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# A certain salesman's yearly income is determined by a base

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A certain salesman's yearly income is determined by a base [#permalink]

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25 Jan 2012, 00:22
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A certain salesman's yearly income is determined by a base salary plus a commission on the sales he makes during the year. Did the salesman's base salary account for more than half of the salesman's yearly income last year?

(1) If the amount of the commission had been 30 percent higher, the salesman's income would have been 10 percent higher last year.

(2) The difference between the amount of the salesman's base salary and the amount of the commission was equal to 50 percent of the salesman's base salary last year.
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25 Jan 2012, 03:10
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devinawilliam83 wrote:
Why is the answer to this A and not D?

A certain salesman's yearly income is determined by a base salary plus a commission on the sales he makes during the year. Did the salesman's base salary account for more than half of the salesman's yearly income last year?

Given: {Income}={salary}+{commission}. Question basically asks: is {salary}>{commission}?

(1) If the amount of the commission had been 30 percent higher, the salesman's income would have been 10 percent higher last year --> 1.1({salary}+{commission})={salary}+1.3{commission} --> {salary}=2{commission} --> {salary}>{commission}. Sufficient.

(2) The difference between the amount of the salesman's base salary and the amount of the commission was equal to 50 percent of the salesman's base salary last year --> |{salary}-{commission}|=0.5{salary}, notice that {salary}-{commission} is in absolute value sign ||, meaning that we can have two cases:

A. {salary}-{commission}=0.5{salary} --> 0.5{salary}={commission} --> {salary}>{commission}, thus the answer would be YES;
Or:
A. {commission}-{salary}=0.5{salary} --> 1.5{salary}={commission} --> {salary}<{commission}, thus the answer would be No.
Not sufficient.

Hope it's clear.
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Re: A certain salesman's yearly income is determined by a base [#permalink]

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21 Jun 2012, 04:04
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jaswinder46 wrote:
please explain why salary - commission is in absoulute value sign?

Because if {salary}>{commission} then {salary}-{commission}=0.5{salary}, since 0.5{salary}>0.

But if {salary}<{commission} then {commission}-{salary}=0.5{salary}.

So, the second statement, which says that "the difference between the amount of the salesman's base salary and the amount of the commission was equal to 50 percent of the salesman's base salary last year" should be expressed as |{salary}-{commission}|=0.5{salary}.
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Re: A certain salesman's yearly income is determined by a base [#permalink]

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01 Aug 2015, 11:34
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Hi stopchange,

The specific question that is asked refers to a base salary and a commission LAST YEAR, so we're dealing with 2 unknowns, NOT 2 variables. This means that the two numbers are constants, but we do NOT know what they are (and thus, we don't know which one is bigger).

Fact 1 uses a 'hypothetical' that points out that increasing JUST the commission (by 30%) would have led to an increase in income (of 10%). By extension, this assumes that the other pieces (in this case, the base salary) stay the same.

