If \(y + |y| = 0,\) which of the following must be true?

Gmat_mission wrote: ↑

Sun Jun 21, 2020 3:35 pm

If \(y + |y| = 0,\) which of the following must be true?

A. \(y > 0\)
B. \(y \ge 0\)
C. \(y < 0\)
D. \(y \le 0\)
E. \(y = 0\)

[spoiler]OA=D[/spoiler]

Source: GMAT Paper Tests

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 quickly find solutions to the given equation, and then use those solutions to test the answer choices.
Now let's give ourselves up to 20 seconds to identify a faster approach.
I don't see a faster approach. So let's start testing . . .

If y + |y| = 0, we can see that it could be the case that y = 0.
More strategy: When looking for solutions to a given equation or inequality, it's useful to first check whether 0 is a solution, since zero is such an easy value to work with.

Now we’ll plug y = 0 into the five answer choices to see which one(s) is/are true:
A. 0 > 0. Not true. Eliminate.
B. 0 ≥ 0. True. Keep.
C. 0 < 0. Not true. Eliminate.
D. 0 ≤ 0. True. Keep.
E. 0 = 0. True. Keep.

We’ve already reduced the options to B, D and E.
Now we’ll test another y-value that satisfies the equation y + |y| = 0
We can see that y = -1 is another possible solution. So, we’ll plug y = -1 into the remaining three answer choices:
B. -1 ≥ 0. Not true. Eliminate.
D. -1 ≤ 0. True. Keep.
E. -1 = 0. Not true. Eliminate.

By the process of elimination, the correct answer is D.