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Re: What is the value of positive integer x?
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19 Jan 2015, 07:16
What is the value of positive integer x?
(1) The sum of all unique factors of x is 31
(2) x = y^2, where y is an integer
Here is my solution though i am not sure that it is correct
Statement 1. 31 is out of scope since 31+1=32. Hence we should look for x<31. We can exclude all prime numbers (2,3,5,7,11,13,17,19,23,29 and 31) and multiples of 10 (10,20,30) so we have numbers such as 1,4,6,8,12,14,16,18,22,24,25,26,27,28. Lets exclude small numbers such as 1,4,6 since sum of their factors is less than 31 for sure. Lets check 12: 1,2,3,4,6,12=30 not enough. 14:1,2,7,14=24<31 16:1,2,4,8,16=31 ok. 25:1,5,25=31 ok. So we have two answers hence statement 1 is insufficient.
Statement 2. Not sufficient since x can be 9 or x can be 16
Both statements together. Still insuffient since x=16 and y=+4 or -4 or x=25 and y=+5 or -5. Hence answer E