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.
OG Diag Test Q doubt OA (0 also an integer)
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key word is three different positive prime factors. 0 is not positive.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.
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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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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
(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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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.
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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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.
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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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).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!
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THANK you!!Testluv wrote: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).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!
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Excellent stuff...nice explanationTestluv 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.
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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.Testluv wrote: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).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!
Ameya
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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.
I don't understand how you come to the assumption that k must be positive. This assumption is not stated anywhere in the question.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
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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Absolutely. The question should specify positive. Otherwise answer is E. I request the experts to have a look at this. It is ambiguous.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.I don't understand how you come to the assumption that k must be positive. This assumption is not stated anywhere in the question.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
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.
Cheers!
Rohan
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich