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505-555 Level|   Absolute Values|         
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Bunuel
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Around the World in 80 Questions (Day 6): If x and y are nonzero 24 Jul 2023, 08:00
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If x and y are nonzero numbers, does |xy| = -xy ?

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


 


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Around the World in 80 Questions (Day 6): If x and y are nonzero 24 Jul 2023, 08:09
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Bunuel
If x and y are nonzero numbers, does |xy| = -xy ?

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


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|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.
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Around the World in 80 Questions (Day 6): If x and y are nonzero 24 Jul 2023, 08:39
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If x and y are nonzero numbers, does |xy| = -xy ?

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


 


This question was provided by GMAT Club
for the Around the World in 80 Questions

Win over $20,000 in prizes: Courses, Tests & more

 

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|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
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Around the World in 80 Questions (Day 6): If x and y are nonzero 24 Jul 2023, 14:59
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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
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Around the World in 80 Questions (Day 6): If x and y are nonzero 24 Jul 2023, 20:42
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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.
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