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OG Diag Test Q doubt OA (0 also an integer)

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by aspiregmat » Mon Aug 10, 2009 6:45 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

I tried searching in the forum with little success. If its already discussed can you plz point me to that thread.



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

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

OA : C

I understand why the answer is so. But it ignores the case k=0. 0 is an integer and 0/15 and 0/10 is also an integer. So IMO the answer should be E.

Any thoughts.
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Re: OG Diag Test Q doubt OA (0 also an integer)

by shahdevine » Mon Aug 10, 2009 7:49 am
aspiregmat wrote:I tried searching in the forum with little success. If its already discussed can you plz point me to that thread.



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

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

OA : C

I understand why the answer is so. But it ignores the case k=0. 0 is an integer and 0/15 and 0/10 is also an integer. So IMO the answer should be E.

Any thoughts.
key word is three different positive prime factors. 0 is not positive.
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by aspiregmat » Mon Aug 10, 2009 11:29 pm
Its not given that K is positive integer. It just asks that if K has 3 distinct positive prime factors. We cannot assume K to be positive.
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Re: OG Diag Test Q doubt OA (0 also an integer)

by life is a test » Tue Aug 11, 2009 7:11 am
aspiregmat - the requirements are that k must be positive (hence k=0 and k = negative number is out). Moreover there has to be three distinct prime factors

(1) k/15 is an integer--> k = 15x --> 3*5*x--> insuff
(2) k/10 is an integer--> k = 10x--> 2*5*x-->insuff
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by jjk » Tue Aug 18, 2009 7:45 am
0 is also not a prime factor.
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by riomadera » Wed Feb 24, 2010 3:48 pm
I too was having trouble understanding this problem, but after reading the thread, I now fully understand why the answer is C.

Statement (1) : k/15 is an integer

If k=0, the number of prime factors is 0

If k is any integer other than 0, k will have at least 2 prime factors.

example 1: k = 15, 15/15 = 3*5 / 3*5 = 1

- In example 1, we see that k has exactly 2 prime factors (3 and 5).

example 2: k = 30, 30/15 = 2*3*5 / 3*5 = 2

- In example 2, we see that k has exactly 3 prime factors (2, 3 and 5).

Since k can be any big number so long as 3 and 5 are prime factors of k, we see through example 2 that the number of prime factors of k is at least 2.

...and because the number of prime factors for k can be either 0 or at least 2, this statement does not give us a single answer, thus it is insufficient.

A similar reasoning can be said about statement 2 alone.
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by Testluv » Wed Feb 24, 2010 7:32 pm
Not only is 0 not a prime factor, in fact it is not a factor of any number at all because you can't divide by 0. 0 is, however, a multiple of all numbers.

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

(1) k/15 is an integer

Yes, k can be 0, in which case k does have at least three different positive prime factors. But it doesn't have to be. In order for k/15 to be an integer k has to have at least 3 and 5 as prime factors. Otherwise it wouldn't be divisible by 15.

(2) k/10 is an integer

By similar reasoning, k has to have at least 2 and 5 as prime factos. Otherwise, it wouldn't be divisible by 10.

Together, you know that k has at least 2, 3 and 5 as prime factors.

Choose C.
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by tnaim » Mon Apr 19, 2010 7:47 am
Hi,
Is 1 not considered a factor?
in this case if we have k/15=I => k=15*I => k=1*3*5*I
thanks for your help!
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by Testluv » Mon Apr 19, 2010 9:21 am
tnaim wrote:Hi,
Is 1 not considered a factor?
in this case if we have k/15=I => k=15*I => k=1*3*5*I
thanks for your help!
1 is a factor but it is not a prime factor. The smallest prime factor is 2 (2 is also the only even prime factor).
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by tnaim » Mon Apr 19, 2010 9:59 am
Testluv wrote:
tnaim wrote:Hi,
Is 1 not considered a factor?
in this case if we have k/15=I => k=15*I => k=1*3*5*I
thanks for your help!
1 is a factor but it is not a prime factor. The smallest prime factor is 2 (2 is also the only even prime factor).
THANK you!!
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by ayankm » Mon Apr 19, 2010 3:22 pm
Testluv wrote:Not only is 0 not a prime factor, in fact it is not a factor of any number at all because you can't divide by 0. 0 is, however, a multiple of all numbers.

