Let a, b, c, d, and e be distinct integers such that (6 − a)(6 − b)(6

Since the prime factorization is 3*3*5

The constraint in the question is that they are distinct so the only possible way is 3,-3,5,1,-1

6-a = 3 => a=3
6-b = -3 => b=9
6-c = 5 => c=1
6-d = 1 => c=5
6-e = -1 => e = 7

Answer is C = 25

The question is exclusively asking for value of a+b+c+d+e so that should be 5.
why are we subtracting it from 30.

Check here: https://gmatclub.com/forum/let-a-b-c-d- ... l#p1274086

Prime factorization of 45 = (3) (3) (5)

However, we have 5 factors that multiply to 45 ———> the other two factors must be 1

(1) (1) (3) (3) (5) = 45

However, each of the variables must be Distinct. Therefore, since 6 is being subtracted by each variable, we can make some of the factors Negative.

Rule: an EVEN count of (-)Negative factors will yield a (+)positive product.

We either need to have 2 of the factors be negative or 4 of the factors be negative.

Since we need each variable to be distinct, it is necessary that the factor produce different signs for (1) and (1) ——- and (3) and (3)

Change (1) (1) (3) (3) (5) ———> to ———-> (-1) (1) (-3) (3) (5)


Furthermore, since the answer asks for the addition of each variable and each factor involves 6 minus a different variable , it does not matter which variable we choose to make which factor. The addition in the end will still be the same.


(6 - a) = -1 ———-> a = 7

(6 - b) = 1 ———-> b = 5

(6 - c) = 3 ———-> c = 3

(6 - d) = -3 ————> d = 9

(6 - e) = 5 ———-> e = 1


And

( a + b + c + d + e ) = ( 7 + 5 + 3 + 9 + 1) =


25

Posted from my mobile device

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.