Each week a certain salesman is paid a fixed amount equal to

Question

Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5 percent of the amount of his sales that week over $1,000. What is the total amount the salesman was paid last week?

(1) The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week.
(2) The salesman's sales last week totaled $5,000.

OG says answer is D. I am confused with their explanation for the statement 1.
 profit = .10Sales and profit = 300 + 0.05(S-1000). And thats how they solve both the equations.

What i don't understand is what if Sale for that week is 500 or less than 1000. He doesn't earn any commission and there isn't any statement which says that he has a penalty. So ideally it should be only 300. But above with above equation he will earn less than 300. Can someone please explain !!!

Bunuel · Accepted Answer

Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5 percent of the amount of his sales that week over $1,000. What is the total amount the salesman was paid last week?

Let's denote the week's sales amount as  S .

Case 1: If  S ≤ 1,000 , the salesman's income is  $300 . 
  Case 2: If  S > 1,000 , the salesman's income is  $300 + (S - 1,000)*0.05 .

(1) The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week.

This means  income = 0.1*S . Clearly, S must be greater than $1,000. Therefore,  $300 + (S - 1,000)*0.05 = 0.1*S . From this equation, we can determine S and subsequently the income. Sufficient.

(2) The salesman's sales last week totaled $5,000.

This provides a direct value for S, allowing us to determine the income. Sufficient.

Answer: D.

Hope it's clear.

JeffTargetTestPrep · Answer

Solution:

We are given that a salesman is paid $300, plus a commission equal to 5 percent of the amount of his sales over $1,000. If we set variable T as the total amount of his sales and A as the amount he earned last week, we can create the following equation:

A = 300 + 0.05(T – 1,000)

We need to determine the value of A.

Statement One Alone:

The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week.

Using the information we can create the following equation:

A = 0.1T

Since A = 0.1T, we can substitute 0.1T for A in the equation A = 300 + 0.05(T – 1,000).

0.1T = 300 + 0.05T – 50

0.05T = 250

5T = 25,000

T = 5,000

Since we have a value for T, we can determine A.

A = 300 + 0.05(5,000 – 1,000)

A = 300 + 0.05(4,000)

A = 300 + 200

A = 500

Statement one is sufficient to answer the question. We can eliminate answer choice B, C, and E.

Statement Two Alone:

The salesman's sales last week totaled $5,000.

Once again, since we have a value for T, we can determine the value of A. Statement two is sufficient to answer the question.

The answer is D.

nt2010 · Answer

For your what if scenario the answer is as follows -

Amount from the commission would be 0 and salesman would have made last week only $300. Typically in GMAT you take the question and statements as facts.

//kudos please, if the above explanation is good.

Skywalker18 · Answer

In a data sufficiency question is it necessary for both the statements to return the same unique value ?
I was going through another post of the same question , in which PiyushK has provided a new statement :modified statement 1 : Sales man income was 50% of his total sale.
The below is the link to the question-
each-week-a-certain-salesman-is-paid-a-fixed-amount-equal-to-6616.html

Experts please help!!

KarishmaB · Answer

Yes, both the statements are a part of the same question. One cannot return that x is 2 if the other says that x is 7. In one question, x can take only one unique value. 
So if both statements are giving you a unique value, the value will be the same. If it isn't, it means you have made a mistake somewhere. 
Of course, it is possible that one statement gives you a bunch of possible values for x and the other gives you a unique value but obviously, the unique value would be a part of the bunch of values given by the other statement.

Skywalker18 · Answer

Thanks a lot VeritasPrepKarishma

"Of course, it is possible that one statement gives you a bunch of possible values for x and the other gives you a unique value but obviously, the unique value would be a part of the bunch of values given by the other statement" As per this if statement 1 returns 2 values of x - a and b and statement 2 returns a single value of x = a Then we can conclude that x=a is the solution. Then our answer choice will be C right ? In other words x can take a value which is intersection of result set 1 and 2 . And if the intersection of the 2 result sets is null then we will have option E .

KarishmaB · Answer

So this is why DS questions are tricky. Think about it:

if statement 1 returns 2 values of x - a and b 
and statement 2 returns a single value of x = a
Then we can conclude that x=a is the solution.

Correct!

Then our answer choice will be C right ?

Wrong! The answer will be (B) in that case (assuming statement II tells you that x = a). If one statement gives you a unique value for x, it alone is sufficient. We don't need the more generic other statement which gives us multiple values for x.

When will the answer be (C)?
When statement 1 gives x = a or b and statement 2 gives x = a or c
Now you need both statements to see that x can take only one value "a", if it has to satisfy both statements.

And if the intersection of the 2 result sets is null then we will have option E . 
If intersection of the two result sets in null, it is a wrong DS question since there has to be at least one common value (your original question). The answer will be (E) when the two sets have multiple values in the overlap.
When statement 1 gives x = a or b or c and statement 2 gives x = a or c.
Using both statements, we can say that x is either a or c. But we do not know which. So answer is (E)

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5 percent of the amount of his sales that week over $1,000. What is the total amount the salesman was paid last week?

