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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8007
GMAT 1: 760 Q51 V42 GPA: 3.82
If (x-7)^2=-|y-5|, xy=?  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 42% (01:32) correct 58% (01:48) wrong based on 120 sessions

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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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Math Expert V
Joined: 02 Aug 2009
Posts: 7960
Re: If (x-7)^2=-|y-5|, xy=?  [#permalink]

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3
3
MathRevolution wrote:
[GMAT math practice question]

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
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If (x-7)^2=-|y-5|, xy=?  [#permalink]

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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.
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Re: If (x-7)^2=-|y-5|, xy=?  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

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

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

|y-5|= sqrt ( y-5)^2

and
(x-7)^2 = sqrt ( (x-5)^2
squaring both sides
(x-7) = (x-5)^2
solve
y^2-10y+32-x=0-- ( 1)

x*y=35
x=7 & y = 5
satisfies the eqn ( 1)
so IMO C
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Joined: 16 Nov 2015
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If (x-7)^2=-|y-5|, xy=?  [#permalink]

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I assume

x=7 because (x-7)=0, therefore x= 7 when you rearrange

then
7= -|y-5|
7= -(y-5)
7= -y+5
y= -2

Therefore x*y= -14

Is it E based on my assumption above? I don't think so but made sense to me.
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Location: India
Re: If (x-7)^2=-|y-5|, xy=?  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

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

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

We can start with plugging in the values for x and y

Only D when plugged in the $$(x-7)^2=-|y-5|$$, gives equal values

1 * 5 or 5 * 1
1 * 7 or 7 * 1
3 * 4 or 4 * 3 or 2 * 6 or 6 * 2
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Re: If (x-7)^2=-|y-5|, xy=?  [#permalink]

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Albs wrote:
I assume

x=7 because (x-7)=0, therefore x= 7 when you rearrange

then
7= -|y-5|
7= -(y-5)
7= -y+5
y= -2

Therefore x*y= -14

Is it E based on my assumption above? I don't think so but made sense to me.

Hi Albs

the highlightedvalue when substituted back in the bold part should had satisfied the modulus, which it doesn't do, Therefore the value cannot be applicable to this case.

so you got y = -2

lets put it back in 7= -|y-5|

7 ! = - 7

You have to search for different cases for x and y to satisfy (x−7)^2=−|y−5|

But then you are provided with the product of x and y, just substitute them in place of x and y and you should be good.
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If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
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If (x-7)^2=-|y-5|, xy=?  [#permalink]

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MathRevolution 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).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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GMAT 1: 570 Q43 V26 GMAT 2: 660 Q48 V34 Re: If (x-7)^2=-|y-5|, xy=?  [#permalink]

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I have a query.

|y-5| will always be +ve an (x-7)^2 = -|y-5| can't be possible as LHS is a square number?
So how can we find a deterministic answer in such case?

Regards,
Rishav
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GMAT 1: 570 Q43 V26 GMAT 2: 660 Q48 V34 Re: If (x-7)^2=-|y-5|, xy=?  [#permalink]

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rish2708 wrote:
I have a query.

|y-5| will always be +ve an (x-7)^2 = -|y-5| can't be possible as LHS is a square number?
So how can we find a deterministic answer in such case?

Regards,
Rishav

Got it.. only 0 it can satisfy!! Thanks
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Re: If (x-7)^2=-|y-5|, xy=?  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

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

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

Since Square of any number is >=0; $$A^2>=0$$
$$(x-7)^2=A,-|y-5|=B$$
since A cant be negative ,So B=0
y=5 and x=7
X*Y=35
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8007
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If (x-7)^2=-|y-5|, xy=?  [#permalink]

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=>
$$(x-7)^2=-|y-5|$$
$$=> (x-7)^2+|y-5| = 0$$
$$=> x = 7$$ and $$y = 5$$
This yields $$xy = 35$$.

Therefore, the answer is D.
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Re: If (x-7)^2=-|y-5|, xy=?  [#permalink]

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MathRevolution

Sorry to say but your answer gives no additional knowledge and thus is not really useful in this case.

The point to observe is that a perfect square has been equated a negative absolute value function.

We must note that a perfect square can never be negative. It can only achieve a value of zero or positive. Same is the case with absolute value function.

This, to ensure that both the functions yield the same answer, we must equate both the function to zero.
This, x=7 and y=5

XY = 35

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Math Revolution GMAT Instructor V
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Posts: 8007
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If (x-7)^2=-|y-5|, xy=?  [#permalink]

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KanishkM wrote:
Albs wrote:
I assume

x=7 because (x-7)=0, therefore x= 7 when you rearrange

then
7= -|y-5|
7= -(y-5)
7= -y+5
y= -2

Therefore x*y= -14

Is it E based on my assumption above? I don't think so but made sense to me.

Hi Albs

the highlightedvalue when substituted back in the bold part should had satisfied the modulus, which it doesn't do, Therefore the value cannot be applicable to this case.

so you got y = -2

lets put it back in 7= -|y-5|

7 ! = - 7

You have to search for different cases for x and y to satisfy (x−7)^2=−|y−5|

But then you are provided with the product of x and y, just substitute them in place of x and y and you should be good.

If x = 7, then we have (x-7)^2 = -|y-5| or (7-7)^2 = -|y-5|.
Thus -|y-5| = 0 and we have y = 5.

x*y = 7*5 = 35.
_________________ Re: If (x-7)^2=-|y-5|, xy=?   [#permalink] 09 Feb 2019, 16:32
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