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

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) \(x^3 = y^3\)


Given: \(\frac{x}{|y|} = -1\);

Cross-multiply: \(|y| = -x\), this implies that x is 0 or negative.

Square: \(y^2 = x^2\).

Answer: D.

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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Hi! There,

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

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

D is the answer

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.

D is the answer
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Thank you Bunuel, clearer than spring water.

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...

Sent from my SM-N920R4 using GMAT Club Forum mobile app

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

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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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
So D is answer..

Also choices give away answer..
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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STRATEGY: Upon reading any GMAT Problem Solving question, we should always ask, Can I use the answer choices to my advantage?
In this case, we can easily test values that satisfy the given equation.
Now let's give ourselves up to 20 seconds to identify a faster approach.
In this case, we we might also try some algebraic manipulation, but it's not immediately clear how successful that would be.
So let's go with testing values.

It may take a little bit of testing to find some x- and y-values that satisfy the equation x/|y| = -1.
One possible solution is x = -2 and y = 2 (since (-2)/|2| = -1)

Now let's plug x = -2 and y = 2 into the five answer choices to see which ones are true. We get:
A) -2 = -2. TRUE. Keep.
B) -2 = 2. Not true. Eliminate.
C) -2 = 2². Not true. Eliminate.
D) (-2)² = 2². TRUE. Keep.
E) (-2)³ = 2³. Not true. Eliminate.

We're down to choices A and D.

Now let's find another pair of x- and y-values that satisfy the equation x/|y| = -1.
Another possible solution is x = -2 and y = -2 (since (-2)/|-2| = -1)

Plug x = -2 and y = 2 into the 2 remaining answer choices:
A) -2 = -(-2). Not true. Eliminate.
D) (-2)² = (-2)². TRUE. Keep.

Answer: D
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