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# If x is a perfect square greater than 1, what is the value of x?

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GRE 1: Q169 V154
Re: If x is a perfect square greater than 1, what is the value of x? [#permalink]
Excellent Question.
Here is what i did in this one ->

We are given that x is a perfect square and are asked its value.
Statement 1->
x has 3 factors.
Some quick facts on factors ->
1 is the only number that has 1 factor.
A prime as 2 factors.
A number of the form Prime^2 has 3 factors.
Hence x must be of the form Prime^2
E.g=> 2^2 or 3^2 etc.
Hence not sufficient.

Statement->2
As 1 is the factor of every number => This statement tells us that x must be even.
E.g => 2^2 or 2^4 or 2^6
Basically it cannot have any prime factor other then one.
So it must be of the form 2^even number .
Hence not sufficient.

Combing the two statements=>
x must be 2^2 to have 4 factors.
Hence sufficient.
Hence C.
Re: If x is a perfect square greater than 1, what is the value of x? [#permalink]
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