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

(1) k/15 is an integer

Yes, k can be 0, in which case k does have at least three different positive prime factors. But it doesn't have to be. In order for k/15 to be an integer k has to have at least 3 and 5 as prime factors. Otherwise it wouldn't be divisible by 15.

(2) k/10 is an integer

By similar reasoning, k has to have at least 2 and 5 as prime factos. Otherwise, it wouldn't be divisible by 10.

Together, you know that k has at least 2, 3 and 5 as prime factors.

Choose C.
Excellent stuff...nice explanation
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by ameya85 » Sun Jan 22, 2012 12:01 am
Testluv wrote:
tnaim wrote:Hi,
Is 1 not considered a factor?
in this case if we have k/15=I => k=15*I => k=1*3*5*I
thanks for your help!
1 is a factor but it is not a prime factor. The smallest prime factor is 2 (2 is also the only even prime factor).
I Googled the entire question just to understand why 1 is not consiered while counting the factors. And from your inputs, I learned something that is very basic yet extremely helpful. Thanks for this info. :)

Ameya
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by llynx » Tue Jul 03, 2012 5:17 am
aspiregmat wrote:Its not given that K is positive integer. It just asks that if K has 3 distinct positive prime factors. We cannot assume K to be positive.
life is a test wrote:aspiregmat - the requirements are that k must be positive (hence k=0 and k = negative number is out). Moreover there has to be three distinct prime factors

(1) k/15 is an integer--> k = 15x --> 3*5*x--> insuff
(2) k/10 is an integer--> k = 10x--> 2*5*x-->insuff
I don't understand how you come to the assumption that k must be positive. This assumption is not stated anywhere in the question.

If you are given that k/15 and k/10 are integers, they are allowed to be negative integers and thus neither (1) nor (2) are sufficient without knowing that k is positive.
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by Rohan Nanda » Wed Jul 25, 2012 8:16 pm
llynx wrote:
aspiregmat wrote:Its not given that K is positive integer. It just asks that if K has 3 distinct positive prime factors. We cannot assume K to be positive.
life is a test wrote:aspiregmat - the requirements are that k must be positive (hence k=0 and k = negative number is out). Moreover there has to be three distinct prime factors

(1) k/15 is an integer--> k = 15x --> 3*5*x--> insuff
(2) k/10 is an integer--> k = 10x--> 2*5*x-->insuff
I don't understand how you come to the assumption that k must be positive. This assumption is not stated anywhere in the question.

If you are given that k/15 and k/10 are integers, they are allowed to be negative integers and thus neither (1) nor (2) are sufficient without knowing that k is positive.
Absolutely. The question should specify positive. Otherwise answer is E. I request the experts to have a look at this. It is ambiguous.
Cheers!

Rohan
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by [email protected] » Mon Feb 19, 2018 8:55 pm
Hi All,

We're told that K is an integer. We're asked if K has AT LEAST three DIFFERENT positive prime factors. This is a YES/NO question and we can solve it by TESTing VALUES.

1) K/15 is an integer

Fact 1 tells us that K must be a multiple of 15:
IF....
K = 15, then its prime factors are 3 and 5 and the answer to the question is NO
K = 30, then its prime factors are 2, 3 and 5 and the answer to the question is YES
Fact 1 is INSUFFICIENT

2) K/10 is an integer

Fact 2 tells us that K must be a multiple of 10:
IF....
K = 10, then its prime factors are 2 and 5 and the answer to the question is NO
K = 30, then its prime factors are 2, 3 and 5 and the answer to the question is YES
Fact 2 is INSUFFICIENT

Combined, we know:
K is a multiple of 15
K is a multiple of 10

By definition, the two Facts combined tell us that K must be a multiple of 30. From our prior work (above), we know that 30 already has 3 prime factors (2, 3, and 5), so any multiple of 30 will also have at least 3 prime factors. Thus, the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer: C

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