Ewa earns a base salary of $1,000 each month plus a fixed co

Question

Ewa earns a base salary of $1,000 each month plus a fixed commission for each cable TV subscription sold beyond the first 10 subscriptions in that month.

What were Ewa’s total earnings in March?

(1) In February, when she sold 3 fewer subscriptions than in March, her earnings were $600 less than in March.

(2) In January, when she sold 18 subscriptions, her earnings were greater than $3,000.

BadalDewani · Answer

Are you sure C is right? Both the statements are contradicting with each other. IMO E

ThatTallGuy · Answer

I was thinking about the same:
(1) Commission is 200$,
(2) Commission is more than 250$.

They contradict each other,
Besides, there is no way of certainty about either March, February or January.

UPD: I missed one scenario:

Base = $1,000. Commission = c per subscription beyond 10. March subscriptions = m. We need March total earnings.
 Statement 1 alone: 
Two possible cases:
 Case A (m > 13):  Both months earn commission.
 
 March = 1000 + c(m − 10) 
 Feb = 1000 + c(m − 13) 
 Difference = 3c = 600 → c = 200 
 But we don't know m, so March earnings = 1000 + 200(m − 10) —  unknown   
 Case B (10 < m ≤ 13):  March earns commission, Feb doesn't (m − 3 ≤ 10).
 
 March = 1000 + c(m − 10) 
 Feb = 1000 
 Difference = c(m − 10) = 600 
 March = 1000 + 600 =  1600   
We don't know which case, so  S1 alone is not sufficient. 
 Statement 2 alone:  January sold 18, earned > $3,000.
 
 1000 + 8c > 3000 → c > 250 
 Doesn't tell us March sales.  Not sufficient.   
 Combined:  S2 says c > 250. In Case A, c = 200 — contradicts S2. So Case A is eliminated. Must be Case B. March earnings =  $1,600. Sufficient.

If I missed something, let me know.

IceSameer · Answer

kevincan  please post the solution

kevincan · Answer

It’s hard for me to improve on that tall guys solution

Bunuel · Answer

kevincan , please check and confirm the OA. Thank you for cooperation!

kevincan · Answer

The answer is C

From statement number one, it’s tempting to conclude that C is equal to 200. however, one mustn’t assume that the difference between February and March’s earnings is equal to 3C. Why not ?

Because as that skinny guy said , those extra three sales in March could have generated c, 2c or 3c dollars in extra earnings , depending on whether Februarys sales were 8, 9 or higher . From statement number one all we can conclude is that his earnings in March were 1600 or higher .

percyboi66 · Answer

What I don't understand exactly is, for statement 1 case 2, m might be less than OR EQUAL TO 13.

Assuming m=13, february doesn't get a commission so for c(m-10)=600, we have c(3)=600 which implies c=200 which would contradict S2 so case 2 cannot be taken as entirely true unless we exclude m=13. So, in this situation, are we rejecting m=13 because of statement 2 (c essentially MUST be > 250 which is only true for m = 11 or 12) to get the answer C?

kevincan · Answer

are we rejecting m=13 because of statement 2 (c essentially MUST be > 250 which is only true for m = 11 or 12) to get the answer C?

That’s exactly it . Remember that the statements are never contradictory, so if 2 tells you that c > 250, and you concluded from 1 that c must be 200, there’s something wrong with your reasoning ( or the question )

percyboi66 · Answer

Thanks for the clarification!

kevincan · Answer

Hope you enjoyed the question. Gems like this one are not easy for me to think up

BadalDewani · Answer

How did you come up with "   Case B (10 < m ≤ 13):  March earns commission, Feb doesn't (m − 3 ≤ 10)"?

BadalDewani · Answer

Can you solve it once for better understanding?

ThatTallGuy · Answer

Ewa earns additional earnings only from the amount of subscriptions beyond 10. This means that for March, she earned 1000 or 1000 + c(m-10) if m>10.
So, if there is a month when she did no more than 10 sales, she will earn only 1000.

Statement (1)
Let's bring down 3 different m ranges (scenarios):
Range 1: m ≤ 10
We get the same 1000$ earning both for March and February, which contradicts the statement itself.

Range 2: 10 < m ≤ 13 (Scenario B)
This means that 7 < m-3 ≤ 10. m-3 is the count of subscriptions for February. Therefore, Ewa earned 1000$ for February and 1600$ for March sales.
No matter the value of m in this range, we will have the same 600$ earnings from subscriptions.
m = 11 -> c = 600$,
m = 12 -> c = 300$,
m = 13 -> c = 200$ (this case will be later excluded).

Total earnings remain the same - 1600$

Range 3: m > 13 (Scenario A)
This means that m - 3 > 10. Therefore, Ewa sold more than 10 subscriptions in February. After simplifying the stuff we have, c = 200.

Statement (1) alone is insufficient because we do not know exactly what the earnings are, only the difference between the February and March earnings.
Statement (2) alone is insufficient as well, because it just brings the info that c > 250$.

Now, let's consider the statements together:
At first glance, if we try to solve it quickly, Statements (1) and (2) contradict each other (c = 200 and c > 250)
In fact, it just completely removes Scenario A and leaves us with two values of m: 11 and 12 from Scenario B. With both values of m, both Statements work, and in both cases, we have the same earnings - 600$ on commissions and 1600$ in total.
There are no other scenarios that can work by combining these 2 statements, and there are no other solutions to this question. We solved the problem.

UPD: The goal is to answer if we can give one exact solution for the problem. Combining the statements, we can surely say that Ewa's March earnings are 1600$.

Hence, the answer is C.

BadalDewani

How did you come up with " Case B (10 < m ≤ 13): March earns commission, Feb doesn't (m − 3 ≤ 10)"?

UPD: The goal is to answer if we can give one exact solution for the problem. Combining the statements, we can surely say that Ewa's March earnings are 1600$. Hence, the answer is C.

kevincan · Answer

Fantastic explanation

ThatTallGuy · Answer

Thank you for this interesting challenge as well, Kevin.

I made the same mistake, but after reviewing found out how incredible it is.

ThatTallGuy · Answer

Yes, you are correct.
Our goal is to find if it is possible to find one exact solution. And the mentioned scenario of 11 or 12 sales on March gives us the only solution without any contradiction (because the commission for each sale beyond 10 is 600$ and 300$, respectively), which is 1600$ total earnings.

The cases are mentioned in the ranges with less than or equal to 13 to visualise the edge case when February earnings do not include anything except the base salary.
The same case can later be excluded thanks to Statement (2).

Ewa earns a base salary of $1,000 each month plus a fixed co

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

Ewa earns a base salary of $1,000 each month plus a fixed co

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