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:

(1) 728=2^3*7*13=p^3*s*t --> as all variables are prime numbers then p must be 2, and s and t either 7 and 13 or 13 and 7 respectively. In either of cases we can calculate p^3*s^3*t^3. Sufficient.

Bunuel's approach is very good, but let's apply a slightly different approach: 1) p^3st=728

st=728/(p^3) --> here we have to pay attention that the last digit of 728 is 8 which is contained only in the cyclicity of 2 and 8. Lets clarify it: the cyclicity of 1, 5, 6 are these numbers themselves (regardless of their power) the cyclicity of 2: 2, 4, 8, 6 the cyclicity of 3: 3, 9, 7, 1 the cyclicity of 4: 4, 6 the cyclicity of 7: 7, 9, 3, 1 the cyclicity of 8: 8, 4, 2, 6 the cyclicity of 9: 9, 1

Hence, 728 is divisible either by 2 or 8. 2^3 = 8 and 8^3 = 512

As you see, 728 is divisible only by 2^3 provided p is a positive prime number.

The result is 728/(2^3) = 91

s × t = 91 can be written as 1 × 91 or 13 × 7. As to the original question p^3 × s^3 × t^3 it does not matter whether we assume s × t is 1 × 91 or vice versa the same is true in case of 13 × 7.

both conditions s × t = 1 × 91 and s × t = 13 × 7 satisfy stmt 1) because 2^3 × 1 × 91 and 2^3 × 13 × 7 yield 728

Thus, we get the same result regardless whether p^3 × s^3 × t^3 is written as either 2^3 × 1^3 × 91^3 or 2^3 × 13^3 × 7^3

Re: If p, s, and t are positive prime numbers, what is the value [#permalink]
15 Oct 2013, 07:59

vaivish1723 wrote:

If p, s, and t are positive prime numbers, what is the value of p^3s^3t^3?

(1) (p^3)*s*t=728 (2) t=13

Just to touch on some key points on this problem. This problem is meant to test prime factorization.

So we need to break 728 into primes first. This will give us (2^3) (13) (7) which is enough to solve the question.

Keep in mind some properties of primes and prime factorization

- All prime numbers except 2 and 5 end in '1','3','7' or '9' - All prime numbers above 3 are of the form '6n+1' or '6n-1' - The first prime number is 2 which is also the only even prime - The Prime Numbers up to 100 are: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97) - The square of any prime number greater than 3 is 1 more than a multiple of 12 - Verifying the primality of a given number 'n' can be done by trial division, that is to say dividing 'n' by all integer numbers smaller than √n

Hope this helps for future questions Cheers!

J

gmatclubot

Re: If p, s, and t are positive prime numbers, what is the value
[#permalink]
15 Oct 2013, 07:59

Well, I’ve had a busy month! In February I traveled to interview and visit three MBA programs. Earlier in the month I also went to Florida on vacation. This...

One of the reasons why I even considered Tepper is the location. Last summer I stopped in Pittsburgh on the way home from a road trip. We were vacationing...

The most time-consuming part of writing the essays comes before and after the act of writing. Jotting down an answer to the questions should take a few hours at most. By then you...