Salesperson A's compensation for any week is $360 plus 6 percent of

Question

Salesperson A's compensation for any week is $360 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of B 's total sales for that week. For what amount of total weekly sales would both salespeople earn the same compensation?

A. 21000
B. 18000
C. 15000
D. 4500
E. 4000

(A) $21,000
(B) $18,000
(C) $15,000
(D) $ 4,500
(E) $ 4,000

Bunuel · Accepted Answer

SOLUTION

Salesperson A's compensation for any week is $360 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of B's total sales for that week. For what amount of total weekly sales would both salespeople earn the same compensation?

(A) $21,000
(B) $18,000
(C) $15,000
(D) $ 4,500
(E) $ 4,000

A's compensation = $360 + 6 percent of the A's total sales above $1,000.
B's compensation = 8 percent of B's total sales.

Whose compensation is greater? Well it depends on the sales:
If each has the sales of $1,000, then A's compensation is $360 and B's compensation is $80, so for $1000 A's compensation is greater than that of B's BUT if each has the sales of $100,000, then A's compensation is $360+0.06*99,000=$6,300 and B's compensation is $8,000, so for $100,000 A's compensation is less than that of B's.

The question asks: for what amount would both salespeople earn the same compensation?

Say that amount is $x, then we need such x for which 360+0.06(x-1,000)=0.08x --> x=$15,000. So, if each has the sales of $15,000, then A's compensation is the same as that of B's.

Answer: C.

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nutshell · Answer

A's Compensation = 360 + 0.06(A's Total Sales amount - 1000)
B's Compensation = 0.08(B's Total Sales amount)

Since we are asked for the amount of total weekly sales in which both salespeople earn the same compensation, we can assume the amount of A's Total Sales = B's Total Sales = x;

360 + 0.06(x - 1000) = 0.08x;
360 + 0.06x - 60 = 0.08x;
300 = 0.02x;
x = 300/0.02 = 30000/2 = 15,000;

Ans is (C).

Manofsteel · Answer

Let A's total sales for the week be 'x'
Let B's total sales for the week be 'y'

Now A gets a fixed salary(salary irrespective of sales) + variable salary = 360 + 0.06*(x-1000)

B gets only a variable salary = 0.08*(y)

Now assuming A sells nothing. i.e 0 $
Then A's weekly income will be 360$
Since income of both has to be same 0.08*y = 360
thus y = 4500 $
Now A gets a fixed income irrespective of his sales. So A's total sales for the week = 0 and B's total sales for the week = 4500
Thus TOTAL weekly sales at which both get the same earnings = x+y = 4500$.  Answer - Option (D)

lool · Answer

Why did you substract 1000 from x while computing A's compensation ? I understand the question as if A made a $2000 total sales, his compensation is 360+ 2000*0,06

Bunuel · Answer

No.

The stem says that "A's compensation for any week is $360 plus  6 percent of the portion of A's total sales  above $1,000   for that week."

Thus if A's sales were $2,000 for a certain week, then the compensation would be $360 plus 6 percent of the portion of A's total sales  above $1,000 , so 6 percent of $2,000-$1,000=$1,000: 360 + 0.06*1,000.

Hope it's clear.

ScottTargetTestPrep · Answer

We are given that salesperson A's compensation for any week is $360 plus 6 percent of the portion of A's total sales above $1,000 for that week.

If we let t = total sales for salesperson A, we can create the following equation:

Salesperson A’s compensation = 360 + 0.06(t - 1000)

We are also given that salesperson B's compensation for any week is 8 percent of B's total sales for that week.

Since we need to determine what total sales would earn salesperson A and B the same compensation, we can also let t = the total sales for salesperson B and create the following equation:

Salesperson B’s compensation = 0.08t

Let’s now equate the two equations and determine t:

360 + 0.06(t - 1000) = 0.08t

360 + 0.06t - 60 = 0.08t

300 = 0.02t

30,000 = 2t

15,000 = t

Answer: C

CyberStein · Answer

This question asks "For  what amount for the total weekly sales  would both salespeople earn the same compensation"
It is not asking for the amount of compensation, rather the total weekly sales. But you do need to make sure what their compensations are the same.

When I first worked this question, I knew right away it was a question where I could manipulate the possible answers to determine the correct answer. Afterward, I reduced it to an equation. I'll show what I did first:

1. Assuming $4,000 is the correct answer, salesperson A's compensation is 6% above $1,000 plus $360. $4,000 is $3,000 above $1,000. So, I took ($3,000 x 6) /100 + $360 = $540. With salesperson B, there is no given condition that states that the percentage is factored only if total sales is above $1,000. So, with salesperson B, you just calculate ($4000 x 8) / 100 = $320 which is not the same as person A's compensation; thus eliminating choice (E)
2. For answer choice (D), $4,500 is $3,500 above $1,000; (3500 x 6) / 100 + 360 = 570 compensation for Sales A. For Sales B, (4500 x 8) / 100 = 360, not the same comp as SP A.
3. I got lucky, because I did not have to eliminate all answers seeing as the right answer was in the middle - (C). (14000 x 6) / 100 + 360 = $1200. (15000 X 8) /100 = $1200, which is the same compensation as SP A. Therefore, the correct answer is (C) $15,000 total sales for both person A and B would give same compensation.

However, on the real GMAT test, this may take too long for some, and a simple equation is needed to account for time.

Let X = total sales

1. 360 + 0.06 (x-1000) = 0.08x 
2. 360 -60 = 0.08x 
3. 300/0.02 = x 
4. 15000 =x

Hope this helps

Elite097 · Answer

Really not understanding this. According to the question, "Compensation" should be the same for A and B, not "sales".

So, why have you assumed the the "sales" of A and B are the same?

avigutman

avigutman · Answer

Let's take a close look at the question,  Elite097 :
 
The implication is that we're searching for  an amount of total weekly sales  for which the compensations are exactly equal. Not  two different amounts of total weekly sales  (one for salesperson A and a different one for salesperson B).

vv65 · Answer

One way of doing the question is to try the weekly sales figures in the answer choices one by one. A and B will have the same compensation for one of the sales figures

Start with the middle value (C)=$15,000

A's compensation 
= 360 + (0.06 * 14,000) = 360 + (6 * 140) = 360 + 840
= 1200

B's compensation 
= .08 * 15000 = 8 * 150
= 1200

Done, (C) is the answer. 
Started with (C) and it worked. Otherwise, I would have tried (B) next.

Posted from my mobile device

Elite097 · Answer

avigutman  then why cant total sales be taken to mean a+b? How do we know we are talking about each's total sales as one figure/

avigutman · Answer

Look at the preceding two sentences,  Elite097 :
 
Without this context, sure, "total sales" can be taken to mean a+b.
Context matters.

ArnauG · Answer

Let's denote the total weekly sales for both salespeople as S.

For Salesperson A, the compensation is $360 plus 6% of the portion of total sales above $1,000. Mathematically, it can be expressed as:

Compensation for Salesperson A = $360 + 0.06(S - $1,000)

For Salesperson B, the compensation is 8% of the total sales. Mathematically, it can be expressed as:

Compensation for Salesperson B = 0.08S

To find the amount of total weekly sales for which both salespeople earn the same compensation, we can set these two equations equal to each other and solve for S:

$360 + 0.06(S - $1,000) = 0.08S

Now, let's solve this equation:

$360 + 0.06S - $60 = 0.08S

$300 = 0.02S

Dividing both sides by 0.02:

$300 / 0.02 = S

S = $15,000

Therefore, both salespeople would earn the same compensation when the total weekly sales amount is (C) $15,000.

chetan2u · Answer

Sourec please..

Salesperson A:  360 + 6% of (A-1000) = 360 + 0.06A - 60 = 300+0.06A
 Salesperson B:  8% of (B) = 0.08B

The question may have missed out on word same weekly sales. So, A=B

300+0.06A = 0.08A ..............0.02A = 300 .............. A = \frac{300}{0.02} = $15,000  
    C

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Salesperson A's compensation for any week is $360 plus 6 percent of

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