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Hi mukherjee.tanuj3,
This DS prompt is based on some Number Properties and is perfect for TESTing VALUES.
We're told that N and T are positive integers. We're asked for the greatest PRIME factor of NT.
Fact 1: The Greatest Common Factor of N and T is 5
For the GCF to be 5, that means that BOTH N and T have to be multiples of 5
If N=5, T=5, then NT = 25 and the answer to the question is 5
If N=5, T=35, then NT = 175 and the answer to the question is 7
Fact 1 is INSUFFICIENT
Fact 2: The Least Common Multiple of N and T is 105
For the LCM to be 105, that means that BOTH N and T have to be ODD (since even numbers can never have an odd LCM) and at least one MUST be a multiple of 5.
Also, since both numbers MUST be ODD, the LCM IS the product of NT.
105 = (3)(5)(7), so no matter how you choose your N and T:
1 and 105
3 and 35
5 and 21
7 and 15
The answer to the question will ALWAYS be 7.
Fact 2 is SUFFICIENT
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
