Bunuel
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
Kudos for a correct solution.
VERITAS PREP OFFICIAL SOLUTION:Upon first glance, 1155 and four variables might look really messy. But take the first step – you know it’s divisible b y 11 and that you have to factor it. 1100 is 11*100 and 55 is 11*5, so you have 11*105. And 105 is much easier to divide out since it ends in a 5. That’s 21*5, which is 7*3*5. Once you’ve factored it down, it’s 11*7*5*3, which are all prime, so when 1 has to be less than any of these, that’s exactly a, b, c, and d. You need the biggest minus the smallest, and 11-3 is 8. What may have looked like a big, intimidating number was actually not so bad once you took the first step. It’s always darkest before the light goes on.