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If |x|y < 0, which of the following must be positive?

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If |x|y < 0, which of the following must be positive?  [#permalink]

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New post 22 Sep 2018, 05:48
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A
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D
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If |x|y < 0, which of the following must be positive?

a) |x| - y
b) |y| - x
c) -|x-y|
d) x|y|
e) xy

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Posts: 3331
Location: Canada
Re: If |x|y < 0, which of the following must be positive?  [#permalink]

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New post 22 Sep 2018, 08:37
Top Contributor
bettatantalo wrote:
If |x|y < 0, which of the following must be positive?

a) |x| - y
b) |y| - x
c) -|x-y|
d) x|y|
e) xy

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GIVEN: |x|y < 0

|x| ≥ 0 so, in order for |x|y < 0, it must be the case that y is NEGATIVE

Now check the answer choices...

a) |x| - y
We know that |x| is greater than or equal to 0.
Also, y is negative, so when we SUBTRACT y from |x|, we are actually adding a positive value to |x|. For example, subtracting -3 is the same as adding 3
So, |x| - y = some number greater than or equal to 0 + some positive value = positive

Answer: A

Cheers,
Brent
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Re: If |x|y < 0, which of the following must be positive?  [#permalink]

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New post 22 Sep 2018, 08:46
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Top Contributor
bettatantalo wrote:
If |x|y < 0, which of the following must be positive?

a) |x| - y
b) |y| - x
c) -|x-y|
d) x|y|
e) xy



The key here is MUST BE TRUE
If we can find an example in which an answer choice is NOT true, then we can eliminate it.

GIVEN: |x|y < 0
One possible pair of value for x and y is: x = 1 and y = -1
Notice that |x|y < 0 becomes |1|(-1) < 0. WORKS

Now plug x = 1 and y = -1 into the answer choices...

a) |1| - (-1) = 2. This IS positive. So, keep A
b) |-1| - (1) = 0. This is NOT positive. ELIMINATE B
c) -|1 - (-1)| = -2. This is NOT positive. ELIMINATE C
d) 1|(-1)| = 1. This IS positive. So, keep D
e) (1)(-1) = -1. This is NOT positive. ELIMINATE E

We're left with 2 remaining answer choices.
Let's test another pair of value for x and y

How about: x = -1 and y = -1
Notice that |x|y < 0 becomes |-1|(-1) < 0. WORKS

Now plug x = -1 and y = -1 into the 2 remaining answer choices...

a) |-1| - (-1) = 2. This IS positive. So, keep A
d) -1|(-1)| = -1. This is NOT positive. ELIMINATE D

Answer: D

Cheers,
Brent
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Re: If |x|y < 0, which of the following must be positive? &nbs [#permalink] 22 Sep 2018, 08:46
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If |x|y < 0, which of the following must be positive?

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