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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Intern Joined: 18 May 2012 Posts: 1 Followers: 0 Kudos [?]: 5 [0], given: 0 Re: A certain salesman's yearly income is determined by a base [#permalink] ### Show Tags 21 Jun 2012, 03:54 please explain why salary - commission is in absoulute value sign? Math Expert Joined: 02 Sep 2009 Posts: 33547 Followers: 5944 Kudos [?]: 73746 [0], given: 9903 Re: A certain salesman's yearly income is determined by a base [#permalink] ### Show Tags 10 Jun 2013, 03:52 Expert's post 2 This post was BOOKMARKED Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HERE Theory on Percent and Interest Problems: math-number-theory-percents-91708.html All DS Percent and Interest Problems to practice: search.php?search_id=tag&tag_id=33 All PS Percent and Interest Problems to practice: search.php?search_id=tag&tag_id=54 _________________ Manager Joined: 14 Nov 2011 Posts: 149 Location: United States Concentration: General Management, Entrepreneurship GPA: 3.61 WE: Consulting (Manufacturing) Followers: 0 Kudos [?]: 5 [0], given: 102 Re: DS - Percentage [#permalink] ### Show Tags 14 Jun 2013, 04:14 1 This post was BOOKMARKED Bunuel wrote: devinawilliam83 wrote: Why is the answer to this A and not D? A certain salesman's yearly income is determined by a base salary plus a commission on the sales he makes during the year. Did the salesman's base salary account for more than half of the salesman's yearly income last year? Given: {Income}={salary}+{commission}. Question basically asks: is {salary}>{commission}? (1) If the amount of the commission had been 30 percent higher, the salesman's income would have been 10 percent higher last year --> 1.1({salary}+{commission})={salary}+1.3{commission} --> {salary}=2{commission} --> {salary}>{commission}. Sufficient. (2) The difference between the amount of the salesman's base salary and the amount of the commission was equal to 50 percent of the salesman's base salary last year --> |{salary}-{commission}|=0.5{salary}, notice that {salary}-{commission} is in absolute value sign ||, meaning that we can have two cases: A. {salary}-{commission}=0.5{salary} --> 0.5{salary}={commission} --> {salary}>{commission}, thus the answer would be YES; Or: A. {commission}-{salary}=0.5{salary} --> 1.5{salary}={commission} --> {salary}<{commission}, thus the answer would be No. Not sufficient. Answer: A. Hope it's clear. Hi Bunnel, If i do assume that C>S, this will contradict information given in A. Is this an Official question? Math Expert Joined: 02 Sep 2009 Posts: 33547 Followers: 5944 Kudos [?]: 73746 [0], given: 9903 Re: DS - Percentage [#permalink] ### Show Tags 14 Jun 2013, 04:16 Expert's post cumulonimbus wrote: Bunuel wrote: devinawilliam83 wrote: Why is the answer to this A and not D? A certain salesman's yearly income is determined by a base salary plus a commission on the sales he makes during the year. Did the salesman's base salary account for more than half of the salesman's yearly income last year? Given: {Income}={salary}+{commission}. Question basically asks: is {salary}>{commission}? (1) If the amount of the commission had been 30 percent higher, the salesman's income would have been 10 percent higher last year --> 1.1({salary}+{commission})={salary}+1.3{commission} --> {salary}=2{commission} --> {salary}>{commission}. Sufficient. (2) The difference between the amount of the salesman's base salary and the amount of the commission was equal to 50 percent of the salesman's base salary last year --> |{salary}-{commission}|=0.5{salary}, notice that {salary}-{commission} is in absolute value sign ||, meaning that we can have two cases: A. {salary}-{commission}=0.5{salary} --> 0.5{salary}={commission} --> {salary}>{commission}, thus the answer would be YES; Or: A. {commission}-{salary}=0.5{salary} --> 1.5{salary}={commission} --> {salary}<{commission}, thus the answer would be No. Not sufficient. Answer: A. Hope it's clear. Hi Bunnel, If i do assume that C>S, this will contradict information given in A. Is this an Official question? What do you mean by official question? Check the tags. It's MGMAT. _________________ Manager Joined: 16 Feb 2012 Posts: 237 Concentration: Finance, Economics Followers: 7 Kudos [?]: 210 [0], given: 121 A certain salesman's yearly income is determined by a base s [#permalink] ### Show Tags 17 Aug 2013, 03:16 A certain salesman's yearly income is determined by a base salary plus a commission on the sales he makes during the year. Was the salesman's commission larger than his base salary last year? (1) If the amount of the commission had been 30 percent higher, the salesman's total income (salary plus commission) would have been 10 percent higher last year. (2) The absolute difference between the amount of the salesman's base salary and the amount of the commission was equal to 50 percent of the salesman's base salary last year. _________________ Kudos if you like the post! Failing to plan is planning to fail. Math Expert Joined: 02 Sep 2009 Posts: 33547 Followers: 5944 Kudos [?]: 73746 [0], given: 9903 Re: A certain salesman's yearly income is determined by a base s [#permalink] ### Show Tags 17 Aug 2013, 03:19 Expert's post Stiv wrote: A certain salesman's yearly income is determined by a base salary plus a commission on the sales he makes during the year. Was the salesman's commission larger than his base salary last year? (1) If the amount of the commission had been 30 percent higher, the salesman's total income (salary plus commission) would have been 10 percent higher last year. (2) The absolute difference between the amount of the salesman's base salary and the amount of