(1) The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week.
(2) The salesman's sales last week totaled $5,000.

If we modify the question, making sales' payment:p, sales amount:s, p=300+(s-1000)5%. There are 2 variables (p,s) and an equation, so we need one more equation when 2 are actually given from the 2 conditions; there is high chance (D) will be our answer.
From condition 1, it is sufficient as p=0.1s
and condition 2 is also sufficient in s=5000. The answer therefore becomes (D)

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

dxhzhu · Answer

Hi all,

I'm a fresh GMATer. for this question, I have only one question(but I think it won't affect the answer)

when his sales > 1000, the commission should be 5%*S. Because I think 1000 is not a value, just a precondition.

I don't know whether my understanding is right or not...

Bunuel · Answer

Please read this: https://gmatclub.com/forum/each-week-a- ... l#p1106484 Say S is the amount of his sales that week, then: If S\leq{1,000} , salesman's profit is $300 ; If S>1,000 , salesman's profit is $300+(S-1,000)*0.05 .

BillyZ · Answer

Why we need to minus 1,000, 0.05*(S-1,000) instead of 0.05*S ?

For example Sales = 2,000, Commission = 0.05*2,000

Bunuel · Answer

No.

Each week a certain salesman is paid a fixed amount equal to $300, plus  a commission equal to 5 percent of the amount of his sales that week    OVER    $1,000 . What is the total amount the salesman was paid last week?

So, if S = 2,000, then commission = (2,000 - 1,000)*0.05 and the profit = 300 + (2,000 - 1,000)*0.05.

Hope it's clear.

BrentGMATPrepNow · Answer

Given : Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5 percent of the amount of his sales that week over $1,000.   
Let T = Total sales last week
So (T - 1000) = the amount that EXCEEDS $1000
Total paycheck = $300 + 5% of (T - 1000)
Or we can write: Total paycheck last week =  $300 + 0.05(T - 1000)

Target question :    What is the total amount the salesman was paid last week?

Statement 1 : The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week.  
We can write:  300 + 0.05(T - 1000)  = 10% of T
In other words,  300 + 0.05(T - 1000)  = 0.1T

ASIDE: at this point, we should recognize that we COULD solve the above equation for T, which means we COULD determine how much the salesman was paid last week. 
So, statement 1 is SUFFICIENT.

That said, let's solve the equation (for "fun")
Take:  300 + 0.05(T - 1000)  = 0.1T
Simplify: 300 + 0.05T - 50 = 0.1T
Simplify: 250 + 0.05T = 0.1T
Subtract 0.05T from both sides: 250 = 0.05T
Solve: T = 5000
If T = 5000, then: Total paycheck last week =  $300 + 0.05(5000 - 1000) 
= 300 + 0.05(4000)
= 300 + 200
= 500
So,  the answer to the target question is $500 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : The salesman's sales last week totaled $5,000  
In other words, T = 5000
Total paycheck last week =  $300 + 0.05(5000 - 1000) 
= 300 + 0.05(4000)
= 300 + 200
= 500
So,  the answer to the target question is $500 
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

GMATinsight · Answer

Answer: Option D

Video solution by  GMATinsight

https://www.youtube.com/watch?v=gVJ10z6r3mw

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=NCsm-wqIoBw

MBAHOUSE · Answer

Classic question from the official source mba.com

avggmatstudent23 · Answer

Hi  Bunuel   KarishmaB   chetan2u 
Reading the question, I understood the commission as the sum of sales that are over 1000. For e.g. If total sales are 4000 split into 1 sale of 2000 and 4 sales of 500 then commission would be 5% of 2000 not 5% of 3000.

Can you help me with where I am going wrong?

Ps. I understood the logic in the answer posts but I think I'm wrong in understanding the language of the question.

KarishmaB · Answer

Here, Sales = Revenue
"amount of revenue" makes perfect sense.

If Sales were meant to be transactions, we would have been given "5% of those sales that brought in more than $1000 each" etc. There is no discussion of the number of transactions etc. Usually, sales will mean revenue.

hemilshihora · Answer

Bunuel   KarishmaB   JeffTargetTestPrep

I have a simple doubt, the question here asks us  What is the total amount the salesman was paid last week?  which means we have to find if we can find the  exact numerical answer of the given question  and not If we can find the data or  not as this is not a Yes/No question

So by this logic we can use  Statement 2 to get exact numeric value  and using  Statement 1 we get an equation  and  not exact numeric value , considering all these facts the shouldn't the answer be Option B instead of D ?

Each week a certain salesman is paid a fixed amount equal to

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Each week a certain salesman is paid a fixed amount equal to

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