Question

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?

• A. 25
• B. 28
• C. 27
• D. 16

Answer 1

The correct option is A

25

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)
$\Rightarrow$ (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.