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

Question

If x, y, and z are negative numbers such that z = 40x + 80y and x + y = -1, is z < -60?

(1) x > y
(2) y < -0.5

Kudos for a correct  solution .

askhere · Answer

z = 40x + 80y = 40x+40y +40y
 = 40 (x+y) +40y
 = -40 +40y
 = -40(1 - y) = -40 (1- (-1-x)) = -40(2+x)

Statement 1 : x > y
Since x + y = -1 x has to be greater than -0.5; When x = -0.5, z = -40(2+ -0.5) = -60 
So when x is greater than -0.5 (i.e. -0.49, -0.4 etc) z will always be less than -60.  Suff

Statement 2 : y < -0.5
When y =-0.5 ; z = -40(1- y) = -40(1- -0.5) = -60 
So when y < -0.5 (i.e. -0.51, -0.6 etc) z will always be less than -60.  Suff

Answer : D

Ambarish

King407 · Answer

Since x + y = -1, possible values of x and y are {-0.1,-0.9}; {-0.2,-0.8}; {-0.3,-0.7} etc. A) x>y, we can pick 2 extreme values to test this, {x=-0.1 and y= -0.9} and {x=-0.4 and y= -0.6} => in both these cases, results are -76 and -64 respectively which both are <-60 --- Sufficient B) y < -0.5, again we pick two extreme cases, which are same as A, , {x=-0.1 and y= -0.9} and {x=-0.4 and y= -0.6} => in both these cases, results are -76 and -64 respectively which both are <-60 --- Sufficient Hence, Answer is D

Bunuel · Answer

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!

fabricioka · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards