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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Prime saturated ##### This topic has 3 expert replies and 0 member replies ## Prime saturated 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. ### GMAT/MBA Expert GMAT Instructor Joined 02 Apr 2010 Posted: 3835 messages Followed by: 523 members Upvotes: 1854 GMAT Score: 770 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. _________________ 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/ Last edited by Anurag@Gurome on Mon Feb 18, 2013 9:47 pm; edited 1 time in total ### GMAT/MBA Expert MBA Admissions Consultant Joined 11 Nov 2011 Posted: 2278 messages Followed by: 266 members Upvotes: 660 GMAT Score: 770 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.
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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.

_________________

Jeffrey Miller
Head of GMAT Instruction
jeff@targettestprep.com

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