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 350,000 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:

Re: a, b, c, and d are positive integers. If (a + b) (c – d) = r [#permalink]
16 Jan 2013, 13:47

5

This post received KUDOS

Expert's post

sambam wrote:

a, b, c, and d are positive integers. If (a + b) (c – d) = r, where r is an integer, is √(c + d) an integer? (1) (a + b) (c + d) = r^2 (2) (a + b) = x^4 y^6 z^2, where x, y, and z are distinct prime numbers.

I'm happy to help with this.

Statement #1: (a + b) (c + d) = r^2 The prompt told us that (a + b) (c – d) = r. If we divide the statement #1 equation by the prompt equation, we get [(c + d)]/[(c - d)] = r, which is intriguing, but which doesn't, by itself, tell us anything about whether (c + d), the numerator, is a perfect square. This is insufficient.

Statement #2: (a + b) = x^4 y^6 z^2, where x, y, and z are distinct prime numbers This one definitively tells us that (a + b) is a perfect square, so we know a perfect square times (c - d) equals r, but we know nothing at all about (c + d). This one by itself, doesn't tell us anything. This is insufficient.

Now, consider the statements combined. Statement #1: (a + b) (c + d) = r^2 Statement #2: (a + b) = x^4 y^6 z^2, where x, y, and z are distinct prime numbers Now, we know that (a + b) is a perfect square, because it has even powers of all prime factors. We also know that r^2 is a perfect square, so it must also have even powers of all prime factors. This can only mean that (c + d) has even powers of all prime factors, and therefore must be a perfect square. Another way to say that --- we could re-arrange the statement #1 equation to (c + d) = [r^2]/[(a + b))], and we know this quotient is a positive integer. If the ratio of two squares is an integer, that integer must also be a perfect square. Either way, the combination of statements is now sufficient to give a definitive answer to the prompt. Answer = C

One thing that's a little unusual about this question --- with the information in both statements, we could answer the prompt question, but as it turned out, the equation given in the prompt was irrelevant. I don't know that this would happen on the GMAT.

Let me know if anyone reading this has any questions.

Re: a, b, c, and d are positive integers. If (a + b) (c – d) = r [#permalink]
06 Jan 2014, 23:18

3

This post received KUDOS

Expert's post

sambam wrote:

a, b, c, and d are positive integers. If (a + b) (c – d) = r, where r is an integer, is √(c + d) an integer?

(1) (a + b) (c + d) = r^2 (2) (a + b) = x^4 y^6 z^2, where x, y, and z are distinct prime numbers.

Thought I'd seen 'em all...then got stumped with this one! Give it a try.

All this question is trying to do is confuse you with a ton of variables. The concept being tested here is simple - the prime factors of a perfect square have even powers.

"is √(c + d) an integer?" is just another way of saying "is (c+d) a perfect square?"

(1) \((a + b) (c + d) = r^2\) \((a + b) (c + d) = (a + b)^2 * (c - d)^2\) \((c+d) = (a+b)(c - d)^2\) We know now that (c+d) is a product of (a+b) and a perfect square. If (a+b) is a perfect square too, then (c+d) is a perfect square. Else it is not. Not sufficient.

(2) (a + b) = x^4 y^6 z^2, where x, y, and z are distinct prime numbers. This tells us that (a+b) is a perfect square. Though alone it is not sufficient since it doesn't tell us anything about (c+d), together with statement 1, it is sufficient.

Re: a, b, c, and d are positive integers. If (a + b) (c – d) = r [#permalink]
02 Apr 2014, 14:43

Thanks Karishma, that was precise.

Do you agree with Mike in that it is unlikely that information given in the prompt of a DS question will not be used? Honestly I've never seen a question in which information is given and then not used. Haven't even seen a case such as this one in which it could be used for one of the statements only

Please advice should we worry about this Thanks! Cheers J

Re: a, b, c, and d are positive integers. If (a + b) (c – d) = r [#permalink]
02 Apr 2014, 20:53

Expert's post

jlgdr wrote:

Thanks Karishma, that was precise.

Do you agree with Mike in that it is unlikely that information given in the prompt of a DS question will not be used? Honestly I've never seen a question in which information is given and then not used. Haven't even seen a case such as this one in which it could be used for one of the statements only

Please advice should we worry about this Thanks! Cheers J

I agree that the question is not very well thought out. It has a lot of clutter as if the question maker had something else in mind but it didn't work out and he changed direction mid way. The prompt equation did not add value to analyzing even statement 1 alone though we figure that out after analyzing it using the prompt equation. It's still equivalent to knowing that r is an integer.

Though it is absolutely fine if the prompt info is useful only for one statement. e.g. often you are given in the prompt that xy is not 0 implying that neither x nor y is 0. x and/or y might be in the denominator in only one statement. It would be fine. _________________

Type of Visa: You will be applying for a Non-Immigrant F-1 (Student) US Visa. Applying for a Visa: Create an account on: https://cgifederal.secure.force.com/?language=Englishcountry=India Complete...