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M28-43

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M28-43  [#permalink]

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New post 16 Sep 2014, 01:31
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  45% (medium)

Question Stats:

56% (01:07) correct 44% (00:45) wrong based on 32 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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Re M28-43  [#permalink]

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New post 16 Sep 2014, 01:31
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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.


Answer: B
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Re: M28-43  [#permalink]

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New post 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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Re: M28-43  [#permalink]

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New post 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.

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Re: M28-43  [#permalink]

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New post 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 ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.


Thanks bro
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Re: M28-43  [#permalink]

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New post 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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Re: M28-43  [#permalink]

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New post 02 Jun 2018, 03:48
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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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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