GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Oct 2019, 19:21

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8007
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

05 Feb 2019, 01:13
00:00

Difficulty:

75% (hard)

Question Stats:

42% (01:32) correct 58% (01:48) wrong based on 120 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 $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" ##### Most Helpful Expert Reply Math Expert Joined: 02 Aug 2009 Posts: 7960 Re: If (x-7)^2=-|y-5|, xy=? [#permalink] ### Show Tags 07 Feb 2019, 20:28 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 _________________ ##### General Discussion NUS School Moderator Joined: 18 Jul 2018 Posts: 1024 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) If (x-7)^2=-|y-5|, xy=? [#permalink] ### Show Tags 05 Feb 2019, 01:30 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 D is the answer. _________________ Press +1 Kudos If my post helps! GMAT Club Legend Joined: 18 Aug 2017 Posts: 4999 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: If (x-7)^2=-|y-5|, xy=? [#permalink] ### Show Tags 05 Feb 2019, 02:29 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) seeing answer option x*y=35 x=7 & y = 5 satisfies the eqn ( 1) so IMO C Intern Joined: 16 Nov 2015 Posts: 30 Location: United Kingdom If (x-7)^2=-|y-5|, xy=? [#permalink] ### Show Tags 05 Feb 2019, 04:57 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. Director Joined: 09 Mar 2018 Posts: 996 Location: India Re: If (x-7)^2=-|y-5|, xy=? [#permalink] ### Show Tags 05 Feb 2019, 05:14 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 _________________ If you notice any discrepancy in my reasoning, please let me know. Lets improve together. Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up. Director Joined: 09 Mar 2018 Posts: 996 Location: India Re: If (x-7)^2=-|y-5|, xy=? [#permalink] ### Show Tags 05 Feb 2019, 05:19 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. _________________ If you notice any discrepancy in my reasoning, please let me know. Lets improve together. Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up. GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 935 If (x-7)^2=-|y-5|, xy=? [#permalink] ### Show Tags 05 Feb 2019, 06:43 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. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net Manager Joined: 12 Jul 2017 Posts: 207 GMAT 1: 570 Q43 V26 GMAT 2: 660 Q48 V34 Re: If (x-7)^2=-|y-5|, xy=? [#permalink] ### Show Tags 05 Feb 2019, 07:40 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 Manager Joined: 12 Jul 2017 Posts: 207 GMAT 1: 570 Q43 V26 GMAT 2: 660 Q48 V34 Re: If (x-7)^2=-|y-5|, xy=? [#permalink] ### Show Tags 05 Feb 2019, 07:41 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 Manager Joined: 05 Feb 2016 Posts: 168 Location: India Concentration: General Management, Marketing WE: Information Technology (Computer Software) Re: If (x-7)^2=-|y-5|, xy=? [#permalink] ### Show Tags 05 Feb 2019, 10:28 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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8007 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If (x-7)^2=-|y-5|, xy=? [#permalink] ### Show Tags 07 Feb 2019, 18:29 => $$(x-7)^2=-|y-5|$$ $$=> (x-7)^2+|y-5| = 0$$ $$=> x = 7$$ and $$y = 5$$ This yields $$xy = 35$$. Therefore, the answer is D. Answer: D _________________ 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$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Manager
Joined: 29 Dec 2018
Posts: 57
Location: India
Schools: HBS '22, Wharton '22

### Show Tags

07 Feb 2019, 19:28
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: 8007
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

09 Feb 2019, 16:32
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 \$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Re: If (x-7)^2=-|y-5|, xy=?   [#permalink] 09 Feb 2019, 16:32
Display posts from previous: Sort by