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Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Salesperson

by BTGmoderatorDC » Thu Sep 07, 2017 5:07 pm
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
Answer : C
How is the option C the answer to this question?
Can any experts explain the fastest way to answer this question?
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by [email protected] » Thu Sep 07, 2017 8:33 pm
Hi Iheiannie07,

We're told the pay rates for two salespeople:
1) Salesperson A = $360 + 6% of sales above $1,000
2) Salesperson B = 8% of sales

We're asked for the total sales that would lead to the SAME pay for each salesperson. This question can be solved algebraically or by TESTing THE ANSWERS. Here's how you can answer the question with the second method:

Let's TEST Answer B: $18,000
Person A = $360 + 6% of $17,000 = $360 + $1020 = $1380
Person B = 8% of $18,000 = $1440
These two values are close but not the same. Since Person B receives a higher percentage of every dollar in sales, a larger sales total would create a larger difference between what the two salespeople are paid. Thus, we need an answer that is SMALLER that $18,000 (but not that much smaller, relatively speaking).

Let's TEST Answer C: $15,000
Person A = $360 + 6% of $14,000 = $360 + $840 = $1200
Person B = 8% of $15,000 = $1200
These two values are EQUAL, so this MUST be the answer.

Final Answer: C

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by Matt@VeritasPrep » Wed Sep 20, 2017 4:11 pm
Put the equation in words, then translate those words to math:

A makes $360 + 6% of (Total - $1000)

B makes 8% of Total

We want these to be equal, so:

$360 + 6% of (Total - $1000) = 8% of Total

Now let's assign a variable to the total (how about t?) and write the percentages as decimals:

360 + .06*(t - 1000) = .08t

... and from there it's just boring arithmetic!
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by Matt@VeritasPrep » Wed Sep 20, 2017 4:16 pm
We could also try to speed up the problem by thinking of the differences in the incomes.

A has a $360 head start. After each salesperson sells $1000 of product, B has $80 and A has the same as (s)he started with, $360, since A gets no commission on the first $1000.

From here, B needs to make up $360 - $80, or $280, to be even with A.

B gets 2% more commission, so if each salesperson sells $x worth of product, 2% of $x must = $280, the difference to be made up.

.02x = 280 gives us x = $14,000, so after *another* $14,000 in sales the reps will be even.

We started with $1000, of course, leaving us a sales total of $1000 + $14,000, or $15,000.
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by BTGmoderatorDC » Thu Oct 12, 2017 1:36 pm
[email protected] wrote:Hi Iheiannie07,

We're told the pay rates for two salespeople:
1) Salesperson A = $360 + 6% of sales above $1,000
2) Salesperson B = 8% of sales

We're asked for the total sales that would lead to the SAME pay for each salesperson. This question can be solved algebraically or by TESTing THE ANSWERS. Here's how you can answer the question with the second method:

Let's TEST Answer B: $18,000
Person A = $360 + 6% of $17,000 = $360 + $1020 = $1380
Person B = 8% of $18,000 = $1440
These two values are close but not the same. Since Person B receives a higher percentage of every dollar in sales, a larger sales total would create a larger difference between what the two salespeople are paid. Thus, we need an answer that is SMALLER that $18,000 (but not that much smaller, relatively speaking).

Let's TEST Answer C: $15,000
Person A = $360 + 6% of $14,000 = $360 + $840 = $1200
Person B = 8% of $15,000 = $1200
These two values are EQUAL, so this MUST be the answer.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich
Thank you, this is a great help :)
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by BTGmoderatorDC » Thu Oct 12, 2017 1:37 pm
Matt@VeritasPrep wrote:Put the equation in words, then translate those words to math:

A makes $360 + 6% of (Total - $1000)

B makes 8% of Total

We want these to be equal, so:

$360 + 6% of (Total - $1000) = 8% of Total

Now let's assign a variable to the total (how about t?) and write the percentages as decimals:

360 + .06*(t - 1000) = .08t

... and from there it's just boring arithmetic!
Thanks a lot!
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by BTGmoderatorDC » Thu Oct 12, 2017 1:41 pm
Matt@VeritasPrep wrote:We could also try to speed up the problem by thinking of the differences in the incomes.

A has a $360 head start. After each salesperson sells $1000 of product, B has $80 and A has the same as (s)he started with, $360, since A gets no commission on the first $1000.

From here, B needs to make up $360 - $80, or $280, to be even with A.

B gets 2% more commission, so if each salesperson sells $x worth of product, 2% of $x must = $280, the difference to be made up.

.02x = 280 gives us x = $14,000, so after *another* $14,000 in sales the reps will be even.

We started with $1000, of course, leaving us a sales total of $1000 + $14,000, or $15,000.
Thanks for helping!
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by Matt@VeritasPrep » Fri Oct 13, 2017 11:16 am
lheiannie07 wrote:
Matt@VeritasPrep wrote:We could also try to speed up the problem by thinking of the differences in the incomes.

A has a $360 head start. After each salesperson sells $1000 of product, B has $80 and A has the same as (s)he started with, $360, since A gets no commission on the first $1000.

From here, B needs to make up $360 - $80, or $280, to be even with A.

B gets 2% more commission, so if each salesperson sells $x worth of product, 2% of $x must = $280, the difference to be made up.

.02x = 280 gives us x = $14,000, so after *another* $14,000 in sales the reps will be even.

We started with $1000, of course, leaving us a sales total of $1000 + $14,000, or $15,000.
Thanks for helping!
My pleasure! Thanks for thanking! :)
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