The annual stockholders' report for Corporation X stated that profits

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

HI GMATGuruNY, MentorTutoring

Can you help me with this problem?

Profits as a percent of sales were down 10 percent -- > How translate to Profits?

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%

Hello, NandishSS. 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

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%

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.

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

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

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

A similar logic
P' = 1.1 P where P' is current year and P is previous year .

Let S' be total sales in current year and S be sales in previous year . From statement ,

P'/S' = 9/10 * P/S .

We need S'/S % - Rearranging and substituting , we get S'/S % = 122% approx

Bunuel @VeritasKarishma Can you please help me understand what I'm doing wrong here?

Let profits last year be 100$. So profits this year is 110$. And let sales last year be 200. So profit as percent of sales for last year will be 50% of 200= 100.

Let sales for this year be x. Since profit as % of sales is 10% lower,
40% of x = 110
So, x = 275

So sales this year as a percent of the sales in the previous year = 275/200 = 11/8 = approx 137%

Hey sherinsam. I'm no Karishma or Bunuel, but I'll have a go. You should revisit the highlighted part.

Since you've calculated profits as a % of sales for last year to be 50, this year should be 10% less than that.
10% of 50 is 5. Hence profits as a % of sales this year = 45

45% of x = 110
x= 244.44

\(\frac{sales - this - year}{sales - last - year} = \frac{244.44}{200} = 1.2222 \)

Therefore, sales this year as a percentage of last year = 122.22 %

not the most efficient but it helped me to understand the concept:
1)New P = 110/100 old P
2)New P/ new S = 90% of Old P/ Old S
SUBSTITUTE new P from the first to the second.

110/100 old p / new S = 90/100 old p/old S
solve so that New S/ old S:
110/90 ~= 1.22 *100 = 122%.

I hope that helps.