Sue's monthly earnings consist of a monthly salary and a 4 percent com

Question

Sue's monthly earnings consist of a monthly salary and a 4 percent commission on the portion of her monthly sales that is in excess of $2,000. If Sue's monthly salary was the same in July as in August, how much greater were her sales in July than in August?

(1) Sue's monthly earnings were $3,620 in July and $3,580 in August.
(2) Sue's monthly salary was $3,500 in July and in August.

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gmatophobia · Accepted Answer

KarishmaB Bunuel

I cannot wrap my head around how option A is the correct answer. The question stem neither mentions that Sue received a commission in both months nor provides any information on Sue's monthly salary. Hence, I would consider Statement 1 not sufficient.

For example, let's consider the following two cases for Statement 1

Case 1

Month : July
Monthly Salary: $3580
Sale: $3000
Monthly Earnings = $3580 + 0.04(3000-2000) = 3580 + 40 = $3620

Month : August
Monthly Salary: $3580
Sale: $1000
Monthly Earnings = $3580

Difference in sale = 3000 - 1000 = $2000

Case 2

Month : July
Monthly Salary: $3500
Sale: $5000
Monthly Earnings = $3500 + 0.04(5000-2000) = 3500 + 120 = $3620

Month : August
Monthly Salary: $3500
Sale: $4000
Monthly Earnings = $3500 + 0.04(4000 - 2000) = 3500 + 80 = $3580

Difference in sale = 5000 - 4000 = 1000

Isn't Statement 1 giving us two possible answers or how did we conclude that the sales made by Sue were greater than $2000 in both months, thereby making her eligible for commissions on both months?

What am I missing here

Could you please help me?

Moderator Note: I believe that the answer posted in GMAT Prep is not correct.

IMO The correct answer to this question should be Option C

Could you please help me? I believe that the answer posted in GMAT Prep is not correct. IMO The correct answer to this question should be Option C

Sanyam_Maheshwari · Answer

Let Monthly Earnings - > E july and E august
MONTHLY SALARY - S
MONTHLY SALES-> sales july and sales Aug

To find sales july - sales Aug

Stmt I

E(july)= s + 4/100(sales july-2000) (1)

E(aug) = s + 4/100(sales aug -2000) (2)

E july and E Aug are given

Subtract 1) - 2 gives sales july- sales aug which is what we need( the s's cancel since is given monthly salary is same for july and aug)

SUFF

Stmt II

Sue’s monthly salary was $3,500 in July and in August

Seevral unknowns like E july,E Aug, sales July and sales Aug

INSUFF

A)

kryinkrumble · Answer

Let the monthly salary of Sue be X

Statement 1  (SUFFICIENT) : 
July commission = 3620-X
August commission =3500-X
Difference in commission (in J and A) = (3620-X)-(3500-X) = 40
Difference in sales (in J and A) = 40/(4/100) = 1000 (since commission is 4% of her monthly sales in excess of $2000 - but we don't care about the $2000 because we just want the difference in her sales)

Statement 2  (INSUFFICENT) :
We are only given salary but we have no information on the commission / sales in July and August

Answer:  A

KarishmaB · Answer

I agree. We are not given that her Sales in both months was at least $2000. So the difference in the Sales could vary using statement 1 alone.

az168 · Answer

Monthly Earnings include both Salary and 4% of Sales that exceed $2000

Hence, the equation for statement would look like this:

Monthly Salary + 4% ( 2000 - Sale in July ) -   = 3620 - 3580

roshaun25 · Answer

Is there an official explanation to this answer? I also got C based on the different possibilities based on only statement 1 but the official practice exam has it as A in spite of the obvious ambiguity.

Bunuel · Answer

Official mocks do not have solutions.

dictavitae · Answer

I got the same official practice exam question, and the answer is wrong. they say it's (A), but it's obviously (C).

dictavitae · Answer

I think the proper equation should use 'maximum' since there is a chance that sales is under $2000 which means commission will be $0.

0.04(max⁡(0, sales in July −2000)−max⁡(0, sales in August −2000))= 3620−3580 = 40

Chibobo · Answer

How do we know if both months’ sales exceeded $2,000?

ponderare · Answer

Goodmorning, even if we don't take into consideration the sales being 0 in one case, we would still have the same problem, right? 
if the fixed salary is 2000, we would have a greater difference between the sales than we would have considering fixed salary equal to 3500. 
in the first case sales would be (3580-2000)=4/100*sales1 and 3620-2000=4/100*sales2.

Usernamevisible · Answer

gmatphobia ,  KarishmaB

Let:

* Monthly salary = S
* July sales = J
* August sales = A

Since earnings consist of salary plus 4% of sales above $2,000:
Earnings = S + 0.04(Sales − 2000)
(assuming sales exceed $2,000; otherwise commission would be zero, but we'll see whether that matters.)

We need:
J − A ?

---

Statement (1)
July earnings = 3620
August earnings = 3580
Difference in earnings:
3620 − 3580 = 40
Salary is the same in both months, so the entire $40 difference comes from commission.
0.04  = 40
0.04(J − A) = 40
J − A = 40 / 0.04 = 1000
Unique value obtained.
Statement (1) is sufficient.

---

Statement (2)
Salary was $3,500 in both months.
We still don't know earnings or commissions.
Many possibilities:
July sales = 5,000, August sales = 4,000 ⇒ difference = 1,000
July sales = 8,000, August sales = 5,000 ⇒ difference = 3,000
Different answers.
Statement (2) is insufficient.
---

Answer
A. Statement (1) alone is sufficient.

---
GMAT Takeaway
When a commission is based on sales above a threshold:
0.04(J − 2000) − 0.04(A − 2000)
the threshold cancels:
0.04 
= 0.04(J − A)

So if salary is unchanged, a difference in earnings translates directly into a difference in sales. This cancellation is the key shortcut

Sue's monthly earnings consist of a monthly salary and a 4 percent com

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GMAT Data Sufficiency (DS) Questions

Sue's monthly earnings consist of a monthly salary and a 4 percent com

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