The annual stockholders' report for Corporation X stated that profits

Question

The annual stockholders' report for Corporation X stated that profits were up 10 percent over the previous year, although profits as a percent of sales were down 10 percent. Total sales for that year were approximately what percent of sales for the previous year?

A. 78%
B. 90%
C. 110%
D. 122%
E. 190%

PS17302.01

A. 78%
B. 90%
C. 110%
D. 122%
E. 190%

PS17302.01

ScottTargetTestPrep · Accepted Answer

We can let the profit last year = 100 and the profit this year = 110. We can let the sales last year = 100 and the sales this year = x. So we can create the equation:

110/x - 100/100 = -1/10

110/x - 1 = -1/10

110/x = 9/10

9x = 1100

x = 1100/9

Therefore, the sales this year is approximately

(1100/9)/100 x 100 = 1100/9 ≈ 122 percent of the sales last year.

Answer: D

Archit3110 · Answer

Profit PY=100
Profit CY = 110
Profit PY/Sales PY = x
Profit CY/Sales CY =0.9x
110/sales CY= (100/sales PY)*0.9
Sales CY/Sales PY = 110/0.9*100 = 122%
IMO D

AndrewN · Answer

The annual stockholders' report for Corporation X stated that profits were up 10 percent over the previous year, although profits as a percent of sales were down 10 percent. Total sales for that year were approximately what percent of sales for the previous year?

A. 78%
B. 90%
C. 110%
D. 122%
E. 190%

PS17302.01

A. 78%
B. 90%
C. 110%
D. 122%
E. 190%

I agree with the approaches outlined above by just about everyone who has posted, so I will spare you a recapitulation. I will add a twist to the mix by outlining how you can often use the answer choices in a PS problem against the test to arrive at an accurate conclusion. Say that you were stumped on this question, and after a minute or so of inactivity, of not being able to figure out a way to make headway into the problem, you decided to size up the answer choices instead. Notice the pairs specifically: 78% and 122% are 22% away from 100, while 90% and 110% form a second pair and are 10% away from 100. The outlier is 190%, and it is so far beyond the second largest value that we can ignore it for now. That is, since GMAC™ designs questions to trap people, it is highly likely that one of the two pairs will lead to the correct answer while the other will lead to a flawed conclusion that is probably based on an assumption. In this case, a reasonable  assumption  is that an increase or decrease of 10%  must  mean that 90 and 110 are the correct numbers. The savvy GMAT™ test-taker will know to avoid this probable trap. The other pair, 78% and 122%, looks more promising.

At this point, you can assess whether the question is asking for the smaller or larger value. Although  that year  is ambiguous,  sales for the previous year  is not, so we know we are looking for a figure that would represent  sales for this year . Logically speaking, if profits were up in general but profits from sales were down, then we can appreciate that  total sales  should have gone  up . Why? Because a percent increase or decrease from a larger value is not as pronounced as that from a smaller value. For example, an increase from 1 to 2 represents a 100% jump, but a decrease from 2 to 1 represents just a 50% drop. A logical guess would be (D), 122%, if you had crossed the 2-minute mark. If you had a little time to spare and wanted to work out a solution, then nothing beats the more rigorous approaches above. You could even back-solve by using 122 as the target value.

I add this point not in an effort to outshine the responses above—those approaches are better—but in a pinch, smart guessing beats out random guessing every time, and a 50-51 scorer can remain calm when a lower scorer might hit the panic button. An analytical approach can help you keep calmer and increase the likelihood that you will arrive at a correct conclusion, nothing more.

- Andrew

ZoltanBP · Answer

The growth factor for a ratio is the ratio of the growth factor for the numerator to the growth factor for the denominator. The growth factor for the profit as a percent of sales is 0.9. The growth factor for the profit is 1.1. Let  s  be the growth factor for the sales.

0.9=\frac{1.1}{s}

s=\frac{1.1}{0.9}=\frac{11}{9}\approx 1.22=122\%

Answer: D

GMATGuruNY · Answer

Previous year:
Let sales = 100 and profit percentage = 10%, implying that the amount of profit = $10.

