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# xy=? 1) y=x-1 2) y^2=-|x-1|

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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xy=? 1) y=x-1 2) y^2=-|x-1|  [#permalink]

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26 Jul 2017, 01:10
00:00

Difficulty:

65% (hard)

Question Stats:

46% (01:09) correct 54% (01:46) wrong based on 79 sessions

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$$xy=?$$

1) $$y=x-1$$
2) $$y^2=-|x-1|$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"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" Retired Moderator Status: Long way to go! Joined: 10 Oct 2016 Posts: 1331 Location: Viet Nam Re: xy=? 1) y=x-1 2) y^2=-|x-1| [#permalink] ### Show Tags 26 Jul 2017, 02:11 2 MathRevolution wrote: $$xy=?$$ 1) $$y=x-1$$ 2) $$y^2=-|x-1|$$ (1) We don't know the value of x and y. Insufficient, (2) Since $$y^2 \geq 0 \quad \forall y \in R$$ and $$-|x-1| \leq 0 \quad \forall x \in R$$, we have $$y^2=-|x-1|=0 \implies y=0$$ and $$x=1 \implies xy=0$$. Sufficient, The answer is B. _________________ Intern Joined: 16 Apr 2017 Posts: 44 xy=? 1) y=x-1 2) y^2=-|x-1| [#permalink] ### Show Tags 26 Jul 2017, 03:49 nguyendinhtuong wrote: MathRevolution wrote: $$xy=?$$ 1) $$y=x-1$$ 2) $$y^2=-|x-1|$$ (1) We don't know the value of x and y. Insufficient, (2) Since $$y^2 \geq 0 \quad \forall y \in R$$ and $$-|x-1| \leq 0 \quad \forall x \in R$$, we have $$y^2=-|x-1|=0 \implies y=0$$ and $$x=1 \implies xy=0$$. Sufficient, The answer is B. for 2) there could be other pairs of values of x and y which could satisfy the equation. For example the only possibility is the below equation y^2=-|x-1|==> y^2= x-1==> which could mean different x and y pairs _________________ KUDOS please, if you like the post or if it helps Intern Joined: 06 Feb 2016 Posts: 47 Location: Poland Concentration: Finance, Accounting GMAT 1: 730 Q49 V41 GPA: 3.5 Re: xy=? 1) y=x-1 2) y^2=-|x-1| [#permalink] ### Show Tags 26 Jul 2017, 11:57 Supermaverick wrote: nguyendinhtuong wrote: MathRevolution wrote: $$xy=?$$ 1) $$y=x-1$$ 2) $$y^2=-|x-1|$$ (1) We don't know the value of x and y. Insufficient, (2) Since $$y^2 \geq 0 \quad \forall y \in R$$ and $$-|x-1| \leq 0 \quad \forall x \in R$$, we have $$y^2=-|x-1|=0 \implies y=0$$ and $$x=1 \implies xy=0$$. Sufficient, The answer is B. for 2) there could be other pairs of values of x and y which could satisfy the equation. For example the only possibility is the below equation y^2=-|x-1|==> y^2= x-1==> which could mean different x and y pairs Other values are not possible. y^2 is always greater than or equal to zero. The same is true for |x-1|. As there is the negative sign before |x-1|, the only possible option is when y^2=0 which means y is equal to 0. Also, |x-1|=0 which means x=0. I hope it helps Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8024 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: xy=? 1) y=x-1 2) y^2=-|x-1| [#permalink] ### Show Tags 28 Jul 2017, 01:15 ==> $$a^2+b^2=0$$ or $$|a|+|b|=0$$ is satisfied by $$a=b=0$$ only. Thus, according to the same logic, $$a^2+|b|=0$$ also must be $$a=b=0$$. Then, you get 2) $$y^2=-|x-1|, y^2+|x-1|=0$$, which is y=0 and x=1. The answer is B. Answer: B _________________ 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"
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xy=? 1) y=x-1 2) y^2=-|x-1|  [#permalink]

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Updated on: 30 Jul 2017, 05:51
3
MathRevolution wrote:
$$xy=?$$

1) $$y=x-1$$
2) $$y^2=-|x-1|$$

We need to find product of x and y

1)
y = x - 1

we do not know the value of either of x or y

Hence Insufficient
2)

y^2 = - | x-1 |

Case 1 : when | x - 1 | is negative

y^2 = -[-(x - 1)]
y^2 = x - 1 ....................equation 1

Case 2 : when | x - 1 | is positive

y^2 = -[(x - 1)]
y^2 = -x + 1 ....................equation 2

equation 1 = equation 2 (as both are equal to y^2 )

x-1 = -x + 1
x = 1

Now keeping value of x in any of the 2 equations

y^2 = -x + 1 (Now x = 1)
y^2 = -1 + 1
y^2 = 0 so y is also 0

It means x * y = 0

Hence B

Thanks

Originally posted by rocko911 on 29 Jul 2017, 01:47.
Last edited by rocko911 on 30 Jul 2017, 05:51, edited 1 time in total.
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Re: xy=? 1) y=x-1 2) y^2=-|x-1|  [#permalink]

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29 Jul 2017, 04:59
Here we have to assume that Y^2 shouldn't be negative? In general in GMAT square of any number cant be negative?
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Re: xy=? 1) y=x-1 2) y^2=-|x-1|  [#permalink]

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29 Jul 2017, 05:08
ashokjha1986 wrote:
Here we have to assume that Y^2 shouldn't be negative? In general in GMAT square of any number cant be negative?

Not only in GMAT , in real world numbers and mathematics , SQUARE OF ANY NUMBER IS ALWAYS POSITIVE
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Re: xy=? 1) y=x-1 2) y^2=-|x-1|  [#permalink]

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26 Mar 2019, 07:21
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Re: xy=? 1) y=x-1 2) y^2=-|x-1|   [#permalink] 26 Mar 2019, 07:21
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