Prime saturated

Expert replies

sana.noor: Legendary Member; Posts: 512; Joined: Mon Jun 18, 2012 11:31 pmFollowed by: 20 members; Thanked: 42 times

by sana.noor » Mon Feb 18, 2013 1:34 am

An integer n that is greater than 1 is said to be "prime saturated" if it has no prime factor greater than or equal to square root of n. which of the following integers is prime-saturated?
6
35
46
66
75

Work hard in Silence, Let Success make the noise.

If you found my Post really helpful, then don't forget to click the Thank/follow me button.

Like this post

Source: Beat The GMAT — Problem Solving | Mon Feb 18, 2013 1:34 am

GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Feb 18, 2013 2:37 am

sana.noor wrote:An integer n that is greater than 1 is said to be "prime saturated" if it has no prime factor greater than or equal to square root of n. which of the following integers is prime-saturated?

In other words, n will be prime saturated if the square of largest prime factor of n is smaller than n. Let's check the options one by one...

A. 6 = 2*3 ---> 3Â² > 6 ---> NO
B. 35 = 5*7 ---> 7Â² > 35 ---> NO
C. 46 = 2*23 ---> 23Â² > 46 ---> NO
D. 66 = 2*3*11 ---> 11Â² > 66 ---> NO
E. 75 = 3*5*5 ---> 5Â² < 75 ---> YES

The correct answer is E.

Last edited by Anurag@Gurome on Mon Feb 18, 2013 9:47 pm, edited 1 time in total.

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/

Like this post

Jim@StratusPrep: MBA Admissions Consultant; Posts: 2279; Joined: Fri Nov 11, 2011 7:51 amFollowed by: 266 members; Location: New York; Thanked: 660 times; GMAT Score:770

by Jim@StratusPrep » Mon Feb 18, 2013 11:33 am

Just to clarify C

46 = 2 * 23

GMAT Answers provides a world class adaptive learning platform.
-- Push button course navigation to simplify planning
-- Daily assignments to fit your exam timeline
-- Organized review that is tailored based on your abiility
-- 1,000s of unique GMAT questions
-- 100s of handwritten 'digital flip books' for OG questions
-- 100% Free Trial and less than $20 per month after.
-- Free GMAT Quantitative Review

Like this post

Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Dec 11, 2017 7:57 am

sana.noor wrote:An integer n that is greater than 1 is said to be "prime saturated" if it has no prime factor greater than or equal to square root of n. which of the following integers is prime-saturated?
6
35
46
66
75

We will find the largest prime factor of each answer choice. If the largest prime factor of the number is greater than the square root of the number, then the number is NOT prime saturated, since by definition no prime factor of the number is greater than or equal to its square root.

Furthermore, instead of comparing the largest prime factor and the square root of the number, we will compare the square of the largest prime factor and square of the square root of the number, i.e., the number itself. That is because if two numbers, x and y, are positive, âˆšx > âˆšy implies x > y.

A) 6

The largest prime factor of 6 is 3. Since 3^2 = 9 is greater than (âˆš6)^2 = 6, 6 is NOT prime saturated.

B) 35

The largest prime factor of 35 is 7. Since 7^2 = 49 is greater than (âˆš35)^2 = 35, 35 is NOT prime saturated.

C) 46

The largest prime factor of 46 is 23. Since 23^2 is greater than (âˆš46)^2 = 46, 46 is NOT prime saturated.

D) 66

The largest prime factor of 66 is 11. Since 11^2 = 121 is greater than (âˆš66)^2 = 66, 66 is NOT prime saturated.

E) 75

The largest prime factor of 75 is 5. Since 5^2 = 25 is NOT greater than (âˆš75)^2 = 75, 75 IS prime saturated.

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review