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Is x^2-y^2 divisible by 8

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Is x^2-y^2 divisible by 8

by Mormuse » Tue Mar 12, 2013 1:11 pm
Hi guys, i have a problem. I don't understand the solution proposed on gmat club for the DS problem i mentioned in the subject.
1) x & y are even
2) x+y is divisible by 8.
One is insufficient, but to me 2) is sufficient since x^2-y^2=(x-y)(x+y) and x+y is divisible by 8. However, the correction says that 2) is not S because if x=7.75 and y=0.25 then the answer is no while the answer is yes if both x and y are integers...
I don't get it, it should still be divisible by 8 as long as x+y is equal to 8 no?
Can you please help me?
Thanks a lot!
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by Brent@GMATPrepNow » Tue Mar 12, 2013 1:28 pm
claudayst wrote:Is x^2-y^2 divisible by 8?
1) x & y are even
2) x+y is divisible by 8.
If we allow x and y to be non-integers, the correct answer is C

Target question: Is x^2 - y^2 divisible by 8?

Since we can factor x^2 - y^2 to get (x+y)(x-y), we can rephrase the target question . . .
Rephrased target question: Is (x+y)(x-y) divisible by 8?

Statement 1: x & y are even
There are several pairs of values that meet this condition. Here are two:
Case a: x=6 and y=2, in which case (x+y)(x-y) is divisible by 8
Case b: x=4 and y=2, in which case (x+y)(x-y) is not divisible by 8
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 1: x+y is divisible by 8.
There are several pairs of values that meet this condition. Here are two:
Case a: x = 6 and y = 2, in which case (x+y)(x-y) is divisible by 8
Case b: x = 7.1 and y = 0.9, in which case (x+y)(x-y) is not divisible by 8
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
Statement 1 tells us that x and y are both integers, which means x-y equals some integer
Statement 2 tells us that (x+y) is divisible by 8. In other words (x+y) equals some multiple of 8
So, (x+y)(x-y) = (some multiple of 8)(some integer)
From this, we can be certain that (x+y)(x-y) is divisible by 8
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

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Brent
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Please ignore!

by TG_GMAT » Wed Mar 13, 2013 8:43 am
Hi, How does statement 1 tell us that x and y are integers?
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by Brent@GMATPrepNow » Wed Mar 13, 2013 8:53 am
TG_GMAT wrote:Hi, How does statement 1 tell us that x and y are integers?
The concepts of "even" and "odd" are restricted to integers.

Having said that, the original question could use some editing to avoid any possible ambiguity.

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by vishugogo » Thu Mar 14, 2013 4:25 am
Brent I am not able to understand why in statement 2 case B

the values take are not divisible by 8 even though x+y=8
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by Brent@GMATPrepNow » Thu Mar 14, 2013 6:59 am
vishugogo wrote:Brent I am not able to understand why in statement 2 case B

the values take are not divisible by 8 even though x+y=8
For a number N to be divisible by 8, it must be the case that we can express N such that N = 8k, where k is an integer.
For example, 24 is divisible by 8 because we can rewrite 24 as follows: 24 = 8(3), where 3 is an integer.
Similarly, -80 is divisible by 8 because we can rewrite -80 as follows: -80 = 8(-10), where -10 is an integer.

In my example, we have x = 7.1 and y = 0.9, in which case (x+y)(x-y) = (7.1 + 0.9)(7.1 - 0.9) = (8)(6.2) = 49.6
We know that 49.6 is not divisible by 8, because we cannot express it such that 49.6 = 8k, where k is an integer.

I hope that helps.

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