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05 Feb 2019, 01:13
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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:
65%
(hard)
Question Stats:
55% (01:34) correct
45%
(01:47)
wrong
based on 707
sessions
History
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Not Attempted Yet
[GMAT math practice question]
If \((x-7)^2=-|y-5|\) , \(xy=\)?
A. 5
B. 7
C. 12
D. 35
E. cannot be determined
If \((x-7)^2=-|y-5|\) , \(xy=\)?
A. 5
B. 7
C. 12
D. 35
E. cannot be determined
07 Feb 2019, 20:28
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MathRevolution
[GMAT math practice question]
If \((x-7)^2=-|y-5|, xy=?\)
\(A. 5\)
\(B. 7\)
\(C. 12\)
\(D. 35\)
E. cannot be determined
If \((x-7)^2=-|y-5|, xy=?\)
\(A. 5\)
\(B. 7\)
\(C. 12\)
\(D. 35\)
E. cannot be determined
A square and a modulus can never be NEGATIVE
So least value of a square or modulus is 0..
\((x-7)^2=-|y-5|\) ..
Here -|y-5| will never be positive as |y-5| is greater than or equal to 0..
A square on left side tells us that (x-7)^2=0, or x=7..
And -|y-5|=0 means y =5
Therefore xy=7*5=35
D
General Discussion
05 Feb 2019, 01:30
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If y>5, then -|y-5| = -(y-5) = 5-y
\(x^2+49-14x = 5-y\)
\(x^2+44-14x+y = 0\)........(1)
If y<5, then -|y-5| = -(-y+5) = y-5
\(x^2+49-14x = y-5\)
\(x^2+54-14x = y\)..........(2)
(1) in (2) gives
\(2x^2+98-28x = 0\)
\(x^2+49-14x = 0\)
\((x-7)^2 = 0\)
x = 7
If x = 7, then -|y-5| = 0; y = 5
xy = 35
D is the answer.
\(x^2+49-14x = 5-y\)
\(x^2+44-14x+y = 0\)........(1)
If y<5, then -|y-5| = -(-y+5) = y-5
\(x^2+49-14x = y-5\)
\(x^2+54-14x = y\)..........(2)
(1) in (2) gives
\(2x^2+98-28x = 0\)
\(x^2+49-14x = 0\)
\((x-7)^2 = 0\)
x = 7
If x = 7, then -|y-5| = 0; y = 5
xy = 35
D is the answer.
