Problem Solving

VJesus12 wrote:If the product of the integers a, b, c, and d is 1,155 and if a > b > c > d > 1, then what is the value of a - d?

(A) 2
(B) 8
(C) 10
(D) 11
(E) 14

This question calls for some prime factorization
1,155 = (3)(5)(7)(11)

Since 1 < d < c < b < a, we can conclude that d = 3, c = 5, b = 7 and a = 11

So, a - d = 11 - 3 = 8.

Answer: B

Cheers,
Brent

Hi VJesus12,

We're told that the product of the INTEGERS A, B, C and D is 1,155 and A > B > C > D > 1. We're asked for the value of A - D. Prime factorization is a great way to approach the 'math' behind this question, but you could also use a little logic and some Number Properties to get to the correct answer.

To start, since 1155 is an ODD number - and we're dealing with the product of 4 DISTINCT INTEGERS that are greater than 1 - each of those numbers MUST be ODD (since Even numbers do NOT divide evenly into Odd numbers). At the minimum, that would make the numbers 3, 5, 7 and 9; in this situation, the difference would be 6. You'll notice that that answer is NOT listed in the Answer choices (so the difference must be GREATER than 6). Increasing any of the numbers severely 'limits' the options though. IF you multiply 3, 5 and 7, you end up with 105, so the 4th number can't be anything greater than about 11 (since 11 x 100 = 1100, which is relatively close to 1155). Thus, it's almost certainly the case that the largest number is 11 and the smallest is 3. Prime Factorizing 1155 would prove it.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

VJesus12 wrote:If the product of the integers a, b, c, and d is 1,155 and if a > b > c > d > 1, then what is the value of a - d?

(A) 2
(B) 8
(C) 10
(D) 11
(E) 14

We can start by expressing 1,155 as the product of its prime factors.

1,155 = 5 x 231 = 5 x 77 x 3 = 5 x 7 x 11 x 3

This means that a = 11, b = 7, c = 5, and d = 3.

Thus, a - d = 11 - 3 = 8.

Answer: B