If x is an integer with n distinct prime factors,is n greater than or equal to 3?
1.x is divisible by 6
2.x is divisible by 10
The answer to this problem is C.
My doubt is that we can consider 0 to be an integer.Therefore the answer to the problem becomes E.
The problem says that x is an integer with n distinct prime factors.So the primes 2,3,5,7... all serve as factors to 0.
0/2=0 0/3=0 0/5=0 Therefore all prime numbers serve as factors to 0.
Had they said that x (lets take x=0) is an integer represented by a product of n distinct prime factors,then we know that there aren't any.
Please clarify about the aspect of having 0 as an integer and its effect on the outcome of the problem.
Thanks
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dddanny2006
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Statement 1 : x is divisible by 2 and 3.dddanny2006 wrote:If x is an integer with n distinct prime factors,is n greater than or equal to 3?
1.x is divisible by 6
2.x is divisible by 10
Insufficient. (we don't know whether it is divisible by other prime numbers)
Statement 2 : x is divisible by 2 and 5
Insufficient. (we don't know whether it is divisible by other prime numbers)
Combination : x is divisible by 2,3, and 5.
Sufficient because x has at least 3 prime factors.
Choose C
Even if x = 0, the answer is still C.dddanny2006 wrote:My doubt is that we can consider 0 to be an integer.Therefore the answer to the problem becomes E.
x = 0 implies that it has infinitely many prime factors.
The question is "is n greater than or equal to 3?"
For x = 0, n is infinity.
So statements 1 and 2 together are sufficient to answer the question.
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Hi dddanny2006,
In these types of questions, it helps to TEST values, using the information that you have. This "proof" will help you to confirm the correct answer.
Here, we're told that x is an integer and we're asked if the number of distinct prime factors is greater than or equal to 3. This is a YES/NO question.
Fact 1: x is divisible by 6
If x = 6, then the prime factors are 2, 3 and the answer to the question is NO
If x = 30, then the prime factors are 2, 3, 5 and the answer to the question is YES
Inconsistent = INSUFFICIENT
Fact 2: x is divisible by 10
If x = 10, then the prime factors are 2,5 and the answer to the question is NO
If x = 30, then the prime factors are 2, 3, 5 and the answer to the question is YES
Inconsistent = INSUFFICIENT
Combined, we know that x is divisble by 6 and 10, so x could be 30, 60, 90, 120, etc.
If x = 30, then the prime factors are 2, 3, 5 and the answer to the question is YES
If x = 60, then the prime factors are (still) 2, 3, 5 and the answer to the question is YES
Since all the possibilities are multiples of 30, then there will always be at least 3 distinct prime factors, so the answer is ALWAYS YES.
SUFFICIENT TOGETHER
GMAT assassins aren't born, they're made,
Rich
In these types of questions, it helps to TEST values, using the information that you have. This "proof" will help you to confirm the correct answer.
Here, we're told that x is an integer and we're asked if the number of distinct prime factors is greater than or equal to 3. This is a YES/NO question.
Fact 1: x is divisible by 6
If x = 6, then the prime factors are 2, 3 and the answer to the question is NO
If x = 30, then the prime factors are 2, 3, 5 and the answer to the question is YES
Inconsistent = INSUFFICIENT
Fact 2: x is divisible by 10
If x = 10, then the prime factors are 2,5 and the answer to the question is NO
If x = 30, then the prime factors are 2, 3, 5 and the answer to the question is YES
Inconsistent = INSUFFICIENT
Combined, we know that x is divisble by 6 and 10, so x could be 30, 60, 90, 120, etc.
If x = 30, then the prime factors are 2, 3, 5 and the answer to the question is YES
If x = 60, then the prime factors are (still) 2, 3, 5 and the answer to the question is YES
Since all the possibilities are multiples of 30, then there will always be at least 3 distinct prime factors, so the answer is ALWAYS YES.
SUFFICIENT TOGETHER
GMAT assassins aren't born, they're made,
Rich
