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

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05 Nov 2004, 17:38

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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.

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.

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.

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.

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;

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 \(y_{average}\)

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.
_________________

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

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

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21 Jan 2017, 07:25

Hello All,

The Answer for me is E.

S-1) Insufficient as Avg X is given. No details for Y S-2) Insufficient as Avg (X+Y) = 126 S-T) Insufficient. Consider a example with numbers. If X = {10,20,30,40 } Avg X= 25. Avg of Y = {25,50,75,90} = Avg Y = 60. But Avg (X+Y) = {10,20,30,40,25,50,75,90} = 340/8 = 42.50. So in general, I understand Avg X + Avg Y <> Avg (X+Y)

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

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09 Oct 2017, 10:27

St 1. Average height of students in Class X is 120 cms, Info on Class Y is not given. Hence, Insufficient. St 2. Avg height of students in class X and Y combined is 126 cms. Now number of Class X students and Class Y students are not known, therefore cannot determine the target info. Hence, insufficient.

St 1 + 2: No new information is added, number of students in class X and Y are still unknown, therefore "E".

Hope this helps.
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