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Intern  Joined: 12 Aug 2004
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What is the ratio of the average (arithmetic mean) height of  [#permalink]

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Question Stats: 67% (01:21) correct 33% (01:11) wrong based on 2015 sessions

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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.
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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.

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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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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Intern  Joined: 02 Nov 2004
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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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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

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

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

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

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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]

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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.

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.

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

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When we apply the weigthed average formula after combining St 1 and 2 we get an equation with 3 variables.

Clearly the information is not sufficient to find the required ratio. Correct Ans is OptionE
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What is the ratio of the average (arithmetic mean) height of  [#permalink]

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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.

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 = [S/N+s/n]/2 = [nS+Ns]/(2xnxN) .......eq(2)
In order for 'A' to be equal to 'a' , N=n, [for which A=a=(S+s)/2n OR (S+s)/2N]
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) .
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Re: What is the ratio of the average (arithmetic mean) height of  [#permalink]

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Can answer be the Option C if it is Mention in the Question stem that number of students in both the class is Equal??
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Re: What is the ratio of the average (arithmetic mean) height of  [#permalink]

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Anshu0012 wrote:
Can answer be the Option C if it is Mention in the Question stem that number of students in both the class is Equal??

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.

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_________________ Re: What is the ratio of the average (arithmetic mean) height of   [#permalink] 03 Aug 2020, 20:27

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