Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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.

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

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

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.

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

(1) \(x\) and \(y\) are even integers. Clearly insufficient, consider \(x=y=0\) for an YES answer and \(x=2\) and \(y=0\) for a NO answer.

(2) \(x + y\) is divisible by \(8\) --> \(x^2 - y^2=(x+y)(x-y)\), if one of the multiples is divisible by 8 then so is the product: true for integers, but we are not told that \(x\) and \(y\) are integers. If \(x=4.8\) and \(y=3.2\), \(x+y\) is divisible by \(8\), BUT \(x^2 - y^2\) is not. Not sufficient.

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

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
_________________

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!
_________________

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

Re: Is x^2 - y^2 divisible by 8? 1. x and y are even integers 2. [#permalink]

Show Tags

09 Jun 2014, 01:06

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

(1) \(x\) and \(y\) are even integers. Clearly insufficient, consider \(x=y=0\) for an YES answer and \(x=2\) and \(y=0\) for a NO answer.

(2) \(x + y\) is divisible by \(8\) --> \(x^2 - y^2=(x+y)(x-y)\), if one of the multiples is divisible by 8 then so is the product: true for integers, but we are not told that \(x\) and \(y\) are integers. If \(x=4.8\) and \(y=3.2\), \(x+y\) is divisible by \(8\), BUT \(x^2 - y^2\) is not. Not sufficient.

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

Answer: C.

I don't know, I think I'm missing something here. If x=4.8 and y=3.2, Still the product would be divisible by 8 IMO. (x+y)(x-y)/8 (4.8+3.2)(4.8-3.2)/8 8(1.6)/8 =1.6 What am I doing wrong here?

gmatclubot

Re: divisible by 8?
[#permalink]
15 Jun 2014, 11:31

Best Schools for Young MBA Applicants Deciding when to start applying to business school can be a challenge. Salary increases dramatically after an MBA, but schools tend to prefer...

Marty Cagan is founding partner of the Silicon Valley Product Group, a consulting firm that helps companies with their product strategy. Prior to that he held product roles at...