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# What is the ratio of the average (arithmetic mean) height of

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What is the ratio of the average (arithmetic mean) height of [#permalink]

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05 Nov 2004, 18:38
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What is the ratio of the average (arithmetic mean) height of students in class X to the average height of students in class Y?

(1) The average height of the students in class X is 120 centimeters.
(2) The average height of the students in class X and class Y combined is 126 centimeters.
[Reveal] Spoiler: OA
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05 Nov 2004, 19:29
I picked C as well. But OA says it is E.
I guess OA is wrong for this one. I got this question from a china site,
and I believe it is an official GMAT question. But the answers might have
some mistakes.
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05 Nov 2004, 20:05
I also picked C.

Had choice (B) been rephrased to say that the average height of all the students in class X and Y is 126, the answer would be E because we wouldn't know how many people are in each class. But here it's phrased to indicate a 1 to 1 relationship, thus the answer should be C.
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07 Nov 2004, 12:57
it is E according to me.. lemme try and explain.

let x and y be the average height of the classes X and Y respectively.

from statement 1--- x=120, y not known, hence insufficient.

from statement 2---- x+y=126, which is insufficient too..

now combining both, we get
SINCE the AVERAGE height of Classes X and Y combines is 126, total height is 126*2= 252 right? (for eg, there are two numbers 2 and 4. their average is 3. so 3*2=6 which is the SUM of the two numbers).
now we CANNOT subtract 120 from 252, because 252 is NOT the average anymore, but the TOTAL HEIGHT. and 120 is the average. So they cannot be subtracted.

Hence, I go with E.
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07 Nov 2004, 14:25
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What is the ratio of the average (arithmetic mean) height of students in class X to the average height of students in class Y?
(1) The average height of the students in class X is 120 centimeters.

Let say total height of class x is k and total students is m so;

k/m=120 insufficient

(2) The average height of the students in class X and class Y combined is 126 centimeters.

Let say total height of class y is n and total students is r so;

(k+y)/(m+r) = 126

k/(m+r) + y/(m+r) = 126

if we combined 1 and 2 there is nothing

so I say e is the correct
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Re: DS - average height of students [#permalink]

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20 Oct 2010, 10:59
i also got c, can someone please shed more light on this q
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Re: DS - average height of students [#permalink]

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20 Oct 2010, 11:36
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djslobo wrote:
i also got c, can someone please shed more light on this q

What is the ratio of the average (arithmetic mean) height of students in class X to the average height of students in class Y?
(1) The average height of the students in class X is 120 centimeters.
(2) The average height of the students in class X and class Y combined is 126 centimeters.

Average height of students in class X: $$x_{average}=\frac{sum \ of \ the \ heights \ in \ X}{n}$$, where $$n$$ is the # of students in class X;

Average height of students in class Y: $$y_{average}=\frac{sum \ of \ the \ heights \ in \ Y}{m}$$, where $$m$$ is the # of students in class Y.

Question: $$\frac{x_{average}}{y_{average}}=?$$

Each statement alone is clearly insufficient.

From (1): $$x_{average}=120$$;
From (2): $$126=\frac{x_{average}*n+y_{average}*m}{n+m}$$;

Above information is not sufficient to calculate $$y_{average}$$, so we can not get the ratio. If you try different values for $$m$$ and $$n$$ you'll get different values of $$y_{average}$$

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Re: DS - average height of students [#permalink]

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20 Oct 2010, 13:22
Yup E.

1) and 2) Combined, you just don't know how the average of x and y are weighted.
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Re: DS - average height of students [#permalink]

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10 Nov 2010, 14:35
+1 E
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Re: DS - average height of students [#permalink]

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10 Nov 2010, 19:37
Expert's post
What is the ratio of the average (arithmetic mean) height of students in class X to the average height of students in class Y?
(1) The average height of the students in class X is 120 centimeters.
(2) The average height of the students in class X and class Y combined is 126 centimeters.

OA will follow. Thank you.

The question deals with weighted averages since the number of students in the two classes might be different. So you cannot say that 126 will be the average of 120 and 132. I suggest you to read up on weighted averages. That will make this question seem straightforward.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews GMAT Club Legend Joined: 09 Sep 2013 Posts: 9609 Followers: 465 Kudos [?]: 120 [0], given: 0 Re: What is the ratio of the average (arithmetic mean) height of [#permalink] ### Show Tags 08 Feb 2015, 21:30 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 6392 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 267 Kudos [?]: 1887 [1] , given: 161 Re: What is the ratio of the average (arithmetic mean) height of [#permalink] ### Show Tags 09 Feb 2015, 12:29 1 This post received KUDOS Expert's post Hi All, When a 'weighted average' question does NOT tell you the number of entities/items involved, you can TEST VALUES to prove if there's more than one possible way to get to that average. Here, we're asked for the ratio of the average height in Class X to the average height in Class Y. We are told NOTHING about the respective number of students in each class. Fact 1: The average height in Class X is 120cm. This tells us nothing about the average height in Class Y. Fact 1 is INSUFFICIENT Fact 2: The average height of all students in both Classes (combined) is 126cm. IF.... Each class has 2 students in it, the average heights could be.... Class X = 126cm Class Y = 126cm The answer to the question is 126:126 = 1:1 Class X = 125cm Class Y = 127cm The answer to the question is 125:127 Fact 2 is INSUFFICIENT Combined, we know.... The average height in Class X = 120cm The average height of both classes = 126cm We DON'T KNOW the number of students in each class though... IF... Each class has 2 students in it The average of Class X = 120cm The average of Class Y = 132cm The answer to the question is 120:132 IF.... Class X has 2 students and Class Y has just 1 student The average of Class X = 120cm The average of Class Y = 138cm The answer to the question is 120:138 Combined, INSUFFICIENT Final Answer: [Reveal] Spoiler: E GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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Re: What is the ratio of the average (arithmetic mean) height of [#permalink]

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21 Feb 2016, 19:40
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: What is the ratio of the average (arithmetic mean) height of   [#permalink] 21 Feb 2016, 19:40
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