CAT Quantitative Aptitude Questions | CAT Algebra - Polynomials questions

The question is about Factorials. We need to find out a range which contains the prime multiple of the factorial series. Polynomials is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept./p>

Question 13: 1(1!) + 2(2!) + 3(3!) + 4(4!)………….50(50!) is a multiple of prime P. P lies in the range........?

1. 30 < P < 40
2. 10 < P < 20
3. 30 < P < 40
4. P > 40

Video Explanation

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Polynomials: It looks like complicated, but not really!

1(1!) + 2(2!) + 3(3!) + 4(4!)………….50(50!)
= 51! – 1 (per the logic we have seen earlier)
51! is a multiple of all prime numbers from 2 upto (and including) 47.
So, 51! – 1 should not be a multiple of any prime from 0 to 50. So, the smallest prime that divides 51! – 1 should be more than 50.

The question is "1(1!) + 2(2!) + 3(3!) + 4(4!)………….50(50!) is a multiple of prime P. P lies in the range........? "

Hence the answer is " P > 40 "

Choice D is the correct answer.