Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 20 Jul 2019, 04:48 ### GMAT Club Daily Prep

#### 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

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

Author Message
TAGS:

### Hide Tags

Director  Joined: 25 Aug 2007
Posts: 714
WE 1: 3.5 yrs IT
WE 2: 2.5 yrs Retail chain
If K is a positive integer, how many different prime numbers  [#permalink]

### Show Tags

5
34 00:00

Difficulty:   55% (hard)

Question Stats: 55% (01:34) correct 45% (01:32) wrong based on 723 sessions

### HideShow timer Statistics 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.

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 56303
Re: Different prime factors - DS  [#permalink]

### Show Tags

14
18
ykaiim wrote:
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.

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 $$k$$if $$k$$ 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.

_________________
##### General Discussion
Senior Manager  Status: Yeah well whatever.
Joined: 18 Sep 2009
Posts: 303
Location: United States
GMAT 1: 660 Q42 V39 GMAT 2: 730 Q48 V42 GPA: 3.49
WE: Analyst (Insurance)
Re: Different prime factors - DS  [#permalink]

### Show Tags

1
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: 415
Concentration: Marketing, Finance
GPA: 3.23
Re: If K is a positive integer, how many different prime numbers  [#permalink]

### Show Tags

3
1
ykaiim wrote:
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.

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.

_________________
Impossible is nothing to God.
Manager  Joined: 20 Dec 2013
Posts: 118
Re: If K is a positive integer, how many different prime numbers  [#permalink]

### Show Tags

ykaiim wrote:
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.

Combining is insufficient:

If k = 4 then there is only one prime number in 4K or 4K^2
If k = 5 then there are two prime numbers in 4K or 4K^2
_________________
76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views

Perfect Scores
http://perfectscores.org
Manager  B
Joined: 27 Aug 2014
Posts: 71
Re: If K is a positive integer, how many different prime numbers  [#permalink]

### Show Tags

Bunuel wrote:
ykaiim wrote:
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.

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 $$k$$if $$k$$ 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.

Another method that worked for me was to find integer K-if we find K we can find its factors.
Both statements have 4 as a multiplier which is not divisible by any of the prime factors on the LHS. Hence K cannot be found as an integer so E. Bunuel, does this logic make sense? Please enlighten!
Manager  B
Joined: 16 Jan 2017
Posts: 60
GMAT 1: 620 Q46 V29 Re: If K is a positive integer, how many different prime numbers  [#permalink]

### Show Tags

Tricky question. But it is E as there is no way to know whether 2 was a factor in K or not. Neither solution alone gives a direct hint to this, and together it can't be solved either.
Senior Manager  G
Joined: 06 Jul 2016
Posts: 360
Location: Singapore
Concentration: Strategy, Finance
Re: If K is a positive integer, how many different prime numbers  [#permalink]

### Show Tags

ykaiim wrote:
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.

K>0
K will have the same number of prime factors as $$K^2$$
So the question is asking for the number of prime factors of K.

1) 4$$K^4$$ = $$P^a$$*$$Q^b$$*$$R^c$$
If K = 15, then 4$$K^4$$ has 3 factors i.e. 2,3,5 and K has 2 factors i.e. 3 and 5.
If K = 30, then 4$$K^4$$ has 3 factors i.e. 2,3,5 BUT K has 3 factors i.e. 2,3 and 5.
Insufficient.

2) 4K= $$P^a$$*$$Q^b$$*$$R^c$$
Same values of K can be used as above. Insufficient.

1+2) Both statements provide the same information. Insufficient.

_________________
Put in the work, and that dream score is yours!
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6968
Location: United States (CA)
Re: If K is a positive integer, how many different prime numbers  [#permalink]

### Show Tags

ykaiim wrote:
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.

We need to determine the number of different prime factors in K^2. We must remember that the number of distinct prime factors of K^n for any positive integer n is same as the number of distinct prime factors of K. Thus, K^2 has the same distinct prime factors as K. That is, if we know the number of distinct prime factors K has, then we know the number of distinct prime factors K^2 has.

Statement One Alone:

Three different prime numbers are factors of 4K^4.

The information in statement one is not sufficient.

For instance, if K = 2 x 3 x 5, then 4K^4 has 3 different prime factors and K^2 also has 3 different prime factors (since K has 3 different prime factors). However, if K = 3 x 5, then 4K^2 has 3 different prime factors; however, K^2 has 2 different prime factors (since K has 2 different prime factors).

Statement Two Alone:

Three different prime numbers are factors of 4K.

The information in statement two is not sufficient.

For instance, if K = 2 x 3 x 5, then 4K has 3 different prime factors and K^2 has 3 different prime factors. However, if K = 3 x 5, then 4K has 3 different prime factors; however, K has 2 different prime factors.

Statements One and Two Together:

We see that using both statements still allows for K to have 2 or 3 different prime factors.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User Joined: 09 Sep 2013
Posts: 11717
Re: If K is a positive integer, how many different prime numbers  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: If K is a positive integer, how many different prime numbers   [#permalink] 02 Sep 2018, 01:46
Display posts from previous: Sort by

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