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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?

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: 1. Please provide your solutions to the questions; 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.

Re: Salesperson A's compensation for any week is $360 plus 6 per [#permalink]
24 Feb 2014, 23:05

Expert's post

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'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.

Re: Salesperson A's compensation for any week is $360 plus 6 per [#permalink]
25 Feb 2014, 01:01

1

This post received KUDOS

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)

Re: Salesperson A's compensation for any week is $360 plus 6 per [#permalink]
25 Feb 2014, 21:08

1

This post received KUDOS

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;

Re: Salesperson A's compensation for any week is $360 plus 6 per [#permalink]
01 Mar 2014, 03:24

Expert's post

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'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.

Re: Salesperson A's compensation for any week is $360 plus 6 per [#permalink]
01 Mar 2014, 03:33

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'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.

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.

Re: Salesperson A's compensation for any week is $360 plus 6 per [#permalink]
01 Mar 2014, 03:59

I just checked up the Official review and it is C... i mean i really, honestly and humbly think that the GMAC either got the question wording wrong or the answer wrong. So i still feel given the question wording D is the right answer. GMAC probably made a mistake with the question wording.(After all they are humans too)

Re: Salesperson A's compensation for any week is $360 plus 6 per [#permalink]
01 Mar 2014, 04:01

Expert's post

Manofsteel wrote:

I just checked up the Official review and it is C... i mean i really, honestly and humbly think that the GMAC either got the question wording wrong or the answer wrong. So i still feel given the question wording D is the right answer. GMAC probably made a mistake with the question wording.(After all they are humans too)

Re: Salesperson A's compensation for any week is $360 plus 6 per [#permalink]
01 Mar 2014, 04:07

Bunuel wrote:

Manofsteel wrote:

I just checked up the Official review and it is C... i mean i really, honestly and humbly think that the GMAC either got the question wording wrong or the answer wrong. So i still feel given the question wording D is the right answer. GMAC probably made a mistake with the question wording.(After all they are humans too)

Check again: D is wrong.

why is it wrong? i still dont get it though! can you explain

Re: Salesperson A's compensation for any week is $360 plus 6 per [#permalink]
01 Mar 2014, 06:20

Expert's post

Manofsteel 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'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.

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.

The questions asks for what amount the two compensation plans would give the same compensation.

Re: Salesperson A's compensation for any week is $360 plus 6 per [#permalink]
10 Mar 2014, 07:18

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'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.

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

Re: Salesperson A's compensation for any week is $360 plus 6 per [#permalink]
10 Mar 2014, 07:26

1

This post received KUDOS

Expert's post

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'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.

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.

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