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# If x and y are perfect squares, which of the following is

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If x and y are perfect squares, which of the following is [#permalink]  03 Oct 2011, 09:49
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Difficulty:

15% (low)

Question Stats:

83% (01:33) correct 17% (00:06) wrong based on 24 sessions
If x and y are perfect squares, then which one of the following is not necessarily a perfect square?

A. x^2
B. xy
C. 4x
D. x+y
E. x^5

[Reveal] Spoiler:
This is a question I came across in a GMAT preparation book (GMAT Prep Course by Jeff Kolby).

If x and y are perfect squares, which of the following is not necessarily a perfect square?

(is it supposed to mean "it might or it might not be a perfect square" or it is a definitive "it is not a perfect square"?)

(a) x^2
(b) xy
(c) 4x
(d) x+y
(e) x^5

The book solution is (d), because if you plug in x=4 and y=9, then x+y=13 which is not a perfect square. Ok, I cannot disagree with it, although if you plug in x=9 and y=16, then x+y=25 which is a perfect square. But can someone explain to me why (e) is not the right answer? x^5 also is not necessarily a square. 4^5 is a perfect square, but 3^5 or 5^5 are not. Help... Dumb book or dumb me?

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-and-y-are-perfect-squares-then-which-one-of-the-133933.html
[Reveal] Spoiler: OA
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Joined: 03 Mar 2011
Posts: 90
Location: United States
Schools: Erasmus (S)
GMAT 1: 730 Q51 V37
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Re: If x and y are perfect squares, which of the following is [#permalink]  03 Oct 2011, 10:27
2
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Perfecr square means $$x^2$$ where x is an integer.
So, it is easy to see on each answer.

Note: not necessarily means either a perfect square or not.

Let assume $$x=a^2$$ and $$y=b^2$$, where a and b are integers.

(A)$$x^2=a^4$$, so, a perfect square
(B)$$xy=a^2b^2=(ab)^2$$, so, a perfect square
(C)$$4x=4a^2=(2a)^2$$, so, a perfect square
(D)$$x+y=a^2+b^2$$. Not necessarily a perfect square. See your own example.
(E)$$x^5=a^10=(a^5)^2$$, so, a perfect square.

All in all, the answer is (D)
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Re: If x and y are perfect squares, which of the following is [#permalink]  03 Oct 2011, 10:49
Bummer. That's me dumb indeed. I forgot x and y have to be squares too, that's why (e) is always a square. Thank you.
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Re: If x and y are perfect squares, which of the following is [#permalink]  20 Jan 2016, 23:48
bagrettin wrote:
Perfecr square means $$x^2$$ where x is an integer.
So, it is easy to see on each answer.

Note: not necessarily means either a perfect square or not.

Let assume $$x=a^2$$ and $$y=b^2$$, where a and b are integers.

(A)$$x^2=a^4$$, so, a perfect square
(B)$$xy=a^2b^2=(ab)^2$$, so, a perfect square
(C)$$4x=4a^2=(2a)^2$$, so, a perfect square
(D)$$x+y=a^2+b^2$$. Not necessarily a perfect square. See your own example.
(E)$$x^5=a^10=(a^5)^2$$, so, a perfect square.

All in all, the answer is (D)

Consider x&Y =1 and substitue...get D as answer...
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Re: If x and y are perfect squares, which of the following is [#permalink]  21 Jan 2016, 02:36
Expert's post
Celesta wrote:
If x and y are perfect squares, then which one of the following is not necessarily a perfect square?

A. x^2
B. xy
C. 4x
D. x+y
E. x^5

[Reveal] Spoiler:
This is a question I came across in a GMAT preparation book (GMAT Prep Course by Jeff Kolby).

If x and y are perfect squares, which of the following is not necessarily a perfect square?

(is it supposed to mean "it might or it might not be a perfect square" or it is a definitive "it is not a perfect square"?)

(a) x^2
(b) xy
(c) 4x
(d) x+y
(e) x^5

The book solution is (d), because if you plug in x=4 and y=9, then x+y=13 which is not a perfect square. Ok, I cannot disagree with it, although if you plug in x=9 and y=16, then x+y=25 which is a perfect square. But can someone explain to me why (e) is not the right answer? x^5 also is not necessarily a square. 4^5 is a perfect square, but 3^5 or 5^5 are not. Help... Dumb book or dumb me?

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-and-y-are-perfect-squares-then-which-one-of-the-133933.html

If x=y=1^2=1, then each option but D is a perfect square, therefore D is NOT necessarily a perfect square.

P.S. Notice that x+y could be a perfect square for example if x=3^2=9 and y=4^2=16 --> x+y=25=5^2.
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Re: If x and y are perfect squares, which of the following is   [#permalink] 21 Jan 2016, 02:36
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