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If (x  y)^2 = x^2  y^2, what is the value of the nonzero integer xy
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14 Jan 2020, 01:46
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Competition Mode Question If \((x  y)^2 = x^2  y^2\), what is the value of the nonzero integer \(xy\)? (1) \(x = 5\) (2) \(xy = 0\) Are You Up For the Challenge: 700 Level Questions
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Re: If (x  y)^2 = x^2  y^2, what is the value of the nonzero integer xy
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14 Jan 2020, 02:18
If \((x  y)^2 = x^2  y^2\), what is the value of the nonzero integer \(xy\)? (1) \(x = 5\) \((x  y)^2 = x^2  y^2\) ... opening the \((x  y)^2\) \(x^2 + y^2  2xy = x^2  y^2 \) .. cancelling out \(x^2\) , we get \(y^2  2xy =  y^2 \) .. rewriting \(2y^2 = 2xy \) .. cancelling \(2y\) both side, we get \(y = x\) .. sufficient ( xy = 25) A D / B C E (2) \(xy = 0\) It says \(x = y\) ... if we put into the main equation, we can get Zero value which we do not want Neither x nor y value is known apart from 'Zero'. They could be anything. So, Insufficient. 'A' is the winner
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Re: If (x  y)^2 = x^2  y^2, what is the value of the nonzero integer xy
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14 Jan 2020, 03:31
Constraint: (xy)^2 = x^2y^2 Question: Value of nonzero Integer xy? Note! xy = nonzero Integer, so neither x nor y is zero. Guys! let’s breakdown the constraint x^2+y^2 2xy = x^2  y^2 2y^2 = 2xy ——> y^2= xy .: y=x (we can divide by y since it ain’t zero) Now constraint: y=x (1) x= 5We know y=x ,and x= 5 .: xy = (5)(5)=25 (Sufficient) (2) x=yJust reiterating the constraint Say x=5 ,xy =25 , again x=2 ,xy=4 (Ain’t Sufficient) Hit that A Posted from my mobile device



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Re: If (x  y)^2 = x^2  y^2, what is the value of the nonzero integer xy
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14 Jan 2020, 06:27
(xy)^2 = x^2  y^2 > y^2 = xy.
1) If x=5, then y=0 or y=5. As a result, xy=0 or xy=25. xy is nonzero integer, thus value of xy is invariably 25. SUFFICIENT
2)x=y > x^2=y^2 and and xy can be 1,4,9,16,... NOT SUFFICIENT
FINAL ANSWER IS (A)
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Re: If (x  y)^2 = x^2  y^2, what is the value of the nonzero integer xy
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14 Jan 2020, 06:42
If \(((x  y)^2 = x^2  y^2)\), what is the value of the nonzero integer \((xy)\)? xy ≠ 0 means x ≠ 0 or y ≠ 0 \((x^2 + y^2  2xy = x^2  y^2)\) \((y^2  2xy =  y^2)\) \((2y^2  2xy = 0)\) \((y(y  x) = 0)\) y = x So either x = ? or y = ? (1) \((x = 5)\) xy = 5 * 5 = 25 SUFFICIENT. (2) \((xy = 0)\) x = y MANY Possibilities INSUFFICIENT. IMO Answer A.
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If (x  y)^2 = x^2  y^2, what is the value of the nonzero integer xy
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Updated on: 15 Jan 2020, 00:56
from given info we can say ; ( xy)^2 = ( x+y) ( xy) simplify the given expression we get 2y^2= 2xy or y=x #1 x=5 so y=5 ; xy= 25 sufficient #2 xy=0 so x+y=0 value of x & y are same but opposite sign insufficient as x*y will vary as it can be zero and non zero both of many possible values insufficient IMO A
If (x−y)2=x2−y2, what is the value of the nonzero integer xyxy?
(1) x=5x=5
(2) x−y=0
Originally posted by Archit3110 on 14 Jan 2020, 07:43.
Last edited by Archit3110 on 15 Jan 2020, 00:56, edited 1 time in total.



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Re: If (x  y)^2 = x^2  y^2, what is the value of the nonzero integer xy
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14 Jan 2020, 09:42
Given, \((x−y)^2=x^2−y^2\) & nonzero integer xy. So, \(x, y ≠ 0\) > \(x^2 + y^2  2xy  x^2 + y^2\) > \(2y^2  2xy = 0\) > \(2y(y  x) = 0\) Since, \(y ≠ 0, y  x = 0\) > \(y = x\)
(1) \(x = 5\) > \(y = x = 5\) > \(xy = 5*5 = 25\) > Sufficient
(2) \(x  y = 0\) > \(x = y\) So, \(xy = x*x = x^2\) > No definite value! > Insufficient
Option A



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Re: If (x  y)^2 = x^2  y^2, what is the value of the nonzero integer xy
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14 Jan 2020, 22:03
Re: If (x  y)^2 = x^2  y^2, what is the value of the nonzero integer xy
(xy)2= x2+y22xy
x^2+y^22xy=x^2  y^2
x^2 cancels out
y^22xy=y^2
2y^22xy=0
y^2xy=0
Therefor y=0 or yx=0
Statement 1:
X=5. if we substitute this in the previous equation we get the values x and y as 5
hence statement 1 is sufficient
Statement 2: xy=0
This is non conclusive as the values can be same or can also be 0
Hence IMO A



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Re: If (x  y)^2 = x^2  y^2, what is the value of the nonzero integer xy
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14 Jan 2020, 22:23
Ans: A
(x−y)2=x2−y2 x2+y22xy=x2y2 y(yx)=0
so, y=0 or y=x
now y cannot be 0 as xy is the nonzero integer as mentioned
so y=x only possible
a states x=5
so, xy=25



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Re: If (x  y)^2 = x^2  y^2, what is the value of the nonzero integer xy
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14 Jan 2020, 23:15
Given that (xy)^2 = x^2  y^2, we are to find the value of the nonzero integer xy. It is worth noting that (xy)^2 can only equal x^2  y^2 when x=y or xy=0. So, to determine xy, we only need to know the value of x or y as xy=x^2=y^2
Statement 1: x=5 This is sufficient as x=y=5 and xy=5*5=25.
Statement 2: x−y=0 Insufficient. we already know from the question stem that xy=0 or x=y. We need an actual value of x or y in order to determine xy. Since that information is not provided, there are infinite possibilities.
The answer is A.



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Re: If (x  y)^2 = x^2  y^2, what is the value of the nonzero integer xy
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15 Jan 2020, 00:44
Remember (x+y)^2 =x^2+y^2+2xy (xy)^2= x^2+y^22xy (x^2y^2) = (xy)(x+y) Think that’s what you missed Archit3110 wrote: from given info we can say ; ( xy)^2 = ( x+y) ( xy) (xy)=(x+y) #1 x=5 insufficient as y is not know ; and y has to be 0 but its against condition #2 xy=0 so x+y=0 value of x & y are same but opposite sign insufficient as x*y will vary from 1 & 2 x=5 so y = 5 x*y = 25 IMO C sufficient
If (x−y)2=x2−y2, what is the value of the nonzero integer xyxy?
(1) x=5x=5
(2) x−y=0 Posted from my mobile device




Re: If (x  y)^2 = x^2  y^2, what is the value of the nonzero integer xy
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15 Jan 2020, 00:44






