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25 Nov 2014, 08:33
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D
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Difficulty:
35%
(medium)
Question Stats:
69% (01:39) correct
31%
(01:45)
wrong
based on 204
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Tough and Tricky questions: Number Properties.
How many distinct factors does positive integer k have?
(1) k has more distinct factors than the integer 9 but fewer distinct factors than the integer 81.
(2) k is the product of two distinct prime numbers.
Source: Chili Hot GMAT
25 Nov 2014, 09:32
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Bunuel
9 = 3^2 thus integer 9 has 3 distinct factors
81 = 3^4 thus 81 has 5 distinct factors
(1) k has more distinct factors than the integer 9 but fewer distinct factors than the integer 81.
that means 3<k<5 thus k = 4. sufficient
(2) k = \(P1 * P2\) where P1 and P2 are two prime numbers
then k has (1+1) * (1+1) = 4 factors
Thus [D]
intheend14
25 Nov 2014, 18:03
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Statement 1 tells us that k has 4 distinct factors (9 has 3 and 81 has 5). Sufficient
Statement 2 tells us that k has 4 distinct factors as the product of two distinct primes will always have the following factors, 1, prime #1, prime #2 and the product of the primes.
D
Statement 2 tells us that k has 4 distinct factors as the product of two distinct primes will always have the following factors, 1, prime #1, prime #2 and the product of the primes.
D
