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# 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 [#permalink]

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21 Jul 2012, 12:30
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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. [Reveal] Spoiler: 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 !!! [Reveal] Spoiler: OA _________________ Please give Kudos if you like the post Kudos [?]: 267 [0], given: 37 Math Expert Joined: 02 Sep 2009 Posts: 41892 Kudos [?]: 129113 [6], given: 12194 Re: Each week a certain salesman is paid a fixed amount equal to [#permalink] ### Show Tags 22 Jul 2012, 03:54 6 This post received KUDOS Expert's post 6 This post was BOOKMARKED summer101 wrote: 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 !!!

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?

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 $$300+(S-1,000)*0.05$$.

So, no penalties there, just two cases for the profit: if $$S\leq{1,000}$$ then the profit is simply $300 and if $$S>1,000$$, then the profit 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. Given: $$profit=0.1*S$$. It's clear that S must be greater than$1,000, so we have that $$300+(S-1,000)*0.05=0.1S$$. We can calculate S, hence calculate the profit. Sufficient.

(2) The salesman's sales last week totaled $5,000. Directly gives the value of S, hence calculate the profit. Sufficient. Answer: D. Hope it's clear. _________________ Kudos [?]: 129113 [6], given: 12194 Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 1545 Kudos [?]: 837 [3], given: 5 Re: Each week a certain salesman is paid a fixed amount equal to [#permalink] ### Show Tags 14 May 2016, 06:24 3 This post received KUDOS Expert's post summer101 wrote: 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.

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. _________________ Jeffery Miller Head of GMAT Instruction GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Kudos [?]: 837 [3], given: 5 Manager Status: Looking to improve Joined: 15 Jan 2013 Posts: 174 Kudos [?]: 72 [2], given: 65 GMAT 1: 530 Q43 V20 GMAT 2: 560 Q42 V25 GMAT 3: 650 Q48 V31 Re: Each week a certain salesman is made a fixed amount equal to [#permalink] ### Show Tags 13 Apr 2013, 10:35 2 This post received KUDOS 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.
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13 Apr 2013, 09:37
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smoothnavigator wrote:
Kindly advise what if the sales were less than USD 1000 , lets say the sales of a last week were USD 800.
How to check sufficiency of A then ??

Statements 1 and 2 in DS never contradict each other.
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13 Apr 2013, 10:36
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smoothnavigator wrote:

For explanation sake how to confirm statement 1 without any help from statement 2. Case being sales less than USD 1000.
I might be missing something but I would certainly like to know how to make statement 1 sufficient without any help from statement 2.

Maybe I don't understand what you are trying to say...

However from the text we can create the formula for the tot amount $$x=300+5%(Sales-1000)$$
Lets esamine statement 1:the total amount the salesman was paid last week is equal to 10 percent of the amount of these sales last week
$$x=10%Sales$$ and we don't know nothing else, I haven't read stetement 2 and I cannot hypothesize the case with Sales<1000$(there is no reason to do so, I have to take into consideration what the text says and nothing else). $$300+0.05(S-1000)=0.1S$$ do some math and obtain the tot sales $$S = 5000$$ Sufficient. I haven't read st 2 and I am able to answer, your "Case being sales less than USD 1000" is a consideration that goes against the info in the text. When you answer a question stick to the text: don't make any hypothesis that could compromize the answer. Hope that I have answered your question, let me know _________________ It is beyond a doubt that all our knowledge that begins with experience. Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b] Kudos [?]: 2330 [1], given: 219 Current Student Joined: 25 Sep 2012 Posts: 287 Kudos [?]: 174 [1], given: 242 Location: India Concentration: Strategy, Marketing GMAT 1: 660 Q49 V31 GMAT 2: 680 Q48 V34 Re: Each week a certain salesman is paid a fixed amount equal to [#permalink] ### Show Tags 28 May 2014, 08:17 1 This post received KUDOS someone please edit the post and put the spoiler Kudos [?]: 174 [1], given: 242 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7676 Kudos [?]: 17378 [1], given: 232 Location: Pune, India Re: Each week a certain salesman is paid a fixed amount equal to [#permalink] ### Show Tags 26 Oct 2015, 22:05 1 This post received KUDOS Expert's post skywalker18 wrote: VeritasPrepKarishma wrote: skywalker18 wrote: 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!! 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. 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 . 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) _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Each week a certain salesman is made a fixed amount equal to $30 [#permalink] ### Show Tags 13 Apr 2013, 09:31 Kindly advise what if the sales were less than USD 1000 , lets say the sales of a last week were USD 800. How to check sufficiency of A then ?? Kudos [?]: 6 [0], given: 5 Intern Joined: 05 Nov 2012 Posts: 36 Kudos [?]: 6 [0], given: 5 Location: India Concentration: General Management, Finance GMAT 1: 700 Q47 V40 GPA: 3.5 Re: salesman [#permalink] ### Show Tags 13 Apr 2013, 10:16 Zarrolou wrote: smoothnavigator wrote: Kindly advise what if the sales were less than USD 1000 , lets say the sales of a last week were USD 800. How to check sufficiency of A then ?? Statements 1 and 2 in DS never contradict each other. For explanation sake how to confirm statement 1 without any help from statement 2. Case being sales less than USD 1000. I might be missing something but I would certainly like to know how to make statement 1 sufficient without any help from statement 2. Kudos [?]: 6 [0], given: 5 Intern Joined: 05 Nov 2012 Posts: 36 Kudos [?]: 6 [0], given: 5 Location: India Concentration: General Management, Finance GMAT 1: 700 Q47 V40 GPA: 3.5 Re: salesman [#permalink] ### Show Tags 13 Apr 2013, 10:46 Zarrolou wrote: smoothnavigator wrote: For explanation sake how to confirm statement 1 without any help from statement 2. Case being sales less than USD 1000. I might be missing something but I would certainly like to know how to make statement 1 sufficient without any help from statement 2. Maybe I don't understand what you are trying to say... However from the text we can create the formula for the tot amount $$x=300+5%(Sales-1000)$$ Lets esamine statement 1:the total amount the salesman was paid last week is equal to 10 percent of the amount of these sales last week $$x=10%Sales$$ and we don't know nothing else, I haven't read stetement 2 and I cannot hypothesize the case with Sales<1000$ (there is no reason to do so, I have to take into consideration what the text says and nothing else).
$$300+0.05(S-1000)=0.1S$$ do some math and obtain the tot sales $$S = 5000$$ Sufficient.
I haven't read st 2 and I am able to answer, your "Case being sales less than USD 1000" is a consideration that goes against the info in the text. When you answer a question stick to the text: don't make any hypothesis that could compromize the answer.

