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14 Jan 2020, 01:46
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Difficulty:
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Question Stats:
62% (01:46) correct
38%
(01:43)
wrong
based on 268
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If \((x - y)^2 = x^2 - y^2\), what is the value of the non-zero integer \(xy\)?
(1) \(x = 5\)
(2) \(x-y = 0\)
Are You Up For the Challenge: 700 Level Questions
14 Jan 2020, 02:18
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If \((x - y)^2 = x^2 - y^2\), what is the value of the non-zero 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
\(y^2 - 2xy = - y^2 \) .. re-writing
\(2y^2 = 2xy \) .. cancelling \(2y\) both side, we get
\(y = x\) .. sufficient ( xy = 25)
A D /B C E
(2) \(x-y = 0\)
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
(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
\(y^2 - 2xy = - y^2 \) .. re-writing
\(2y^2 = 2xy \) .. cancelling \(2y\) both side, we get
\(y = x\) .. sufficient ( xy = 25)
A D /
(2) \(x-y = 0\)
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
14 Jan 2020, 03:31
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Constraint: (x-y)^2 = x^2-y^2
Question: Value of non-zero Integer xy?
Note! xy = non-zero 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= 5
We know y=x ,and x= 5
.: xy = (5)(5)=25
(Sufficient)
(2) x=y
Just reiterating the constraint
Say x=5 ,xy =25 , again x=-2 ,xy=4
(Ain’t Sufficient)
Hit that A
Posted from my mobile device
Question: Value of non-zero Integer xy?
Note! xy = non-zero 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= 5
We know y=x ,and x= 5
.: xy = (5)(5)=25
(Sufficient)
(2) x=y
Just reiterating the constraint
Say x=5 ,xy =25 , again x=-2 ,xy=4
(Ain’t Sufficient)
Hit that A
Posted from my mobile device
