If x, y, and z are negative numbers such that z = 40x + 80y and x + y

VERITAS PREP OFFICIAL SOLUTION:

Many test-takers will see a problem like this and immediately start working with the number properties and testing cases. Could this get you to a correct answer? Sure, but look what happens if we give the warp pipe a try and spend some time with the prompt first. I’d rather work with two variables than three (especially since I only see x and y in the statements), so first I’ll substitute 40x + 80y to replace z in the question inequality. Now the question becomes

Is 40x + 80y < -60?

I know that x + y = -1, so now I want to manipulate the inequality in such a way that I can make another substitution. If I divide both sides by 40, I get

Is x + 2y < -1.5? or, more helpfully, Is x + y + y < -1.5?

Now I can substitute -1 for x + y to get

Is -1 + y < -1.5?

Add 1 to both sides, and we can see that this question really becomes

Is y < -0.5?

That’s so much simpler than the given prompt, and looking at Statement 2, I can immediately see that the GMAT has given me a room full of bonus coins to reward my work! Is y < -0.5? Why yes, it is – an easy, immediate sufficient. Moving on to Statement 1, I’m still looking for opportunities to substitute with info from the prompt, so I add y to both sides to get

x + y > 2y

Now I can substitute -1 on the left side

-1 > 2y

And finally, divide both sides by 2

-0.5 > y

Done! Another straightforward sufficient, and I can answer D with confidence. This is a question that seems much more difficult than it really is – as we can see, the GMAT rewards test-takers who are patient enough to work with the prompt before moving on to the statements. Take advantage of opportunities to simplify the question, and your room full of coins awaits!

Here is how i worked the problem:

Since x+y=-1 and both must be negative, x and y could be {-0,5,-0,5} or {-0,3,-0,7}, etc.

z=40x+80y
Using x+y=-1 we have x=-y-1
Substituting in the z equation we get: z=40y-40

For z to be less than -60 we need "40y" to be less than -20. Thus, we need y to be less than -0.5, so we can get a result less than -20, for example {-0.51}.

Statement 1: x>y
That means that x must be bigger than -0.5, or -0.49.
SUFICIENT

Statement 2: y<-0.5
That is exactly what we were looking for.
SUFICIENT

ANSWER D

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