Got the answer with many thanks.

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Re: Each week a certain salesman is paid a fixed amount equal to [#permalink]

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28 May 2014, 09:35
b2bt wrote:
someone please edit the post and put the spoiler

_____________
Done. Thank you.
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20 Aug 2015, 23:14
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. Kudos [?]: 9 [0], given: 4 Math Expert Joined: 02 Sep 2009 Posts: 41892 Kudos [?]: 129113 [0], given: 12194 Re: Each week a certain salesman is paid a fixed amount equal to [#permalink] ### Show Tags 20 Aug 2015, 23:50 zahraf wrote: 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.

Merging topics.

Please refer to the discussion above.
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Re: Each week a certain salesman is paid a fixed amount equal to [#permalink]

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23 Oct 2015, 23:04
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

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Re: Each week a certain salesman is paid a fixed amount equal to [#permalink]

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25 Oct 2015, 22:48
skywalker18 wrote:
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

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.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 17378 [0], given: 232 Math Forum Moderator Status: Greatness begins beyond your comfort zone Joined: 08 Dec 2013 Posts: 1530 Kudos [?]: 953 [0], given: 72 Location: India Concentration: General Management, Strategy GPA: 3.2 WE: Information Technology (Consulting) Re: Each week a certain salesman is paid a fixed amount equal to [#permalink] ### Show Tags 25 Oct 2015, 23:38 VeritasPrepKarishma wrote: skywalker18 wrote: 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!! 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. 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 . _________________ When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long +1 Kudos if you find this post helpful Kudos [?]: 953 [0], given: 72 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 4142 Kudos [?]: 2899 [0], given: 0 GPA: 3.82 Re: Each week a certain salesman is paid a fixed amount equal to [#permalink] ### Show Tags 27 Oct 2015, 23:48 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.
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Re: Each week a certain salesman is paid a fixed amount equal to [#permalink]

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07 May 2016, 05:22
Bunuel wrote:
summer101 wrote:
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 !!! 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? 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 $$300+(S-1,000)*0.05$$. So, no penalties there, just two cases for the profit: if $$S\leq{1,000}$$ then the profit is simply$300 and if $$S>1,000$$, then the profit 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. Given: $$profit=0.1*S$$. It's clear that S must be greater than $1,000, so we have that $$300+(S-1,000)*0.05=0.1S$$. We can calculate S, hence calculate the profit. Sufficient. (2) The salesman's sales last week totaled$5,000. Directly gives the value of S, hence calculate the profit. Sufficient.

Hope it's clear.

well Bunuel , can you please tell me that where it is clear(in statement 1) that the sales must be more than \$ 1000 ??

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Re: Each week a certain salesman is paid a fixed amount equal to   [#permalink] 07 May 2016, 05:22

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