Help with question from the Manhattan Gmat flash cards #20

[RonPurewal]

I'm stuck... I calculate r = -200,000 and thus c = -25,000. And obviously negative numbers should be impossible?

what equations did you use?

So it should be a linear relationship, right? If sales revenue increases 25%, shouldn't her commission increase 25%? Am I missing something?

no, it's nonlinear because of that first 50,000 that doesn't count toward the commission. (if something is linearly proportional to x – 50,000, then it's definitely NOT linearly proportional to x.)

[RonPurewal]

incidentally, for this problem to make sense, it must say this: 'If sales had been %25 higher, Carla's COMPENSATION [= total of salary AND commission] would have been %20 higher.'

the problem can't just say 'commission', because the commission, by itself, will always increase by a greater percentage than will the sales amount.

what does the problem say?
(the words 'commission' and 'compensation' look a lot like each other.)

[CharlesG754]

incidentally, for this problem to make sense, it must say this: 'If sales had been %25 higher, Carla's COMPENSATION [= total of salary AND commission] would have been %20 higher.'

the problem can't just say 'commission', because the commission, by itself, will always increase by a greater percentage than will the sales amount.

what does the problem say?
(the words 'commission' and 'compensation' look a lot like each other.)

The problem says commission - not compensation. So it's a typo in the flashcard, right?

[CharlesG754]

I'm stuck... I calculate r = -200,000 and thus c = -25,000. And obviously negative numbers should be impossible?

what equations did you use?

So it should be a linear relationship, right? If sales revenue increases 25%, shouldn't her commission increase 25%? Am I missing something?

no, it's nonlinear because of that first 50,000 that doesn't count toward the commission. (if something is linearly proportional to x – 50,000, then it's definitely NOT linearly proportional to x.)

I used the equations on the flashcard:

c = 0.1(r - 50,000)
1.2c = 0.1(1.25r - 50,000)

plugging the first equation into the second:

0.12r - 6,000 = 0.125r - 5,000
-1,000 = 0.005r
r = -200,000

plugging back into the first equation:

c = 0.1(-200,000 - 50,000) = -25,000

I even graphed the two equations to make sure I wasn't going crazy and this is the point the two lines intersect.

If (as you mentioned) the statement said that her compensation would have been 20% higher, then the values end up being in the positive and make sense with different equations:

compensation = p
p = 30,000 + 0.1(r - 50,000)
1.2p = 30,000 + 0.1(1.25r - 50,000)

r = 1,000,000
p = 125,000

if r = 1,250,000, p would equal 150,000

Thanks for the explanation on the relationship being linear, I see where I was mistaken.

[tim]

incidentally, for this problem to make sense, it must say this: 'If sales had been %25 higher, Carla's COMPENSATION [= total of salary AND commission] would have been %20 higher.'

the problem can't just say 'commission', because the commission, by itself, will always increase by a greater percentage than will the sales amount.

what does the problem say?
(the words 'commission' and 'compensation' look a lot like each other.)

The problem says commission - not compensation. So it's a typo in the flashcard, right?

I've looked at the flashcard. Based on the explanation, it is clear that there is a typo, but not regarding the commission/compensation distinction. As Ron indicated, the 25% and 20% numbers don't work, as they produce negative c and r. The problem should have swapped the 25% and 20% (along with the corresponding change in the explanation).

[AlexR115]

what does c and r equal?

[tim]

If you'd like to show us your calculations for c and r, we will be happy to look them over and let you know if your calculations check out or where your mistake is.