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

Question

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.

Bunuel · Accepted Answer

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 cannot get the ratio. If you try different values for  m  and  n  you'll get different values of  y_{average}

Answer: E.

EMPOWERgmatRichC · Answer

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:  E

GMAT assassins aren't born, they're made,
Rich

ruhi · Answer

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.

efebaba · Answer

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

KarishmaB · Answer

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.

ScottTargetTestPrep · Answer

We want to find the ratio of the average height of students in class X to the average height of students in class Y. If we know the average height of students in each class, then we can find the ratio.
 
Statement One Alone:
 
The average height of the students in class X is 120 centimeters.

Without knowing the average height of the students in class Y, we can’t determine the ratio of the average height of students in class X to the average height of students in class Y.
 
Statement one alone is not sufficient.

Statement Two Alone:
 
The average height of the students in class X and class Y combined is 126 centimeters.
 
Even knowing that the combined (overall) average of the two classes is 126 centimeters, without knowing the average height of the students in each class, we still can’t determine the ratio of the average height of students in class X to the average height of students in class Y.
 
Statement two alone is not sufficient. 
Statements One and Two Together:
 
Using statements one and two together, we can create a weighted average equation using the following:
 
a = the number of students in class X
 
120 = the average height of the students in class X
 
b = the number of students in class Y
 
y = the average height of the students in class y
 
126 = (120a + yb)/(a + b)
 
Now multiply both sides of the equation by (a + b) to get
 
126a + 126b = 120a + yb
 
6a + 126b = yb
 
(6a + 126b)/b = y
 
We need to determine the ratio of the average height of the students in class X to the average height of the students in class Y, or 120/y. Since we cannot determine a value for y, we cannot answer the question.
 
Answer: E

debtanuB · Answer

1st please clear your concept about mean from this example below-

Mean of 'N' elements of a set whose sum is 'S' = M = S/N
Mean of 'n' elements of another set whose sum is 's' = m = s/n

Now, average of all the elements 'N+n' would be, A = (S+s)/(N+n) ......eq(1)
Average of means of both the sets, a = (M+m)/2 =  /2 =  /(2xnxN) .......eq(2)
In order for 'A' to be equal to 'a' , N=n,  
Else, both 'A' & 'a' would have different value OR same value depending on values of 's' & 'S' => In order to solve this problem we need no. of students in class X as well as in class Y OR atleast whether they have same no. of students or not?

In this problem we are asked about eq(1) and not eq(2) ;
Those who opted for option (C) by solving the problem as =>(Xavg+Yavg)/2=126 are wrong as we don't know whether 'X' & 'Y' have equal no. of students/elements or not ;

Correct answer is option (E) .

Anshu0012 · Answer

Can answer be the Option C if it is Mention in the Question stem that number of students in both the class is Equal??

EMPOWERgmatRichC · Answer

Hi Anshu0012,

IF additional information was included in the prompt that stated that each class has the SAME number of students in it, then the correct answer would be C. However, that extra information would make this DS question a lot easier to answer - and DS questions are often written to test the 'thoroughness' of your thinking (in simple terms, can you recognize all of the possible situations that could exist based on the limited information that you are given?). On Test Day, with most DS questions, you have to be prepared to work through the various possibilities to PROVE what the correct answer is.
 
GMAT assassins aren't born, they're made,
Rich

Basshead · Answer

We can solve this problem by using weighted averages.

What is the ratio of the height of students in class X to the height of students in class Y?

(1) No information regarding the average height of the students in class Y -- clearly insufficient.

(2) The combined average height is 126. Clearly insufficient to derive the height of the students in class X and the height of the students in class Y.

(1&2) We know the average height combined is 126 centimeters and we know the average height of the students in class X is 120 centimeters. If both classes had the same number of students, the average height of students in class Y would be 132. However, we DON'T KNOW how many students are in each class. Class X could have more students and skew the average. INSUFFICIENT.

Answer is E.

GMATinsight · Answer

Answer: Option E

Video solution by  GMATinsight

https://www.youtube.com/watch?v=OTwAXbKFp3Q

avigutman · Answer

Video solution from Quant Reasoning starts at 0:26 Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=vS6Jqxp3Z9U

Anonymous · Answer

KarishmaB   Bunuel   avigutman   GMATCoachBen   chetan2u

I totally agree that each statement alone is insufficient but since  we're looking for average height of class X/average height of class Y (if I'm not mistaken)  then combining these statements we can calculate the fraction since in the second one we can plug in the value of average class X from the first statement and so we will find the average class Y, and as a result we will be able to calculate the fraction above.

Could you help me?

Thank you in advance!

KarishmaB · Answer

You are assuming that the number of students is the same in the two classes but that needn't be true. Say class X has 4 students and class Y has 6 students. Avg of class X is 120, total avg is 126 so avg of class Y will be 130. Now say class X has 7 students and class Y has 3 students. Avg of class X is 120, total avg is 126 so avg of class Y will be 140. (You can verify the calculations if you wish) The concept tested here is weighted averages and once you understand that, you can immediately see with 0 calculations that answer is (E). Check weighted averages here: https://www.youtube.com/watch?v=_GOAU7moZ2Q

Anonymous · Answer

Oh okey now I got it, I just thought it like a puzzle in which the frst part (numerator) is from statement (1) and the other (denominator) can be found from the second statement. Thanks  KarishmaB  !!

Bro102 · Answer

I do a comman thing that in statment 1 they just give us avg hight of class x and in quesiton we need X:Y so first is insufficient
 
In second they give hights combination X+Y=126 but here also we dont know what is the X and Y so Second is also insufficient
 
Now if we add them togather we have equation like 120+Y/2 = 126 BUT its also dont make any sense so it is also insufficient

ManifestDreamMBA · Answer

Ratio of the average (arithmetic mean) height of students in class X to the average height of students in class Y?
We need average (arithmetic mean) height of students in class X and the average height of students in class Y or some relation to help identify this ratio.

S1
The average height of the students in class X is 120 centimeters.
No info on the average height of students in class Y
Insufficient

S2
The average height of the students in class X and class Y combined is 126 centimeters.
No info on the weights/ratio of students in class X and class Y
Insufficient

Combined, we still have no info on the weights/ratio of students in class X and class Y to calculate the average height of students in class Y. Insufficient

Answer E

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

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