IMO answer should be (D).
Can you please recheck your OA. Explanation after confirmation.
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CATPREP3 - DS - ODD/EVEN
Source: Beat The GMAT — Data Sufficiency |
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codesnooker
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Notice that x^2 - y^2 = (x + y)(x - y). This is a commonly known formula, so I advise you to remember it.
1. x + y is odd helps partially, but it's not enough. You get that x^2 - y^2 = (odd number)*(unknown number). Since x - y can be either odd or even (and depending on that x^2 - y^2 will be odd or even), 1 is insufficient
2. again, you only have part of the picture: x^2 - y^2 = (unknown number)*(odd number). Using the same line of thought as above, 2 is insufficient.
But put both stmts together and get that x^2 - y^2 = (odd number)*(odd number), which will always be odd. This is why the answer is C[/spoiler]
1. x + y is odd helps partially, but it's not enough. You get that x^2 - y^2 = (odd number)*(unknown number). Since x - y can be either odd or even (and depending on that x^2 - y^2 will be odd or even), 1 is insufficient
2. again, you only have part of the picture: x^2 - y^2 = (unknown number)*(odd number). Using the same line of thought as above, 2 is insufficient.
But put both stmts together and get that x^2 - y^2 = (odd number)*(odd number), which will always be odd. This is why the answer is C[/spoiler]
Agree with Code on D) inspite of the OA supposedly being C
X^2-Y^2 = (X+Y) (X-Y)
Stmt I
x+y is odd
odd+even = odd
even+odd = odd
If x+y is odd x-y must also be odd therefore
X^2-Y^2 = (X+Y) (X-Y)
= odd*odd
= odd
Stmt II
Similar explanation to I
Choose D
Must be missing something if the OA is correct and turns out be C
X^2-Y^2 = (X+Y) (X-Y)
Stmt I
x+y is odd
odd+even = odd
even+odd = odd
If x+y is odd x-y must also be odd therefore
X^2-Y^2 = (X+Y) (X-Y)
= odd*odd
= odd
Stmt II
Similar explanation to I
Choose D
Must be missing something if the OA is correct and turns out be C
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codesnooker
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Okay lets look at this way....DanaJ wrote:Notice that x^2 - y^2 = (x + y)(x - y). This is a commonly known formula, so I advise you to remember it.
ODD-EVEN Rules
even + even = even
even + odd = odd
odd + even = odd
odd + odd = even
even - even = even
even - odd = odd
odd - even = odd
odd - odd = even
odd^2 = odd
even^2 = even
odd^2 - odd^2 = odd - odd = even
odd^2 - even^2 = odd - even = odd
even^2 - odd^2 = even - odd = odd
even^2 - even^2 = even - even = even
Now let's solve real question,
As per statement 1,
X + Y is ODD
that means following two rules are applicable:-
even + odd = odd OR
odd + even = odd
Now it means if X is ODD then Y must be EVEN or vice-versa.
So if X is ODD then Y must be EVEN.
i.e. ODD^2 - EVEN^2 = ODD - EVEN = ODD
or if Y is ODD then X must be EVEN.
i.e. EVEN^2 - ODD^2 = EVEN - ODD = ODD
So both cases results in ODD answer. Hence statement I should be alone sufficient.
Now let's take statement II,
X - Y = ODD
that means following two rules are applicable:-
even - odd = odd OR
odd - even = odd
Now it means if X is ODD then Y must be EVEN or vice-versa.
So if X is ODD then Y must be EVEN.
i.e. ODD^2 - EVEN^2 = ODD - EVEN = ODD
or if Y is ODD then X must be EVEN.
i.e. EVEN^2 - ODD^2 = EVEN - ODD = ODD
So both cases results in ODD answer. Hence statement II also should be alone sufficient.
Since both statements alone are suffice to deduce the result hence IMO OA should be (D) rather than (C).
Any thoughts....
The only technicality I did miss was x and y doesnt have to be integers
Stmt I
x=1.5 y=1.5
x+y-> odd and x^2-y^2 is even
x=7 y=2
x+y odd and x^2-y^2 is odd
INSUFF
Stmt II
x=4.5 y=1.5
x=7 y=2
INSUFF
Together:
odd*odd =odd
SUFF
Hence C
Nice one....
Regards,
CR
Stmt I
x=1.5 y=1.5
x+y-> odd and x^2-y^2 is even
x=7 y=2
x+y odd and x^2-y^2 is odd
INSUFF
Stmt II
x=4.5 y=1.5
x=7 y=2
INSUFF
Together:
odd*odd =odd
SUFF
Hence C
Nice one....
Regards,
CR
Last edited by cramya on Sat Mar 21, 2009 11:35 pm, edited 1 time in total.
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codesnooker
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Hmm.... thanks CR.cramya wrote:The only technicality I did miss was x and y doesnt have to be integers
