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

Question

(1) x has exactly 3 distinct factors.
 (2) x has exactly one positive odd factor.

yezz · Answer

X is a square of an integer, x could be 1, 4 , 9, 16, 25.. etc

From 1

4 , 9 , 25 all has 3 distinct factors .. insuff

From 2

Since 1 is a factor of all perfect squares and it s odd then x is 1 or even ... insuff

Both

X is even perfect square that has only 3 distinct factors .. x is 4... suff

C

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JeffTargetTestPrep · Answer

We are given that x is a perfect square greater than 1 and need to determine the value of x.

Statement One Alone:

x has exactly 3 distinct factors.

Since we know that x is a perfect square and has 3 distinct factors, we can determine that x is the square of a prime number.

For instance, x could equal 2^2 = 4, which has distinct factors of 1, 2, and 4, or x could equal 3^2 = 9, which has distinct factors of 1, 3, and 9. Thus, statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

x has exactly one positive odd factor.

If x has exactly one positive odd factor, then that odd factor must be 1, since 1 is a factor of every number. This leads us to the conclusion that any other factors of x must be even.

In fact, x must be the square of a power of 2. For example, x could be (2^1)^2 = 2^2 = 4 or (2^2)^2 = 4^2 = 16. In the former case, the distinct factors of x are 1, 2 and 4; exactly one of them is odd. In the latter case, the distinct factors of x are 1, 2, 4, 8, and 16; again, exactly one of them is odd. Because x can equal, for example, 4 or 16, we don’t have a unique value for x. We can eliminate answer choice B.

Statement One and Two Together:

From our analysis of statement one, we determined that x is the square of a prime number, and from our analysis of statement two, we determined that x is the square of a power of 2. Since 2 is the only prime that is a power of 2, x must equal 2^2 = 4.

Answer: C

stonecold · Answer

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.

bumpbot · Answer

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

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