Help required (Applied problems, simultaneous Equation)

[Dblooos]

Salesperson A's compensation for any week is $360 plus 6 percent of the portion of A's total sale 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

[Uva@90]

Salesperson A's compensation for any week is $360 plus 6 percent of the portion of A's total sale 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

Hi Dblooos,
Let's take compensation for A is Ca
and compensation for B is Cb.

Total Sale made by A for week be Sa
and Sale made by B for week is Sb.

We can form an equation
Ca = 360 + (6/100)(Sa-1000) and
Cb = (8/100)*Sb

Now select answer such that which satisfies both equation, i.e. Ca = Cb
Only Option matches is C

Regards,
Uva.

[Dblooos]

Uva
Thank you for your quick response. However, my confusion is emanating from the fact that Question says, "for what amount of TOTAL weekly sales would both salespeople earn the same compensation". So am I doing a mistake by assuming Sa=Sb=15,000 should it not be Sa+Sb=30,000 (total weekly sales) Please explain..

[GMATGuruNY]

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 can plug in the answers, which represent the total sales.
When the correct answer is plugged in, A's compensation = B's compensation.
Start with C, the middle answer choice.

C: 15,000
Here, A's sales above 1000 = 15000-1000 = 14000.
A's compensation = 360 + .06(14000) = 360 + 840 = 1200.
B's compensation = .08(15000) = 1200.
Success!

The correct answer is C.

[Dblooos]

GmatGuru,

Thank you for your quick response. I appreciate your help. However, I have two questions:

1. Here we kind of knew the answer so we solved backward but won't it be time consuming to solve through all the choices if the right choice was choice E. I am struggling to bring my time under 2 mins per question. So any strategies would be much appreciated.

2. Equation for A's compensation is incorrect as 15,000 is total weekly sale and not A's weekly sale. Am I thinking wrong?

[Uva@90]

Uva
Thank you for your quick response. However, my confusion is emanating from the fact that Question says, "for what amount of TOTAL weekly sales would both salespeople earn the same compensation". So am I doing a mistake by assuming Sa=Sb=15,000 should it not be Sa+Sb=30,000 (total weekly sales) Please explain..

Hi Dblooos,

Question States,

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?

If you see the Highlighted things in green color. we can understand, what ever given for A's compensation is TOTAL for that week, Similarly What ever given for B's compensation is TOTAL for that week.

What we are asked to find is for what amount will both their TOTAL Compensation will be same.

In question no-where it is mentioned to find the SUM of TOTAL compensation for the week.

Hope I made it clear.

Regards,
Uva.

[sanju09]

Uva
Thank you for your quick response. However, my confusion is emanating from the fact that Question says, "for what amount of TOTAL weekly sales would both salespeople earn the same compensation". So am I doing a mistake by assuming Sa=Sb=15,000 should it not be Sa+Sb=30,000 (total weekly sales) Please explain..

Hi Dblooos,

Question States,

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?

If you see the Highlighted things in green color. we can understand, what ever given for A's compensation is TOTAL for that week, Similarly What ever given for B's compensation is TOTAL for that week.

What we are asked to find is for what amount will both their TOTAL Compensation will be same.

In question no-where it is mentioned to find the SUM of TOTAL compensation for the week.

Hope I made it clear.

Regards,
Uva.

Testing the choices to match the conditions of the question is the best, accurate, and the fastest approach in such kind of questions where there are known numbers in the answers. GMATGuruNY did the same thing. Starting from C has a cause behind the strategy, so it wasn't by chance.

[Dblooos]

Thank you UVA, I see what you are saying. I wish they wrote for what amount of THEIR total weekly sales..... It would have become more clear. Anyways Thank you so much.

Sanju,
Can you please elaborate on testing answer choices strategies?

[sanju09]

Thank you UVA, I see what you are saying. I wish they wrote for what amount of THEIR total weekly sales..... It would have become more clear. Anyways Thank you so much.

Sanju,
Can you please elaborate on testing answer choices strategies?

Hi Dblooos,

When there are numbers in the answers, knowing the fact that ETS writes numbers in order (ascending or descending), we can exploit it to our favor by starting testing from C. If it works, nothing like that; but if it doesn't work, not an issue, by some smart reasoning we can decide where to move, up or down. This approach would enable us eliminate three answer choices in a single go. Now, we can either make a guess if time is short, or we can test one of the remaining two choices (say D & E), if D works, hooray, otherwise it's blindly E.

Some GMAT trainers call it Plug In The Answers Strategy while some call it Back Solving Strategy. This is often the elusive technique that high-scorers don't think of when under time pressure on hard questions. Therefore it can be very powerful. Not sure what to do? Numbers in the answers? Try Plug In The Answers Strategy.

[GMATGuruNY]

Here we kind of knew the answer so we solved backward but won't it be time consuming to solve through all the choices if the right choice was choice E. I am struggling to bring my time under 2 mins per question. So any strategies would be much appreciated.

The best way to understand how to PLUG IN THE ANSWERS efficiently is to study examples and then to practice on your own.
In the upper right corner of BTG is a search bar.
Enter "gmatguruny" and "plug in the answers", and you'll get a list of problems that I've solved by plugging in the answer choices.