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• ### $450 Tuition Credit & Official CAT Packs FREE February 15, 2019 February 15, 2019 10:00 PM EST 11:00 PM PST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### Free GMAT practice February 15, 2019 February 15, 2019 10:00 PM EST 11:00 PM PST Instead of wasting 3 months solving 5,000+ random GMAT questions, focus on just the 1,500 you need. # If (x-7)^2=-|y-5|, xy=?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6949 GMAT 1: 760 Q51 V42 GPA: 3.82 If (x-7)^2=-|y-5|, xy=? [#permalink] ### Show Tags 05 Feb 2019, 00:13 00:00 Difficulty: 65% (hard) Question Stats: 40% (01:40) correct 60% (01:48) wrong based on 60 sessions ### HideShow timer Statistics [GMAT math practice question] If $$(x-7)^2=-|y-5|, xy=?$$ $$A. 5$$ $$B. 7$$ $$C. 12$$ $$D. 35$$ E. cannot be determined _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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07 Feb 2019, 19:28
1
1
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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##### General Discussion
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05 Feb 2019, 00:30
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

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05 Feb 2019, 01:29
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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05 Feb 2019, 03:57
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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05 Feb 2019, 04:14
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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05 Feb 2019, 04:19
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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05 Feb 2019, 05:43
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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05 Feb 2019, 06:40
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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05 Feb 2019, 06:41
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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05 Feb 2019, 09:28
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
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GMAT 1: 760 Q51 V42
GPA: 3.82

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07 Feb 2019, 17:29
=>
$$(x-7)^2=-|y-5|$$
$$=> (x-7)^2+|y-5| = 0$$
$$=> x = 7$$ and $$y = 5$$
This yields $$xy = 35$$.

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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 29 Dec 2018 Posts: 7 Re: If (x-7)^2=-|y-5|, xy=? [#permalink] ### Show Tags 07 Feb 2019, 18:28 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 Posted from my mobile device Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6949 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If (x-7)^2=-|y-5|, xy=? [#permalink] ### Show Tags 09 Feb 2019, 15:32 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. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: If (x-7)^2=-|y-5|, xy=?   [#permalink] 09 Feb 2019, 15:32
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