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Is |x| = y + z? 29 Nov 2022, 23:27
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Is |x| = y + z?

(1) x + y = z
(2) x < 0

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I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.
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Question:
Is |x| = y + z?
We don't know what to do when we have absolute values in the equation so we should remove it.
The question is this:
If x >= 0, is x = y + z?
and if x < 0, is -x = y + z?

(1) x + y = z
We don't know whether x is positive/zero or negative so for now we don't know what we have to answer actually (which equation we have to consider).
Not sufficient.

(2) x < 0
So our question is: Is -x = y + z?
But this statement alone doesn't even mention y and z. Not sufficient.

Using both, x is negative and we need to answer whether -x = y + z i.e. whether x = -y - z?
We know that x + y = z (statement 1) so we know that x = -y + z.
But is x = -y - z? We cannot say. If z = 0, then x could be equal to -y - z. Else not.

So even after using both statements we cannot answer our question.
Not sufficient.

Answer (E)
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Is |x| = y + z? 31 May 2024, 12:31
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Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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