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:

This came up in my review, my answer was incorrect.

If r and s are positive integers, is (r/s) an integer?

(1) Every factor of s is also a factor of r.

(2) Every prime factor of s is also a prime factor of r.

Can you provide rationale as well?

E - each statement is sufficient. here is my rational:

1 - if each factor of r is also a factor of s then when you break down the numbers into their factors you will cancel each other out and have an integer. actually this will probably yield to one. 2 - each number can be broken down to a set of prime factors. a number is either prime(divisible only by 1 and itself) or can be broken down into prime numbers. so the same thing here as with 1. all prime will cancel each other out and yield an integer.

(2) Every prime factor of s is also a prime factor of r.

2 is insufficient because consider s=4 r=10

prime factor of S is 2 prime factor of r is 5 and 2

so back to stat 2, every prime factor of S (which 2 is the only prime factor) is also a prime factor of R (which is 10) well 2 is prime factor of 10 as well

First statement sufficient as every factor of s is a factor of r as well so they cancel out to make an integer Remember we cannot take example of r=6 and s=4 as somebody has taken previously as there are two factors of two in 4 but only one factor of 2 in 6. Statement 2 insufficient e.g r=9 and s=6 and r=9 and s=3

I'm not a fan of this question. If, for example S = 12, its prime factorization is 2^2 * 3.

According to statement 2, EVERY prime factor of s (I took this to mean 2, 2, and 3 since it has two 2's, which are both prime factors). Basically I thought the trick was that you had to understand that for every integer, there is a prime factorization, and therefore the two statements were basically the same. I guess I misinterpreted (2), but still, how would you KNOW how to interpret that?

I'm not a fan of this question. If, for example S = 12, its prime factorization is 2^2 * 3.

According to statement 2, EVERY prime factor of s (I took this to mean 2, 2, and 3 since it has two 2's, which are both prime factors). Basically I thought the trick was that you had to understand that for every integer, there is a prime factorization, and therefore the two statements were basically the same. I guess I misinterpreted (2), but still, how would you KNOW how to interpret that?

What a worst coincidence! I did the same. I was looking for numbers that had the same prime factors. But I guess we are wrong.

Every prime factor of s is also a prime factor of r.

does not mean that every prime factor of s need not be a prime factor of r as many times in s. It can just be a subset of the numbers. as some said 4,8 good 4,6 not good