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Is x^2 - y^2 divisible by 8? 1. x and y are even integers 2. [#permalink]
09 May 2009, 10:25

3

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00:00

A

B

C

D

E

Difficulty:

5% (low)

Question Stats:

27% (02:21) correct
72% (01:13) wrong based on 43 sessions

Is x^2 - y^2 divisible by 8?

1. x and y are even integers 2. 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

Re: divisible by 8? [#permalink]
09 May 2009, 11:51

ST1 - x and y are even....even integers are from 0,2,4,6....etc ST2 - x+y divisible by 8, suppose x+y=8 then x will be anything from 1 to 8 and same with y.

ST1 and 2 are also not possible, as per the above approach x may be 0,2,4,6 and y may be 0,2,4,6.

Re: divisible by 8? [#permalink]
09 May 2009, 15:29

icandy wrote:

Is x^2 - y^2 divisible by 8?

1. x and y are even integers 2. 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

1) x^2 - y^2

x-y *x+y

x=4 y=2 --> 2*6 --> not divisible by 8 x=6 y=2 --> 4*8 --> divisble by 8

not sufficient

2)

x + y is divisible by 8

here we are not sure whether x and y are integers or not.

say x=7.6and y=0.4 x+y=8 but x-y =7.2 8*7.2 is not disible by 8

not sufficient

combined

suffcient because x and y are integers,and x+y is divisible by 8

C
_________________

Your attitude determines your altitude Smiling wins more friends than frowning

Re: divisible by 8? [#permalink]
10 May 2009, 08:06

lamhe and typhoidx,

I guess I am not alone. But I tell you what we are not alone. This is a bit crooked and twisted. I realized why x2suresh is correct. Thanks X2

say x=7.6and y=0.4 x+y=8 but x-y =7.2 8*7.2 is not divisible by 8

When x2suresh is saying this, what he is alluding to is that yeah you will see 7.2 but what we are not realizing is that 7.2 itself is a fraction. 7 .2 is 72/10 and not just 7

Re: divisible by 8? [#permalink]
14 May 2009, 13:26

1

This post received KUDOS

icandy wrote:

Is x^2 - y^2 divisible by 8?

1. x and y are even integers 2. 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

Question:((x^2-y^2)/8 an integer)? Question:(((x-y)(x+y))/8 an integer)?

(1) x & y are even Insufficient

If we look at it from an even/odd perspective, even-even=even & even+even=even, and even*even=even, which ensures we have 2^2, but we need 3 2's in the prime factorizations to be sure. Here is a case that discards it.

x=2,y=0, (x-y)(x+y) = 2*2 which is NOT divisible by 8, so we have a NO answer. and of course 4 & 0, which gives us a YES answer.

YES & NO ==> Insufficient.

(2) x+y divisible by 8

Let's rewrite this to:

x+y = 8(\lambda), where \lambda is any integer. y = 8(\lambda) - x Substitute above equation into question, Question:(((x-(8(\lambda) - x))(x+(8(\lambda) - x)))/8 an integer)? Question:(((2x-8(\lambda))(8(\lambda)))/8 an integer)? Question:(((8(\lambda))(2x-8(\lambda)))/8 an integer)? Question:((\lambda)(2x-8(\lambda)) an integer)? Question:(2x-8(\lambda) an integer)? Question:(2x an integer)? Question:(x an integer)?

We don't know.

Insufficient.

(1&2) Sufficient, as if X & Y are even this implies they are both integers, sufficient.

Re: divisible by 8? [#permalink]
17 Aug 2009, 08:06

1

This post received KUDOS

x2suresh wrote:

icandy wrote:

Is x^2 - y^2 divisible by 8?

1. x and y are even integers 2. 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

1) x^2 - y^2

x-y *x+y

x=4 y=2 --> 2*6 --> not divisible by 8 x=6 y=2 --> 4*8 --> divisble by 8

not sufficient

2)

x + y is divisible by 8

here we are not sure whether x and y are integers or not.

say x=7.6and y=0.4 x+y=8 but x-y =7.2 8*7.2 is not disible by 8

not sufficient

combined

suffcient because x and y are integers,and x+y is divisible by 8

C

Hi

Agree with C, works for even negative integer choices

Re: divisible by 8? [#permalink]
05 Sep 2009, 19:00

2

This post received KUDOS

Expert's post

Is x^2 - y^2 divisible by 8?

1. x and y are even integers 2. x + y is divisible by 8

(1) not suff (just plug numbers) (2) if x+y divisible by 8 => x^2 - y^2=(x+y)(x-y) if one of the multiples is divisible product also divisible: true for integers, but we are not told that x and y are integers. Not sufficient.

(1)+(2) x and y integers. x+y divisible by 8. Hence (x+y)(x-y) is divisible by 8. Sufficient.

Re: divisible by 8? [#permalink]
05 Sep 2009, 20:23

Is x^2 - y^2 divisible by 8?

1. x and y are even integers 2. x + y is divisible by 8

hi... 1) if x is 8...y is 2 ans is 'no' and if x is 8 and y is 4 ans is yes .. so insufficient 2) x^2-y^2=(x+y)(x-y) .. and if (x+y) is divisible by 8 .... and it is not given they r integers , it is not sufficient... for eg... nos are 11.6 and 4.4 ...so (11.6+4.4)(11.6-4.4)=16(7.2)... now 16(7.2) is divisible by 8 but in decimals.. combining two sufficient..... C pl post original ans

Re: divisible by 8? [#permalink]
12 Nov 2009, 18:31

icandy wrote:

Is x^2 - y^2 divisible by 8?

1. x and y are even integers 2. 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

This question is tricky - most people will pick B because most of GMAT DS questions state that X, Y are integers. However, the correct answer should be C. X-Y might not be an integer and 1) will ensure that X-Y is an integer.

I would have totally picked B on the test given the time constraint on each problem. It also looks like such an easy question too!
_________________

Re: divisible by 8? [#permalink]
02 Sep 2010, 15:22

I x, y are even then (x+y) is even (x-y) is even and their product is even . not sufficient

II. x+y div by 8 means that I can write x=8a y =8b so x+y =8a+8b=8(a+b) that is div by 8. (x-y)=8a-8b=8(a-b) that is div by 8. (x+y)(x-y)=8(a+b)8(a-b) this is div by 8 so the answer is b