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If X is the average of Y numbers, what is Y?

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Bunuel
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If X is the average of Y numbers, what is Y? [#permalink] New post  28 Mar 2016, 02:48
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If X is the average of Y numbers, what is Y?

(1) X = 54.5

(2) The sum of the Y numbers for which X is the average is 2,616.
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Re: If X is the average of Y numbers, what is Y? [#permalink] New post  28 Mar 2016, 03:25
Bunuel wrote:
If X is the average of Y numbers, what is Y?

(1) X = 54.5

(2) The sum of the Y numbers for which X is the average is 2,616.


To solve for Y, we need the 'total sum of Y numbers' and the 'value of X'

Statement 1) We have X but the sum of Y numbers is not given - Not sufficient

Statement 2) Sum of Y numbers is given but X not given - Not sufficient

Both statements put together, we have X = 54.5, and Sum of Y numbers = 2616
Hence, Y = 2616/54.5. Therefore, both statements together are sufficient to solve this.

Answer C
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Re: If X is the average of Y numbers, what is Y? [#permalink] New post  28 Mar 2016, 03:29
Average of Y numbers , X= Sum of Y numbers/ Y

(1) X = 54.5
We have no information about Y
Not sufficient

(2) The sum of the Y numbers for which X is the average is 2,616
Not sufficient
Combining 1 and 2 , we get
54.5 = 2616/Y
Now we can calculate the value of Y , although it is not necessary to calculate the exact value here .
=>Y = 48

Sufficient
Answer C
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Re: If X is the average of Y numbers, what is Y? [#permalink] New post  28 Mar 2016, 09:04
I thought of C as well, but then I realised that if I add e.g. 100 and -100 to the set, the average would not change but Y would. As there is no statement telling that the numbers have to be positive, E should be the right answer.

Please tell me if this approach is wrong!
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Re: If X is the average of Y numbers, what is Y? [#permalink] New post  28 Mar 2016, 19:04
JAYEM wrote:
I thought of C as well, but then I realised that if I add e.g. 100 and -100 to the set, the average would not change but Y would. As there is no statement telling that the numbers have to be positive, E should be the right answer.

Please tell me if this approach is wrong!


Consider this situation,

Set A {1,2,3} then the arithmetic mean of this set is \(6/3\), which is \(2\)

But if you add -100 and 100 to the set, it would look like this {-100,1,2,3,100} and then again the arithmetic mean changes to \((-100 + 1 + 2 + 3 + 100)/5\) -> \(6/5\)

So, if you add more members the average will change.

Hope it helps
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Re: If X is the average of Y numbers, what is Y? [#permalink] New post  03 Feb 2020, 01:09
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Re: If X is the average of Y numbers, what is Y? [#permalink]
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