Around the World in 80 Questions (Day 6): If x and y are nonzero

Question

If x and y are nonzero numbers, does |xy| = -xy ?

(1) Both x and y are negative numbers.
(2) x - y = 0.

rsvelc · Answer

|xy| = -xy
Pre-think:
result of Modulus is never negative, but if the question asks that result of modulus is negative then, the product xy has to be negative.
Which means x and y has to be opposite sign (Given that both the numbers are not zero)

1) Both x and y are negative numbers
If so, product will be positive and the absolute value of product is positive.
This clearly says |xy| != -xy. Hence, statement 1 is Sufficient

2) x-y=0
which means x = y 
Two cases either x and y are positive or x and y are negative. But their product always remains positive.
This clearly says |xy| != -xy. Hence, statement 2 is Sufficient

Hence Answer D.

missionmba2025 · Answer

|p| = -p indicates p is negative (or p is zero, but we can ignore zero). We need to find out whether xy is negative.

(1) Both x and y are negative numbers.

If x and y are negative number, the product xy is positive. Hence xy is not negative.

Sufficient.

(2) x - y = 0

This can happen when x and y share the same magnitude and the same sign. We already know that x and y cannot be zero. Hence, x and y are both positive or both negative.

In both the cases, xy is positive. Hence xy is not negative.

Sufficient.

IMO D

TargetKellogg2024 · Answer

If x and y are nonzero numbers, does |xy| = -xy ?

|a| = -a ONLY when a = (-)ve. So the question is asking if xy is negative

(1) Both x and y are negative numbers. 
- Since x and y both are negative, therefore, (-)(-) = (+). Therefore, xy is (+)ve. Therefore, |xy| = xy
Hence, 1 is sufficient

(2) x - y = 0.
- Since x-y=0, x=y. Therefore, x and y both have same signs. Therefore, xy is positive. Therefore, |xy| = xy
Hence, 2 is sufficient

Therefore, the answer is D

Rahulbasu007 · Answer

Given: 
If x and y are nonzero numbers, does |xy| = -xy ?
(1) Both x and y are negative numbers.
(2) x - y = 0.

Let's evaluate each statement one by one.

Statement (1): Both x and y are negative numbers.

Both x and y are negative.
The product xy will be positive.
The absolute value of a positive number is always positive, so |xy| will be positive. 
However, -xy will be negative (since xy is positive). Therefore, |xy| ≠ -xy.
We can get a definite answer for this, so, statement (1) is sufficient to answer the question.

Statement (2): x - y = 0.

This implies that x = y. We can consider 3 cases here:

Case 1: Both x and y are positive, then xy is positive, so |xy| = xy, and -xy is negative. So |xy| ≠ -xy.
Case 2: Both x and y are negative, then, |xy| ≠ -xy. (already solved in statement 1)
Case 3: We cannot take x = 0 or y = 0 as it's given in the statement that the two numbers are non zero numbers.
We can also not take x = -y in this case as it contradicts the statement itself.
Also, taking a fraction does not impact anything here.

So, I think statement (2) is also sufficient to answer the question.

I will go with option D.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Around the World in 80 Questions (Day 6): If x and y are nonzero

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Around the World in 80 Questions (Day 6): If x and y are nonzero

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards