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greater than the greatest

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by sanju09 » Sat Jun 21, 2014 11:21 pm
If the set of proper factor(s) of a given positive integer x does not include 1 and x, which of the following is the smallest prime number greater than the greatest proper factor of 81?
(A) 5
(B) 11
(C) 29
(D) 79
(E) 83

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by poojavarun » Sun Jun 22, 2014 3:29 am
As 81 in clue 27 as largest factor so 29 ...imo. c
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by poojavarun » Sun Jun 22, 2014 3:32 am
As 81 in clue 27 as largest factor so 29 ...imo. c
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by BestGMATEliza » Tue Jun 24, 2014 2:34 am
I like to find the largest factor by trying to find the smallest, I find it easier and faster in most cases.
So, lets take a look:
1- doesn't count for this problem
2- doesn't go into 81
3- smallest proper fraction that goes into 81. goes into 81 27 times, so 27 is the largest proper fraction.

Now, how to find the smallest prime greater than 27? If you don't already have the primes memorized, work your way up:
28- even, so not prime
29- ding ding ding!!! we have our answer
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