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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] New post 05 Nov 2004, 17:38
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A
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C
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67% (01:50) correct 32% (00:46) wrong based on 52 sessions
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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 [#permalink] New post 05 Nov 2004, 18:29
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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 [#permalink] New post 05 Nov 2004, 19:05
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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 [#permalink] New post 07 Nov 2004, 11:57
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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 [#permalink] New post 07 Nov 2004, 13:25
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] New post 20 Oct 2010, 09:59
i also got c, can someone please shed more light on this q
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Re: DS - average height of students [#permalink] New post 20 Oct 2010, 10:36
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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}

Answer: E.
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Re: DS - average height of students [#permalink] New post 20 Oct 2010, 12:22
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] New post 10 Nov 2010, 13:35
+1 E 8-)
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Re: DS - average height of students [#permalink] New post 10 Nov 2010, 18:37
Expert's post
LADodgers wrote:
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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Re: DS - average height of students   [#permalink] 10 Nov 2010, 18:37
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