If x and y are positive integers, is x a factor of y?

Question

(1) x = y^2
(2) y > 1

gmat6nplus1 · Answer

statement 1: assume x=1 then y/x = integer; assume y=2 then y/x is not integer.

statement 2: not sufficient.

1+2) y is a positive integer greater than 1.

Answer C

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Solution: C

Statement (1) tells us that x = y^2, so x seemingly cannot be a factor of y as numbers greater than other numbers are not factors of those others numbers. x could be 1, however, if x is 1 then y is 1 and is a factor of y. If y is any other integer, however, x is not a factor of y; INSUFFICIENT. Statement (2) tells us nothing about x; INSUFFICIENT. Together we know that y isn't 1, so x must be greater than 1 and cannot possibly be a factor of y; SUFFICIENT, C.

KarishmaB · Answer

A point to note - Even if it doesn't occur to you that in statement 1, y could be 1 and x could be 1 so x could be a factor of y, when you read statement 2, you must check for y = 1 in statement 1. There could be something special about y = 1 because of which statement 2 gives you y > 1. So statement 2 could give you a hint about statement 1. Use it to your advantage.

stonecold · Answer

See here we need to use a basic principle that for any positive integer P its factors must be all less than P or P itself. 
Statement 1 =>for y=1 the answer is yes & for y=2 => the answer is no.=> insuff
Statement 2 => no clue of x => insuff
Combining them -> Y>1 and we know that for any number greater than 1 => t^2>t hence x must be greater than y
So x can never be a factor of y 
Suff
SMASH THAT C

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If x and y are positive integers, is x a factor of y?

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