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# Is X^2 - Y ^2 divisible by 8? x and y are even integers x +

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Is X^2 - Y ^2 divisible by 8? x and y are even integers x + [#permalink]  11 Sep 2008, 19:28
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Is X^2 - Y ^2 divisible by 8?

x and y are even integers
x + y is divisible by 8

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

My ans to this was B. if x+y = 8m , x^2-y^2 will always be divisible by 8, even if x and y are not integers..so stub 2 suffices IMO.
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Re: DS- DIVISIBILITY [#permalink]  11 Sep 2008, 19:41
kaushikb wrote:
Is X^2 - Y ^2 divisible by 8?

x and y are even integers
x + y is divisible by 8

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

My ans to this was B. if x+y = 8m , x^2-y^2 will always be divisible by 8, even if x and y are not integers..so stub 2 suffices IMO.

thats not true

x^2-y^2 = (x-y)(x+y)

if x and y are not integers.
x=4.6 y=3.4
x+y=8
x-y= 1.2

x^2-y^2 = 1.2 *8 is this divisable by 8? No
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Re: DS- DIVISIBILITY [#permalink]  11 Sep 2008, 19:43
kaushikb wrote:
Is X^2 - Y ^2 divisible by 8?

x and y are even integers
x + y is divisible by 8

My ans to this was B. if x+y = 8m , x^2-y^2 will always be divisible by 8, even if x and y are not integers..so stub 2 suffices IMO.

any example?

lets say x = 6.75 and y = 1.25
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Re: DS- DIVISIBILITY [#permalink]  11 Sep 2008, 19:47
I choose B. But is should be C.

X^2-Y^2=(X+Y)(X-Y)

1 ) x and y even => (X+Y) and (x-y) both even => so (X+Y)(X-Y) will be divisible by 4, but not sure abt 8

2 ) x + y is divisible by 8 => sufficient

= >>> I did not consider the non integer part.. Grrrrrrrrr.. ya it should be C ( as it says x and y are even integers )
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Re: DS- DIVISIBILITY [#permalink]  12 Sep 2008, 03:40
ssandeepan wrote:
I choose B. But is should be C.

X^2-Y^2=(X+Y)(X-Y)

1 ) x and y even => (X+Y) and (x-y) both even => so (X+Y)(X-Y) will be divisible by 4, but not sure abt 8

2 ) x + y is divisible by 8 => sufficient

= >>> I did not consider the non integer part.. Grrrrrrrrr.. ya it should be C ( as it says x and y are even integers )

Same here.....chose B in a hurry without realizing that x and / or y could be non-integers.
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Re: DS- DIVISIBILITY [#permalink]  12 Sep 2008, 05:54
Whenever you talk about divisibility you are implicitly talking about integers. To ask if x^2-y^2 is divisible by 8 in my opinion implies that x^2-y^2 is an integer. Divisibility has no meaning outside the set of integers.

For instance the question is 10 divisible by 2.5 in my opinion is not a meaningful question since divisibility has no meaning outside of the integers. You might as well be asking is an apple divisible by an orange.

Since the question has no meaning you cannot determine if it is true of false. What is the source of the question?
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Re: DS- DIVISIBILITY [#permalink]  12 Sep 2008, 10:09
What's the source of the question? And what's the OA
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Re: DS- DIVISIBILITY [#permalink]  12 Sep 2008, 19:24
Answer B. If it said X^2 + Y^2 divisible by 8 then the answer would be C, because they would both have to be even, and their sum, divisible by 8. But it says X^2 - Y^2, so all we need is their sum divisible by 8 to tell us their sum is an integer.

X and Y are even integers, not enough. (statement 2 also lets us know they are integers)

X+Y is divisible by 8.
take 16, X=3, Y=13. X^2 - Y^2=160. divisible by 8
24 X=3, Y=21. X^2 - Y^2=432. divisible by 8

Try it with X^2 + Y^2 there you will need both numbers to be even.
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Re: DS- DIVISIBILITY   [#permalink] 12 Sep 2008, 19:24
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