Problem Solving

What is the greatest prime factor of 12!11! + 11!10!?

(A) 7
(B) 11
(C) 13
(D) 17
(E) 19

IMO Ans. Is 19

rupamroy wrote:What is the greatest prime factor of 12!11! + 11!10!?

(A) 7
(B) 11
(C) 13
(D) 17
(E) 19

solution:
12!11! + 11!10!
= 12 x 11 x 10! x 11! + 11!10!
= 11!10! (12 x 11 + 1)
= 11!10! (133)
check the options = 19 x 7 is 133
Hence greatest is 19.

Answer E

Yes, Answer is E) 19

pritish2301 wrote:

rupamroy wrote:What is the greatest prime factor of 12!11! + 11!10!?

(A) 7
(B) 11
(C) 13
(D) 17
(E) 19

solution:
12!11! + 11!10!
= 12 x 11 x 10! x 11! + 11!10!
= 11!10! (12 x 11 + 1)
= 11!10! (133)
check the options = 19 x 7 is 133
Hence greatest is 19.

Answer E

Exactly. Really, this is a fairly straightforward factoring question, but it's made pretty difficult by giving you factorials instead of terms that you're used to factoring, like variables.

V True bill.. and I have also noticed a definite shift in the characteristic of PS questions in GMAT. It was not so long ago, that PS used to test more of mathematical ability than logic intertwined with maths ability. But after going through the GMAT Prep 1, I feel there is now more stress on reasoning and on cognitive abilities. I should admit, I have myself made mistakes on a couple of those. Would post them separately.

True. I think the shift is a good thing; you are rewarded more for actually leaning than for simply memorizing.