rahulvsd wrote:How many distinct prime divisors does a positive integer N have?
A. 2N has one prime divisor
B. 3N has one prime divisor
[spoiler]OA: C. [/spoiler]
Statement 1: 2N has one prime divisor
2 is a prime divisor of 2N.
For 2N to have no OTHER distinct prime divisors, N = 2^x.
If N = 2^0 = 1, then it has NO prime divisors.
If N = 2^x (where x>0), then it has ONE distinct prime divisor: the number 2 itself.
INSUFFICIENT.
Statement 2: 3N has one prime divisor
3 is a prime divisor of 3N.
For 3N to have no OTHER distinct prime divisors, N = 3^x.
If N = 3^0 = 1, then it has NO prime divisors.
If N = 3^x (where x>0), then it has ONE distinct prime divisor: the number 3 itself.
INSUFFICIENT.
Statements 1 and 2 combined:
The only value that satisfies both statements is N=1, in which case N has NO distinct prime divisors.
SUFFICIENT.
The correct answer is
C.
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