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Let a, b, c, d and e be distinct integers such that (6 - a) (6 - b) (6 - c) (6 - d) (6 - e) = 45. What is a+b+c+d+e?


Options:
A .   25
B .   28
C .   27
D .   16
Answer: Option A
:
A
If 45 is expressed as a product of five distinct integral factors, the unique way is:
45 = (+1) (-1) (+3) (-3) 5 (no factor has its absolute value greater than 5)
(6 - a) (6 - b) (6 - c) (6 - d) (6 - e) = (1) (-1) (3) (-3) 5
The corresponding values of a, b, c, d and e are 5, 7, 3, 9 and 1 and their sum is 5 + 7 + 3 + 9 + 1 = 25.

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