If (x-7)^2=-|y-5|, xy=?

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If (x-7)^2=-|y-5|, xy=?

by Max@Math Revolution » Mon Feb 04, 2019 11:58 pm

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[GMAT math practice question]

If (x-7)^2=-|y-5|, xy=?

A. 5
B. 7
C. 12
D. 35
E. cannot be determined

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If (x-7)^2=-|y-5|, xy=?

by fskilnik@GMATH » Tue Feb 05, 2019 5:29 am
Max@Math Revolution wrote:[GMAT math practice question]

If (x-7)^2=-|y-5|, xy=?

A. 5
B. 7
C. 12
D. 35
E. cannot be determined
$${\left( {x - 7} \right)^2} = - \left| {y - 5} \right|\,\,\,\,\,\left( * \right)$$
$$? = xy$$

$$\left. \matrix{
{\left( {x - 7} \right)^2} \ge 0\,\,\, \hfill \cr
- \left| {y - 5} \right| \le 0 \hfill \cr} \right\}\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,{\left( {x - 7} \right)^2} = 0 = - \left| {y - 5} \right|\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\{ \matrix{
\,x - 7 = 0 \hfill \cr
\,y - 5 = 0 \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 5 \cdot 7 = 35$$


The correct answer is therefore (D).


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by Max@Math Revolution » Thu Feb 07, 2019 12:31 am
=>
(x-7)^2=-|y-5|
=> (x-7)^2+|y-5| = 0
=> x = 7 and y = 5
This yields xy = 35.

Therefore, the answer is D.
Answer: D