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Manager  Joined: 12 Nov 2015
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If x/|y| = -1 which of the following must be true?  [#permalink]

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Question Stats: 67% (01:02) correct 33% (01:04) wrong based on 1112 sessions

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If x/|y| = -1 which of the following must be true?

A) x = -y
B) x = y
C) x = y^2
D) x^2 = y^2
E) x^3 = y^3
Math Expert V
Joined: 02 Sep 2009
Posts: 62498
If x/|y| = -1 which of the following must be true?  [#permalink]

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Avigano wrote:
If x/|y| = -1 which of the following must be true?

A) x = -y
B) x = y
C) x = y^2
D) x^2 = y^2
E) x^3 = y^3

x/|y| = -1

|y| = -x, this implies that x is 0 or negative.

Square: y^2 = x^2.

Alternatively you can try number plugging: try x = -2 and y = 2 or -2. You'll see that only D is always true.
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Re: If x/|y| = -1 which of the following must be true?  [#permalink]

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4
4
Avigano wrote:
If x/|y| = -1 which of the following must be true?

A) x = -y
B) x = y
C) x = y^2
D) x^2 = y^2
E) x^3 = y^3

Hi! There,

x/|y| = -1
x= -1 |y|

Squaring both sides
x^2= (-1 |y|) ^2= y^2

Squaring any -ve number yields +ve number.

Let's see why other options are not right
A) x = -y What if x= 2 and y= 2. This does'nt hold good then.

B) x = y If x=-2 and y=2. This is not right.

C) x = y^2 This means x is +ve and |y| is always +ve. In this case x/|y| can not be -ve. not correct.

D) x^2 = y^2. Explained above.

E) x^3 = y^3. If x= -2 and y= 2. This will not hold true.

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Manager  Joined: 12 Nov 2015
Posts: 55
Location: Uruguay
Concentration: General Management
Schools: Goizueta '19 (A)
GMAT 1: 610 Q41 V32
GMAT 2: 620 Q45 V31
GMAT 3: 640 Q46 V32
GPA: 3.97
Re: If x/|y| = -1 which of the following must be true?  [#permalink]

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Thank you Bunuel, clearer than spring water.
Retired Moderator G
Joined: 26 Nov 2012
Posts: 553
Re: If (x/|y|)=-1,Which of the following must be true ?  [#permalink]

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1
NandishSS wrote:
If (x/|y|)=-1,Which of the following must be true ?
A) x = —y
B) x = y
C) x=y^2
D) x^2 = y^2
E) x^3 = y^3

Quick way to solve?

Why option A is wrong

Given (x/|y|)=-1

Then we can take two cases and the options must satisfy both cases.
1. x/y = -1
2. x/-y = -1

Option A : sub x = -y in two cases then in one case satisfies and the other doesn't
B) x = y : sub x = y in two cases , then in one case satisfies and the other doesn't
C) x=y^2 : sub x = y^2 in two cases then in one case satisfies and the other doesn't
D) x^2 = y^2 => x = √y^2 = |y| in both case we get the same result. ( in one case assume +ve and other case -ve)--> Correct option.
E) x^3 = y^3 => x = y => sub x = y in two cases , then in one case satisfies and the other doesn't...
Intern  Joined: 13 May 2014
Posts: 11
Re: If (x/|y|)=-1,Which of the following must be true ?  [#permalink]

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2
NandishSS wrote:
If (x/|y|)=-1,Which of the following must be true ?
A) x = —y
B) x = y
C) x=y^2
D) x^2 = y^2
E) x^3 = y^3

Quick way to solve?

Why option A is wrong

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Math Expert V
Joined: 02 Aug 2009
Posts: 8311
Re: If x/|y| = -1 which of the following must be true?  [#permalink]

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1
2
mjhoon1004 wrote:
Hello Gmatclubbers,

I stumbled upon this question on one of the Prep packs and am having a trouble understanding it.
I'd appreciate if any of you can help explain. Thanks.

Hi,

If x/|y|=-1....
Two things can be made out...
X must be numerically similar to y, may not be the sign...
X must be NEGATIVE....
We do not know whether y is +or-......
So if we say x=-y and y is -, x will become +, and ans will be 1...
Only x^2=y^2 will be true irrespective of SIGN....
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Re: If x/|y| = -1 which of the following must be true?  [#permalink]

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mjhoon1004 wrote:
Hello Gmatclubbers,

I stumbled upon this question on one of the Prep packs and am having a trouble understanding it.
I'd appreciate if any of you can help explain. Thanks.

x / |y| = -1

y can be +ve or -ve

case 1 : y is +ve
x/y = -1 implies x = -y
case 2 : y is -ve
x/-y = -1 implies x = y

from 1 and 2 we can always say x2 = y2
i would go with D

whats OA?
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Re: If x/|y| = -1 which of the following must be true?  [#permalink]

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Since absolute value is always >= 0, we can safely square it.

x / |y| = -1

Square both sides.

x^2 / y^2 = 1
x^2 = y^2

This must be true.

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Re: If x/|y| = -1 which of the following must be true?  [#permalink]

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1
Hi mjhoon1004,

This question can be solved by TESTing VALUES.

