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If x and y are perfect squares, then which one of the [#permalink]
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05 Jun 2012, 03:48
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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 Seems like a straight forward problem, however the answer choices are a little confusing .
both D& E seem to be contendors for the right answer though the OA is D
D> Because the sum of two perfect square needn't necessarily be a perfect square e.g 4+9=13, not a perfect square, however 9 & 16 = 25 which is a perfect square) E> Because a perfect square to the power 5 (an ODD number) cannot be a perfect square right ?
Please explain.
Thanks, Shreya
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Re: If X & Y are perfect squares, then which one of the [#permalink]
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05 Jun 2012, 03:53
X = m^2; m = integer. Now X^5 = m^10 which is a perfect square (root being m^5).
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Re: If X & Y are perfect squares, then which one of the [#permalink]
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05 Jun 2012, 03:57
x = a^2 y = b^2
a) (a^2)^2, ok b) a^2 * b^2 = (ab)^2, ok c) 4*a^2 = 2^2*a^2 = (2a)^2, ok d) a^2 + b^2, clearly not ok for all a/b, e.g a = 8, b = 2, 64 + 4 = 68 which is not a perfect square. e) (a^2)^5 = (a^5)^2, ok



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Re: If x and y are perfect squares, then which one of the [#permalink]
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23 Apr 2013, 00:09
Option B is not clear to me.... X=a^2 Y=b^2 Therefore X*Y = (ab)^2 But, if x=4 and y=9 , then xy=25 However, if x= 4 and y = 25, then xy = 100 which is not perfect square So, how can we rule out B? Please explain
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Re: If x and y are perfect squares, then which one of the [#permalink]
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23 Apr 2013, 00:31
sdas wrote: Option B is not clear to me.... X=a^2 Y=b^2
Therefore X*Y = (ab)^2 But, if x=4 and y=9 , then xy=25 However, if x= 4 and y = 25, then xy = 100 which is not perfect square
So, how can we rule out B?
Please explain If x=4 and y=9 xy =36 which is a perfect square. and xy=100 is a perfect square. its the square of 10. for that matter , product of any two perfect squares is a perfect square. as you pointed out (ab)^2. so square root of the product is ab an integer. 4*9 or 9*25 or 16*25



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Re: If x and y are perfect squares, then which one of the [#permalink]
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23 Apr 2013, 02:48
sdas wrote: Option B is not clear to me.... X=a^2 Y=b^2
Therefore X*Y = (ab)^2 But, if x=4 and y=9 , then xy=25 However, if x= 4 and y = 25, then xy = 100 which is not perfect square
So, how can we rule out B?
Please explain XY = 36 = 6^2 XY for x=4 and Y = 25 is 100 = 10^2, which is a perfect square.
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Re: If x and y are perfect squares, then which one of the [#permalink]
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23 Apr 2013, 05:06
shreya717 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 Seems like a straight forward problem, however the answer choices are a little confusing .
both D& E seem to be contendors for the right answer though the OA is D
D> Because the sum of two perfect square needn't necessarily be a perfect square e.g 4+9=13, not a perfect square, however 9 & 16 = 25 which is a perfect square) E> Because a perfect square to the power 5 (an ODD number) cannot be a perfect square right ?
Please explain.
Thanks, Shreya If x=y=1^2=1, then each option but D is a perfect square, therefore D is NOT necessarily a perfect square. Answer: D. 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, then which one of the [#permalink]
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23 Apr 2013, 07:54
Darn....I forgot perfect square of 10.
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Re: If x and y are perfect squares, then which one of the [#permalink]
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28 Jan 2018, 05:57
Since x and y are perfect squares, we can write: x=n^2 and y=m^2, for some integers m and n.
Let's evaluate the options now: 1. x^2 = (n^2)^2. Thus, x^2 is a perfect square (the square of n^2). 2. xy = (n^2)(m^2)= (nm)^2. Thus, xy is a perfect square (the square of xy) 3. 4x = 4(n^2)= (2n)^2. Thus, 4x is a perfect square (the square of 2n) 4. x+y= (n^2)+(m^2). This is NOT necessarily a perfect square.
Hence, we have our answer. It is D.




Re: If x and y are perfect squares, then which one of the
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