ardz24 wrote:How many factors of 6! are greater than 100?
(A) 4
(B) 5
(C) 7
(D) 10
(E) 12
Start with the GREATEST FACTOR and work down to the smallest factor greater than 100.
6! =
6*5*4*3*2.
Case 1: Combine 5 of the values in blue to yield a product greater than 100
6*5*4*3*2
Total options = 1.
Case 2: Combine 4 of the values in blue to yield a product greater than 100
6*5*4*3
6*5*4*2
6*5*3*2
6*4*3*2
5*4*3*2
Total options = 5.
Case 3: Combined 3 of the values in blue to yield a product greater than 100
6*5*4
Discard this option, since 6*5*4 is the same as 5*4*3*2, counted above.
Total options = Case 1 + Case 2 = 1+5 = 6.
The OA is not among the answer choices.
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