If K is a positive integer, how many different prime numbers

Oldest

Best Reply

Author

Message

TAGS:

Director

Joined: 25 Aug 2007

Posts: 959

WE 1: 3.5 yrs IT

WE 2: 2.5 yrs Retail chain

Followers: 38

Kudos [?]: 555 [0], given: 40

If K is a positive integer, how many different prime numbers [#permalink]

10 Jun 2010, 01:33

00:00

Question Stats:

30% (03:03) correct

70% (01:45) wrong

based on 8 sessions

If K is a positive integer, how many different prime numbers are factors of the expression K^2?

1) Three different prime numbers are factors of 4K^4.
2) Three different prime numbers are factors of 4K.
_________________

Want to improve your CR: cr-methods-an-approach-to-find-the-best-answers-93146.html
Tricky Quant problems: 50-tricky-questions-92834.html
Important Grammer Fundamentals: key-fundamentals-of-grammer-our-crucial-learnings-on-sc-93659.html

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11522

Followers: 1795

Kudos [?]: 9551 [2] , given: 826

Re: Different prime factors - DS [#permalink]

10 Jun 2010, 04:40

This post received
KUDOS

ykaiim wrote:

First of all k^x (where x is an integer \geq{1}) will have as many different prime factors as integer k. Exponentiation doesn't "produce" primes.

Next: p^y*k^x (where p is a prime and y is an integer \geq{1}) will have as many different prime factors as integer k if k already has p as a factor OR one more factor than kif k doesn't have p as a factor .

So, the question basically is: how many different prime numbers are factors of k?

(1) Three different prime numbers are factors of 4k^4 --> if k itself has 2 as a factor (eg 30) than it's total # of primes is 3 but if k doesn't have 2 as a factor (eg 15) than it's total # of primes is 2. Not sufficient.

(2) Three different prime numbers are factors of 4k --> the same as above: if k itself has 2 as a factor (eg 30) than it's total # of primes is 3 but if k doesn't have 2 as a factor (eg 15) than it's total # of primes is 2. Not sufficient.

(1)+(2) Nothing new, k can be 30 (or any other number with 3 different primes, out of which one factor is 2) than the answer is 3 or k can be 15 (or any other number with 2 different primes, out of which no factor is 2) than the answer is 2. Not sufficient.

Answer: E.
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!

What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates

Senior Manager

Status: Yeah well whatever.

Joined: 18 Sep 2009

Posts: 351

Location: United States

GMAT 1: 660 Q42 V39
GMAT 2: 730 Q48 V42

GPA: 3.49

WE: Analyst (Insurance)

Followers: 4

Kudos [?]: 40 [0], given: 17

Re: Different prime factors - DS [#permalink]

10 Jun 2010, 16:53

Dang, Bunnuel. I'm about to just study your explanations for the quant section of the GMAT. lol What was your undergrad degree in? GMAT math? I'm jk. Thanks for your help
_________________

He that is in me > he that is in the world. - source 1 John 4:4

Senior Manager

Joined: 13 Aug 2012

Posts: 468

Followers: 12

Kudos [?]: 75 [1] , given: 11

Re: If K is a positive integer, how many different prime numbers [#permalink]

21 Jan 2013, 22:40

This post received
KUDOS

ykaiim wrote:

I notice that stopping to analyze the question first before going straight to the statements make it easier to solve this DS questions.
The question is looking for the number of distinct prime numbers of K. Whether it be K^4, K^100 or K^9, the number of distinct prime numbers would be the same with just K.

Statement 1: 3 prime number factors for 4K^4. Well there are two possibilites:
(a) either K has "2" and 2 other prime numbers (e.g. 2, 3 and 7; 2, 5 and 11) OR
(b) K just have two prime numbers and no "2" (e.g. 5 and 7)

Thus, we know K could have 2 or 3 distinch prime number factors. INSUFFICIENT.

Statement 2: Once you get used to it, you will notice Statement (2) is just the same as Statement (1).. It throws in "2" outside the K making it blurry whether "2" is within K or not. Thus, INSUFFICIENT.

If Statement (1) and Statement (2) are just similar givens. Then together, they are INSUFFICIENT.

Answer: E

Re: If K is a positive integer, how many different prime numbers [#permalink] 21 Jan 2013, 22:40

		Similar topics	Author	Replies	Last post
Similar Topics:		X is prime and y is positive integer, How many different	gamjatang	13	11 Dec 2005, 06:36
		How many different prime numbers are factors of the positive	gmacvik	4	22 Oct 2006, 23:37
	5	If k is a positive integer, is k a prime number?	bhandariavi	12	19 Jun 2010, 11:37
	2	How many different prime numbers are factors of the positive	xyzgmat	11	08 Oct 2010, 17:50
	10	How many different prime numbers are factors of the positive	enigma123	11	29 Jan 2012, 18:31

If K is a positive integer, how many different prime numbers

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

If K is a positive integer, how many different prime numbers

If K is a positive integer, how many different prime numbers

Main navigation

GMAT Resources

Partners

MBA Resources