This year:
Since the profit percentage decreases by 10%, this year's profit percentage = 9%.
Since the amount of profit increase by 10%, this year's amount of profit = $11.
Since $11 must be equal to 9% of this year's sales, we get:
 11 = .09x 
 x = \frac{11}{.09} = \frac{1100}{9} ≈ 122

Thus:
 \frac{this-year's-sales}{last-year's-sales} = \frac{122}{100} =  122%

D

msali1983 · Answer

Let profit last year be = P1
Sales last year = S1
Profit current year = P2
Sales Current year = S2

Condition 1 : Profit current year = 1.1 x Profit last year
 = P2 = 1.1 P1
 = P2/ P1 = 1.1
Condition 2: P2 / S2 = 0.9 P1/ S1
 P2/P1= 0.9S2/S1

Question is asking : S2/S1 as percentge

Requirement = Solving the above questions: S2/S1 = 1.1/0.9 == 1.22 
 Answer =122%

dave13 · Answer

AndrewN hey they Happy New Year greetings

this is how understood problem number of stocks sold last year = s price per stock last year p profits last year = s*p=100 since this year profits were higher despite decline in number of sold stocks then logically price of stock have risen this year, right ? number of stocks sold this year = 0.9s (cause this is how i understood this " although profits as a percent of sales were down 10 percent " ) price per stock this year p(1+x/100) where x is a percent increase total profit this year = p(1+x/100) *0.9s (where x is percent increase) now its getting scary cause i m getting too many variables...

so question is: Total sales for that year were approximately what percent of sales for the previous year? so i do this p(1+x/100) *0.9s / s now here i got stuck ,

whats wrong with my solution p.s. unless i dont understand what mistake i am making in my solution, i wont understand other posts above.

AndrewN · Answer

Hello,  dave13 . Happy New Year to you, too. I will respond inline below.

The highlighted parts mark where I think your approach took a detour. You cannot say that the  number  of stocks sold this year is 90 percent of the number sold last year. The problem states that   profits  were up 10 percent over the previous year , but that   profits as a percent of sales  were down 10 percent . In your equation above, if s * p = 100, then this year, the product of s and p would be 1.1(100), or 110. But you would still need to keep apart information about  total profits  and  profits from sales  specifically. I would recommend an altogether different approach. (Alphabet soup makes me just as uncomfortable as it makes you.)

I would start there. If you work around some target numbers, then the process should prove more manageable. (I would be happy to oblige if you still find yourself stumped.)

Thank you for thinking to ask me about this tough question.

- Andrew

dave13 · Answer

thanks AndrewN

looks like i took a dramatic detour from the very start and quickly landed in alphabet soup

i got it now i missed the fact that sales=profit +costs thats why had trouble solving it profit last year 100 % profit this year 110 % Sales last year 100 % Sales this year = s (S is unknown cause profits as percent sales are 0.9) profits this year i.e 110% )/ sales this year = 0.9 Profits as a percent of sales were down 10 percent this year = 0.9 = 1.1/s Sales this year 122 Total sales for that year were approximately what percent of sales for the previous year? 122/ 100 * 100 =122

AndrewN · Answer

Now you have it,  dave13 . I would  never  introduce another variable if I did not have to. It is kind of like a question asking about how far someone ran. I am not interested in where the person ran or in what form or shoes he may have done so, but just in what the question is asking. When you take a direct approach, you get answers; an indirect approach leads to confusion (even if you enjoy alphabet soup from time to time).

Good luck with your studies.

- Andrew

1616 · Answer

Hello  Bunuel

Can you please explain what does profit as a percentage of sale means? How to decode this into a mathematical equation?

Bunuel · Answer

The phrase "profits as a percent of sales were down 10 percent" simply means if profits/sales were x last year, then this year profits/sales are 0.9x.

Assuming the profits last year were $100, this year profits would be $110.

Last year  \frac{profits}{sales} =\frac{ 100}{s_1} .

This year  \frac{profits}{sales} = \frac{110}{s_2} .

We are told that  0.9*\frac{100}{s_1} = \frac{110}{s_2}

\frac{s_2}{s_1} = \frac{110}{0.9*100} \approx 1.22

Answer: D.

Udniez · Answer

I always prefer smart numbers for this type of questions. I will use the number 1 to refer to the previous year. Profit1/Sales1= 90/100=0.9, for the next year the profit was 10% more so we have profit2= 99 but the ratio profit to sales went down by 10% hence Profit2/ Sales2=0.9(0.9) -> 99/Sales2=0.81 after some little calculation we have Sales2=122 which is 122% more than 100.

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The annual stockholders' report for Corporation X stated that profits

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The annual stockholders' report for Corporation X stated that profits

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