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Percentage

by rutto_hp » Tue Sep 14, 2010 11:01 pm
Anyone please help me with this question in Data suff?
X equals to Y% of what number?
1) X=3Y
2) 6Y+2X=56X/14

As I understand, X equal Y% of what number (Z) mean X=Y% * Z (for example: 20=50%*40 and we have to find 40 as the result). I choose E but the answer is D with the explanation that from 1) or 2) we both know X=300%Y.

Another question:
M is a positive integer, is M odd?
1) 2M^3 + 2M is divisible by 8
2) M+10 is divisible by 10

I choose answer D because from 1) we have 2M(M^2+1) is divisible by 8 so M(M^2+1) is divisible by 4. If M is odd, M^2+1 then must be divisible by 4, but it is not. (2n+1)^2+1 is divisible by 2 only, not by 4. Anything wrong with my argument?
Last edited by rutto_hp on Tue Sep 14, 2010 11:18 pm, edited 1 time in total.
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by goyalsau » Tue Sep 14, 2010 11:15 pm
rutto_hp wrote:Anyone please help me with this question in Data suff?
X equals to Y% of what number?
1) X=3Y
2) 6Y+2X=56X/14

As I understand, X equal Y% of what number (Z) mean X=Y% * Z (for example: 20=50%*40 and we have to find 40 as the result). I choose E but the answer is D with the explanation that from 1) or 2) we both know X=300%Y.
Conceptual Question.
from 1 equation. x/y=3/1
so by this equation x =3, y=1 now the x is 1% of 300.

2 equation is all the same.
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by Rahul@gurome » Tue Sep 14, 2010 11:22 pm
Let X = Y% of a
Or X/Y = a/100.
Consider first (1) alone.
It means X/Y = 3.
Or 3 = a/100.
Or a = 300.
So (1) alone is sufficient.
Next consider (2) alone.
It means 6Y = 4X - 2X = 2X.
Or 6Y = 2X.
X = 3Y. This is same as statement (1).
So (2) alone is also sufficient.

The correct answer is hence (D).
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by Rahul@gurome » Tue Sep 14, 2010 11:50 pm
M is a positive integer, is M odd?
1) 2M^3 + 2M is divisible by 8
2) M+10 is divisible by 10
Consider first (1) alone.
It means 2M(M^2 + 1) is divisible by 8.
Or M(M^2 + 1) is divisible by 4.
Let M be even.
So let M = 2k, k being an integer.
Or M(M^2 + 1) = 2K(4k^2 + 1). This is divisible by 4 only if k is even.
So if M(M^2 + 1) is divisible by 8, it is possible that M is even.
This can be verified by taking M = 4.
Next let us check that if M is odd, will M(M^2 + 1) will be divisible by 4 or not.
If M is odd, we can write it as 2K + 1 where k is an integer.
So M(M^2 + 1) = (2k + 1)( 4k^2 + 4K + 1 +1) = (2k+1)(4K^2 + 4k + 2).
= 2(2k+1)(2k^2 + 2K + 1).
Now both (2k+1) and (2k^2 + 2k + 1) are odd.
So they are not divisible by 2.
Or 2(2k+1)(2k^2 + 2k + 1) is only divisible by 2 and not by 4.
Or for M(M^2 + 1) to be divisible by 4, M cannot be odd.
Or statement (1) alone is sufficient to answer the question.
Next consider (2) alone.
Since M + 10 is divisible by 10, M is divisible by 10.
So M has to be even.
Or M is not odd.
So (2) alone is also sufficient.

The correct answer is hence (D).
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