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03 Oct 2011, 10:49
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
76% (01:00) correct
24%
(00:59)
wrong
based on 114
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Not Attempted Yet
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
OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-and-y-are-perfect-squares-then-which-one-of-the-133933.html
A. x^2
B. xy
C. 4x
D. x+y
E. x^5
Can someone please help me to understand the explanation?
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?
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
03 Oct 2011, 11:27
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Bookmarks
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)
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)
