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Dear People,,Need some help..Confused!!!

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Dear People,,Need some help..Confused!!!

by dddanny2006 » Sun Aug 18, 2013 4:07 pm
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.


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by melguy » Sun Aug 18, 2013 9:55 pm
Hi dddanny2006

0 is an even integer.
0 is not prime nor composite.
0 is nor positive nor negative.
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by ganeshrkamath » Mon Aug 19, 2013 12:57 am
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
Statement 1 : x is divisible by 2 and 3.
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

dddanny2006 wrote:My doubt is that we can consider 0 to be an integer.Therefore the answer to the problem becomes E.
Even if x = 0, the answer is still C.
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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by [email protected] » Mon Aug 19, 2013 12:44 pm
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

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