Does the integer k have at least three different positive prime factor

Question

Does the integer k have at least three different positive prime factors?

(1) k/15 is an integer.
(2) k/10 is an integer.

Bunuel · Answer

SOLUTION

Does the integer k have at least three different positive prime factors?

(1) k/15 is an integer --> since k is divisible by 3*5=15, then it's divisible by 3 and 5, hence k has at least those two prime factors, though it might have more (consider k=30). Not sufficient.

(2) k/10 is an integer --> since k is divisible by 2*5=10, then it's divisible by 2 and 5, hence k has at least those two prime factors, though it might have more (consider k=30). Not sufficient.

(1)+(2) At least 3 primes are factors of k: 2, 3, and 5. Sufficient.

Answer: C.

cyberjadugar · Answer

Hi,

For integer k to have atleast 3 different positive prime factors,
k = a.b.c, where a, b, c are prime numbers.

Using (1),
k/15 is an integer,
least value of k =15, which has two different prime factors 3 & 5. Insufficient.

Using (2),
k/10 is an integer,
least value of k =10 which has two different prime factors 2 & 5. Insufficient.

Using both,
least value of k =30 which has two different prime factors 2, 3 & 5. Sufficient.

Answer is (C)

Regards,

greatps24 · Answer

If  a  divides  b , then all the primes in  a  along with their powers are in  b

Bunuel · Answer

0 is a multiple of all positive integers. Thus if k=0 it still has at least three different positive prime factors.

stonecold · Answer

Here is my solution->
We need to check if the number of prime factors of p are atleast 3 i.e.≥3
Statement 1
p=15 => no
p=15*17 => yes
Not sufficient 
Statement 2
p=10 => no
p=10*13 => yes
Not sufficient 
Combining the two statements we can say that p=2*3*5*x for some integer x. 
Clearly p must have atleast 3 prime factors 
Hence C

kanusha · Answer

I solved this problem using Plug In

1, If k=30, have 2,3,5 prime factors 
 If K=75, have 3,5 only 
Insufficient 
2, If k = 70 , have 2,5,7 prime factors
 If k = 80, Only 2,5 prime factors
Insufficient
3, K/15 and K/10
If k=30 2,3,5
 K=90 2,3,5 prime factors

Irrespective K value , these only both meet conditions
C

Is my approach Right? 
Thanks

Jerald · Answer

Here is my solution:

Question: Does K have at-least 3 different positive prime factors.

Statement 1:  \frac{k}{15}  is an integer.

Hence the values of k are multiples of 15 such as 15,30,45...
Factors of 15 = 5 and 3 (2 factors)
Factors of 30 = 5 , 3 and 2 (3 factors)
Hence not sufficient.

Statement 2:  \frac{k}{10}  is an integer

Hence the values of k are multiples of 10 such as 10,20,30
Factors of 10 = 5 and 2 (2 factors)
Factors of 30 = 5 , 3 and 2 (3 factors)
Hence not sufficient.

Stmt 1 + Stmt 2:

k should be multiples of 10 and 15 such as 30,60...
All these values have atleast 3 positive different prime factors.

Hence C.

brightandamen · Answer

Hi, does 1 counted as a prime factor?

Bunuel · Answer

No, 1 is not a prime number. The smallest prime is 2.

ScottTargetTestPrep · Answer

We need to determine whether k has at least three different prime factors.

Statement One Alone:

k/15 is an integer.

Statement one alone is not sufficient to answer the question. If k = 15, then k has two different prime factors; however, if k = 30, then k has three different prime factors.

Statement Two Alone:

k/10 is an integer.

Statement two alone is not sufficient to answer the question. If k = 10, then k has two different prime factors; however, if k = 30, then k has three different prime factors.

Statements One and Two Together:

Using statements one and two, we see that k is a multiple of both 10 and 15, and thus it is a multiple of their least common multiple, which is 30. Since all multiples of 30 have at least three different prime factors, the two statements together are sufficient.

Answer: C

KarishmaB · Answer

This concept is discussed in detail here: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/0 ... r-factors/

TriumphKai · Answer

Could integer k be 0?

If so, both conditions (k/10 is an integer) and (k/15 is an integer) would both be met as 0/anything = 0. Does 0 have an infinite number of prime factors?

Thank you all!

prabsahi · Answer

Hello,

Bunnel has already mentioned this in above thread..

0 is a multiple of all integers except 0 itself. Thus if k=0 it still has at least three different positive prime factors.

Hope it helps !!

Prazard · Answer

Why can't be k or the 3 factors be negative integers given question didn't state it was positive or greater than 0?

rebinh1982 · Answer

Hi,

I had E as an answer.

When k is an integer, then K can also be 0 or any other integer.

St1: When K= 0 answer is no
 When k= 30 answer is yes

St2: When K= 0 answer is no
 When k= 30 answer is yes

St1&2

When K = 0 is again no
When K =30 is again yes

So the answer to this question must be E.
Unless you assume k is a positive integer, then the answer is C. You can’t assume on DS questions.

swapnils10 · Answer

Condition 1 :

K/15 = Integer (I) ; K =15*I = 5*3*I 
here 'I' could be anything and not necessary that it will give 3 different prime number

Condition 2 :

K/10 = Integer (I) ; K =10*I = 5*2*I 
here 'I' could be anything and not necessary that it will give 3 different prime number,

But if we combine both condition then its LCM is 30 and it will give 3 different prime number

Hope it helps !

totaltestprepNick · Answer

C https://www.youtube.com/watch?v=Ab8YCf5AOnQ Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

Does the integer k have at least three different positive prime factor

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