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If x is a prime factor of y, is x^2 a factor of y?

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Bunuel
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If x is a prime factor of y, is x^2 a factor of y? [#permalink] New post   04 Jan 2021, 21:15
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If x is a prime factor of y, is x^2 a factor of y?

(1) y = 18.
(2) x is not even integer.
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C
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Re: If x is a prime factor of y, is x^2 a factor of y? [#permalink] New post   05 Jan 2021, 00:36
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Statement 1
18 has two prime factors 2 and 3, there is still not a definite answer.
Statement 2
This information is insufficient in itself
Statement 1 and 2
Together these two statements can eliminate the possibility of 2
So the answer is C
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If x is a prime factor of y, is x^2 a factor of y? [#permalink] New post   Updated on: 09 Jan 2021, 00:48
Statement 1:Not Sufficient
y=18 gives us no idea about x
Statement 2:Not suficient
x is not even integers provide us no information about y. y could be 3 and x could be 3 where the answer is No or y=9 and x=3 will give us a Yes

Statement 1 and 2:Sufficient
y=18, x is not even
Prime factors of 18 =2,3
x can not be 2
So x must be 3. Hence x^2 = 9 is also a factor of y

Answer C

Originally posted by XSatishX on 04 Jan 2021, 22:33.
Last edited by XSatishX on 09 Jan 2021, 00:48, edited 2 times in total.
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Re: If x is a prime factor of y, is x^2 a factor of y? [#permalink] New post   05 Jan 2021, 01:51
Bunuel wrote:
If x is a prime factor of y, is x^2 a factor of y?

(1) y = 18.
(2) x is not even integer.



(1) y = 18 = 2x3x3
if x = 2, answers is no.
if x = 3, answer is yes.
Therefore no definite answer.

(2) x is not even integer.
no information on y.
if y=9, x=3x3 -- answer would be yes.
if y=21, x=3x7 -- answer would be no.
Therefore no definite answer.

Together,
x=3.

Therefore (1) and (2) together are sufficient.
Answer C.
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Re: If x is a prime factor of y, is x^2 a factor of y? [#permalink] New post   06 Jan 2021, 07:10
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Bunuel wrote:
If x is a prime factor of y, is x^2 a factor of y?

(1) y = 18.
(2) x is not even integer.


(1) \(\frac{18}{2}, \frac{18}{3}; x^2=4 \ or \ 9;\) 4 is not a factor of 18 though 9 is a factor of 18. Insufficient.

(2) We don't know about y. Insufficient.

Considering both:

\(y=18, x=3\); Sufficient.

The answer is C
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Re: If x is a prime factor of y, is x^2 a factor of y? [#permalink]
06 Jan 2021, 07:10
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Bunuel
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