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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 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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New post 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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New post 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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New post 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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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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New post 20 Oct 2010, 10:59
i also got c, can someone please shed more light on this q
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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]

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

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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


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

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New post 21 Jan 2017, 08:25
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)

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

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New post 17 Aug 2017, 02:46
Class X. let total student x
Class Y let total student y

1) average ht of Class X =120 cms
as no info of x,y as well as avg ht of class Y AD gone Insufficient

2) Average ht combined of Class X and Y is 126
Now x and y are unknown , if they were known soln was possible but in this case B is gone

Combine

differential for Class X is 6cms on lesser side as avg ht both class is 126
but again we dont know x and y so we cant find out avg ht of Class y

Diff ht X x Nr of stud X = Diff ht Y x Nr student Y
6x= (Diff ht Y) * y. tooo manay unkowns C is gone

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

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New post 09 Oct 2017, 11:27
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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Re: What is the ratio of the average (arithmetic mean) height of   [#permalink] 09 Oct 2017, 11:27
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