We're told that X/|Y| = -1. We're asked which of the following MUST be true (meaning "which is ALWAYS TRUE no matter how many different examples you come up with??").

IF....
X = -2
Y = 2
Then we can eliminate Answers B, C and E

IF...
X = -2
Y = -2
Then we can eliminate Answer A

GMAT assassins aren't born, they're made,
Rich
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GMAT 2: 620 Q42 V33 If x/|y|=-1, which of the following must be true?  [#permalink]

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2
If $$\frac{x}{|y|}=-1$$, which of the following must be true?

A)$$x=-y$$
B)$$x=y$$
C) $$x=y^2$$
D) $$x^2=y^2$$
E) $$x^3=y^3$$
Math Expert V
Joined: 02 Aug 2009
Posts: 8311
Re: If x/|y|=-1, which of the following must be true?  [#permalink]

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2
felippemed wrote:
If $$\frac{x}{|y|}=-1$$, which of the following must be true?

A)$$x=-y$$
B)$$x=y$$
C) $$x=y^2$$
D) $$x^2=y^2$$
E) $$x^3=y^3$$

Hi

$$\frac{x}{|y|}=-1$$ means the NUMERIC value of x and y has to be same , sign may not be..
The second point is that since |y| will be positive, x will be NEGATIVE..
Now two cases
1) x = y...
x=y=-3..
So $$\frac{-3}{|-3|}=\frac{-3}{3}=-1$$

2) x=-y..
X=-3, y=3...
$$\frac{-2}{|3|}=-1$$..

ONLY an EVEN power can make two values equal in both cases

Say A is the answer then D also must be true.. but can we have two answers..NO
If B is the answer, then D and E also must be true..
This way you can home on to D
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Re: If x/|y|=-1, which of the following must be true?  [#permalink]

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felippemed wrote:
If $$\frac{x}{|y|}=-1$$, which of the following must be true?

A)$$x=-y$$
B)$$x=y$$
C) $$x=y^2$$
D) $$x^2=y^2$$
E) $$x^3=y^3$$

$$\frac{x}{|y|}=-1 \implies x=-|y| \implies x^2 = y^2$$

C is out.
$$x=-|y| \implies x=y$$ if y<0 or $$x=-y$$ if y>0. A, B is out.
$$x=-|y| \implies x^3=-|y|^3 \implies x^3=y^3$$ if y<0 or $$x^3=-y^3$$ if y>0. E is out
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Re: If x/|y| = -1 which of the following must be true?  [#permalink]

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x/sqrt (y^2)=-1
x=-sqrt(y^2)
Squaring both side
X^2=y^2
D

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GMAT 2: 620 Q42 V33 If x/|y| = -1 which of the following must be true?  [#permalink]

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Here is my theoretical approach to the problem.

A real good one to solidify concepts

Posted from my mobile device

TIP: If you are still struggling with the objective of the question, look at the equations as sausage-maker machines. The goal is to produce similar products despite the ingredients (but the amount of them must be equal). In other words, if I plug in signals within them, the output MUST be equal.
Attachments Screenshot_20161202-102216.jpg [ 411.95 KiB | Viewed 13174 times ]

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Re: If x/|y| = -1 which of the following must be true?  [#permalink]

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1
Why would we square a modulus??? Omg I dont understand ANYTHING if this...
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Re: If x/|y| = -1 which of the following must be true?  [#permalink]

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1
If x/|y| = -1 which of the following must be true?

A) x = -y
B) x = y
C) x = y^2
D) x^2 = y^2
E) x^3 = y^3

my 2 cents.

x=-|y| this means x=-y or x=-(-y)
So, A) and B) are out.
C), doens't make sense.
D), if we square both then signs in front of a variable does not matter so this is good.
E), if we cute, then negative signs remain, so out.

Hence D.
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Re: If x/|y| = -1 which of the following must be true?  [#permalink]

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TEST IT: to get -1, X could be -1, then y could be -1 or 1.

a) -1 = - (1) but not -(-1) ---> OUT
b) -1 = -1 but not 1 ---> OUT
c) -1 not equal to (-1)^2 nor (1)^2 ---> OUT
d) (-1)^2 = (-1)^2 and (1)^2 ---> CORRECT
e) (-1)^3 = (-1)^3 but not (1)^3 ---> OUT
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Re: If x/|y| = -1 which of the following must be true?  [#permalink]

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Bunuel wrote:
Avigano wrote:
If x/|y| = -1 which of the following must be true?

A) x = -y
B) x = y
C) x = y^2
D) x^2 = y^2
E) x^3 = y^3

x/|y| = -1

|y| = -x, this implies that x is 0 or negative.

Square: y^2 = x^2.

Alternatively you can try number plugging: try x = -2 and y = 2 or -2. You'll see that only D is always true.

Absolute value cannot equal negative number. Shouldn't the representation be x=-|y| instead of |y|=-x?
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Re: If x/|y| = -1 which of the following must be true?  [#permalink]

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Divyadisha - I have a question. My understanding was that you can square both sides in an equation when both sides are positive. Is that true or am I not looking at this question right? Re: If x/|y| = -1 which of the following must be true?   [#permalink] 16 Dec 2019, 11:07

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