\text{average}=\frac{12.2x+13.1y}{x+y}$$ we'd get $$\text{average}=\frac{25.3 x + 524}{2x+40}$$. Without knowing x or y, we cannot get the single numerical value of this expression, so cannot answer the question.

Check Study Plans for Novice and Advanced GMAT Takers.

For all other QUANT subjects:
ALL YOU NEED FOR QUANT ! ! !

Hope it helps.

Thanks bro
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Joined: 20 Apr 2018
Posts: 36
Location: United States (DC)
GPA: 3.84

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01 Jun 2018, 12:02
Hi Bunuel, great breakdown of statement 1. I completely understand why statement 1 is insufficient (ie x can be anything), but what I do not understand is why (25.3x+5242)/(2x+40) is not considered one variable, one equation situation. Can you please explain? Is it because average itself is considered an unknown?
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02 Jun 2018, 03:48
1
norovers wrote:
Hi Bunuel, great breakdown of statement 1. I completely understand why statement 1 is insufficient (ie x can be anything), but what I do not understand is why (25.3x+5242)/(2x+40) is not considered one variable, one equation situation. Can you please explain? Is it because average itself is considered an unknown?

Because it's NOT an equation. If it were (25.3x+5242)/(2x+40) = (some number), then yes, we'd be able to solve for x. For example, imagine that we want to find the value of x + 10. We have one variable x but we cannot find the value of x + 10 because for that we need the value of x. If it were x + 10 = 11, then we'd be able to find that x = 1.

Hope it helps.
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Re: M28-43 &nbs [#permalink] 02 Jun 2018, 03:48
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# M28-43

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