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:

If r and s are positive integers, is r/s a terminating decimal?

1) r is a factor of 100 2) s is a factor of 500

Target question:Is r/s a terminating decimal?

Statement 1: r is a factor of 100 There are several pairs of values that meet this condition. Here are two: Case a: r = 1 and s = 4, in which case r/s = 1/4 = 0.25, which is a terminating decimal Case b: r = 1 and s = 3, in which case r/s = 1/3 = 0.333.., which is not a terminating decimal Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: s is a factor of 500 There's a nice rule that says something like, If the prime factorization of the denominator contains only 2's and/or 5's, then the decimal version of the fraction will be a terminating decimal. Since 500 = (2)(2)(5)(5)(5), any factor of 500 will contain only 2's and/or 5'2 (or the denominator can be 1, in which case the decimal will definitely terminate). Since the denominator of r/s must contain only 2's and/or 5's, r/s must be a terminating decimal Since we can answer the target question with certainty, statement 2 is SUFFICIENT

==> If you change the original condition and the problem, in order for r/s to be the terminating decimal, prime factors of s should be 2 or 5. In the case of 2), from 500=2^25^3, prime factors of 500 should always be either 2 or 5, hence yes, and sufficient. The answer is B. Answer: B
_________________

If r and s are positive integers, is r/s a terminating decimal? 1) r is a factor of 100 2) s is a factor of 500

When solving this problem, we should remember that there is a special property about fractions that allows their decimal equivalents to terminate. This property states:

In its most-reduced form, any fraction with a denominator whose prime factorization contains only 2s, only 5s, or both 2s and 5s, produces decimals that terminate. A denominator with any other prime factors produces decimals that do not terminate.

We must determine whether r/s is a terminating decimal, or in other words, whether s has only 2s, 5s, or both as prime factors.

Statement One Alone:

r is a factor of 100.

Since we do not have any information about s, statement one alone is not sufficient to answer the question.

Statement Two Alone:

s is a factor of 500.

Since 500 = 2^2 x 5^3 and s is a factor of 500, s will contain only 2s, 5s, or both as prime factors. If r/s is already in its most-reduced form, then r/s is a terminating decimal. If r/s is not in its most-reduced form, then the most-reduced form of r/s, say r’/s’, will also be a terminating decimal since s’ will then be a factor of s and it will contains only 2s, 5s or both as prime factors. Statement two alone is sufficient to answer the question.

Answer: B
_________________

Scott Woodbury-Stewart Founder and CEO

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions