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Math Expert V
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Salesperson A's compensation for any week is \$360 plus 6 per  [#permalink]

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Question Stats: 70% (02:11) correct 30% (02:27) wrong based on 908 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Problem Solving
Question: 114
Category: Algebra Applied problems; Simultaneous equations
Page: 76
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

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Re: Salesperson A's compensation for any week is \$360 plus 6 per  [#permalink]

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4
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.

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GMAT 1: 590 Q45 V27 Re: Salesperson A's compensation for any week is \$360 plus 6 per  [#permalink]

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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).
##### General Discussion
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Re: Salesperson A's compensation for any week is \$360 plus 6 per  [#permalink]

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2
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)
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Re: Salesperson A's compensation for any week is \$360 plus 6 per  [#permalink]

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Option C

I solved taking answer. Took C first and solved to get \$1200 for A and B.
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Re: Salesperson A's compensation for any week is \$360 plus 6 per  [#permalink]

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1
Option C.
The equation is:360+6%(x-1000)=8% of x
Solving,
360=8% of x-6% of x +60
300=2% of x
x=15000
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Re: Salesperson A's compensation for any week is \$360 plus 6 per  [#permalink]

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Bunuel wrote:
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.

I didnt get it.... Question says for what amount of TOTAL SALES...Total Sales = A's sale + B's sale ....so it has to be be A's sales = 0 and B's sales = 4500 and Option D.
If it is 15000 \$ = B's sale then the answer should be 30000\$ as the total sales.

Thus If each has a sales of \$15000 then the total sales will be \$ 30000 Option C just cant be the right answer. unless u interpret - For what amount of total weekly sales would both salespeople earn the same compensation? - as sales of any one person!!! - which isnt the intended meaning conveyed by the english of the question.
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Salesperson A's compensation for any week is \$360 plus 6 per  [#permalink]

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Re: Salesperson A's compensation for any week is \$360 plus 6 per  [#permalink]

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Bunuel wrote:
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.

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
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Re: Salesperson A's compensation for any week is \$360 plus 6 per  [#permalink]

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lool wrote:
Bunuel wrote:
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.

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

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.
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Re: Salesperson A's compensation for any week is \$360 plus 6 per  [#permalink]

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Really? Which one is correct? total weekly sales or individual sales?
IMO if each has \$15k of sales then the total weekly sales must be \$30k

Bunuel wrote:
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.

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Re: Salesperson A's compensation for any week is \$360 plus 6 per  [#permalink]

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evdo wrote:
Really? Which one is correct? total weekly sales or individual sales?
IMO if each has \$15k of sales then the total weekly sales must be \$30k

Bunuel wrote:
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.

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Re: Salesperson A's compensation for any week is \$360 plus 6 per  [#permalink]

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evdo wrote:
Really? Which one is correct? total weekly sales or individual sales?
IMO if each has \$15k of sales then the total weekly sales must be \$30k

Bunuel wrote:
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.

You are over analyzing the question stem. It asks us to calculate that 1 particular value of total weekly sales that will give us the same compensation for both A and B. "Total" here means total weekly sales for either one of them.
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Salesperson A's compensation for any week is \$360 plus 6 per  [#permalink]

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Problem Solving
Question: 114
Category: Algebra Applied problems; Simultaneous equations
Page: 76
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

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Hi Bunuel ,
Can you please specify ? why do we need to take both salesperson's sales equal ? (It is not given in the question that both sales are equal)
we are asked for "what amount of total weekly sales would both salespeople earn the same compensation?"

I think we need to calculate Sales of A + Sales of B = ? (at the same compensation earned )
After seeing your solution if x = \$15000 (which is supposed to be 1 person's sales amount)
then Sales A + Sales B should be \$30000,
which is not even in the options...

Can you please explain where am I wrong ?
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Re: Salesperson A's compensation for any week is \$360 plus 6 per  [#permalink]

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Let the amount be 'x' at which their compensation is equal.

Then A's compensation will be = 360+ .06(x-1000)
B's compensation will be= .08x

360+ .06(x-1000) = .08x
360-60= .08x-.06x
300= .02x
15000= x
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Re: Salesperson A's compensation for any week is \$360 plus 6 per  [#permalink]

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nutshell wrote:
... 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;

This is the key I think else it takes much time as you end up having something like that

30000 + 6A = 8B and then by back-solving you can find C

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Re: Salesperson A's compensation for any week is \$360 plus 6 per  [#permalink]

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

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

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Re: Salesperson A's compensation for any week is \$360 plus 6 per  [#permalink]

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Problem Solving
Question: 114
Category: Algebra Applied problems; Simultaneous equations
Page: 76
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
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It's best to backsolve here. You can eliminate B because the commissions do not match. Afterwards, you can eliminate A as well because the "pure percentage" commission of B was greater than the flat fee + percentage commission of A. As a result, answer choice A which has a higher value than B would only widen that gap. So the answer is C after you eliminate D because the flat fee is too high.
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Salesperson A's compensation for any week is \$360 plus 6 per  [#permalink]

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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
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Re: Salesperson A's compensation for any week is \$360 plus 6 per  [#permalink]

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Problem Solving
Question: 114
Category: Algebra Applied problems; Simultaneous equations
Page: 76
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

For this, I will use a combo of ratio and plugin.s
i.e Spilt the full (8%) commission into part of the partial commission i.e .02 + 0.06, which is ratio 1: 3
Now I will choose an option that will give me good % for 6 and 8%s and 15,000 is a perfect candidate, 8% of which is 1200
Finally, comes the ratio part i.e check 1/4 (1200) = 360. Surely C is the answer
Although not needed, but certainly, the other part would match the above 1000 constraint. Just to check this would be 840 which is 0.06(15000-1000)

I hope this helps someone.

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