the commission was equal to 50 percent of the salesman's base salary last year. Merging similar topics. _________________ Manager Joined: 16 Feb 2012 Posts: 237 Concentration: Finance, Economics Followers: 7 Kudos [?]: 210 [0], given: 121 Re: A certain salesman's yearly income is determined by a base [#permalink] ### Show Tags 17 Aug 2013, 03:24 Where could I find more of these kind of questions? _________________ Kudos if you like the post! Failing to plan is planning to fail. Manager Joined: 16 Feb 2012 Posts: 237 Concentration: Finance, Economics Followers: 7 Kudos [?]: 210 [0], given: 121 Re: A certain salesman's yearly income is determined by a base [#permalink] ### Show Tags 17 Aug 2013, 07:36 Could this question be solved by picking numbers? _________________ Kudos if you like the post! Failing to plan is planning to fail. Intern Joined: 23 Mar 2011 Posts: 30 Followers: 0 Kudos [?]: 4 [0], given: 9 Re: DS - Percentage [#permalink] ### Show Tags 17 Aug 2013, 11:01 Bunuel wrote: devinawilliam83 wrote: Why is the answer to this A and not D? A certain salesman's yearly income is determined by a base salary plus a commission on the sales he makes during the year. Did the salesman's base salary account for more than half of the salesman's yearly income last year? Given: {Income}={salary}+{commission}. Question basically asks: is {salary}>{commission}? (1) If the amount of the commission had been 30 percent higher, the salesman's income would have been 10 percent higher last year --> 1.1({salary}+{commission})={salary}+1.3{commission} --> {salary}=2{commission} --> {salary}>{commission}. Sufficient. I don't know how answer choice A can be sufficient. See example below. Using your statement: 1.1({salary}+{commission})={salary}+1.3{commission} 1.1 s + 1.1 c = s + 1.3 c ; for sake of simplicity, let's say that salary = 100 and commission = 100 1.1 (100) + 1.1 (100) = 100 + 1.3 (100) 110 + 110 = 100 + 130 220 < 230 ; Insufficient ^^ I'm confused, do we have to take a salary that's greater than commission to solve the question "Is salary > commission?" Another way I thought of it was... If instead of plugging in values, is you decide isolate salary (s) and commission (c) using your formula in bold, it would be: .10 s = .02 c In this case, for all positive values where salary > commission, it holds true. Sufficient. Can someone please help explain how Bunuel got salary = 2 commission? What am I doing wrong above? Am I missing something? ~ Im2bz2p345 Last edited by Im2bz2p345 on 17 Aug 2013, 11:16, edited 2 times in total. Director Joined: 14 Dec 2012 Posts: 842 Location: India Concentration: General Management, Operations GMAT 1: 700 Q50 V34 GPA: 3.6 Followers: 51 Kudos [?]: 1044 [0], given: 197 Re: DS - Percentage [#permalink] ### Show Tags 17 Aug 2013, 11:09 Im2bz2p345 wrote: Using your statement: 1.1({salary}+{commission})={salary}+1.3{commission} 1.1 s + 1.1 c = s + 1.3 c ; for sake of simplicity, let's say that salary = 100 and commission = 100 1.1 (100) + 1.1 (100) = 100 + 1.3 (100) 110 + 110 = 100 + 130 220 < 230 If instead of plugging in values, you decide isolate salary (s) and commission (c) using your formula, it would be: .10 s = .02 c In this case, for all positive values salary > commission. Can someone please help explain how Bunuel got salary = 2 commission? What am I doing wrong above? Am I missing something? ~ Im2bz2p345 hi, the above highlited part is wrong. in that you are assuming salary = comission = 100 if both are equal how can you compare which one is bigger. let say salary = $$s$$ comission =$$c$$ $$1.1(s + c) = s + 1.3 c$$ $$1.1s + 1.1c = s + 1.3 c$$ taking s items one side and c item one side $$0.1s = 0.2c$$ ok now multiply both sides with 10 $$s = 2c$$ hope its clear now _________________ When you want to succeed as bad as you want to breathe ...then you will be successfull.... GIVE VALUE TO OFFICIAL QUESTIONS... GMAT RCs VOCABULARY LIST: vocabulary-list-for-gmat-reading-comprehension-155228.html learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat- ... assessment : http://www.youtube.com/watch?v=APt9ITygGss Intern Joined: 23 Mar 2011 Posts: 30 Followers: 0 Kudos [?]: 4 [0], given: 9 Re: DS - Percentage [#permalink] ### Show Tags 17 Aug 2013, 11:17 blueseas wrote: Im2bz2p345 wrote: Using your statement: 1.1({salary}+{commission})={salary}+1.3{commission} 1.1 s + 1.1 c = s + 1.3 c ; for sake of simplicity, let's say that salary = 100 and commission = 100 1.1 (100) + 1.1 (100) = 100 + 1.3 (100) 110 + 110 = 100 + 130 220 < 230 If instead of plugging in values, you decide isolate salary (s) and commission (c) using your formula, it would be: .10 s = .02 c In this case, for all positive values salary > commission. Can someone please help explain how Bunuel got salary = 2 commission? What am I doing wrong above? Am I missing something? ~ Im2bz2p345 hi, the above highlited part is wrong. in that you are assuming salary = comission = 100 if both are equal how can you compare which one is bigger. let say salary = $$s$$ comission =$$c$$ $$1.1(s + c) = s + 1.3 c$$ $$1.1s + 1.1c = s + 1.3 c$$ taking s items one side and c item one side $$0.1s = 0.2c$$ ok now multiply both sides with 10 $$s = 2c$$ hope its clear now Thank you blueseas! I missed that last step of multiplying both sides by 10, shoot - should have realized it before I posted. Appreciate your quick response. ~ Im2bz2p345 GMAT Club Legend Joined: 09 Sep 2013 Posts: 10225 Followers: 482 Kudos [?]: 124 [0], given: 0 Re: A certain salesman's yearly income is determined by a base [#permalink] ### Show Tags 19 Aug 2014, 02:25 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Manager Joined: 27 Aug 2014 Posts: 99 Concentration: Finance, Strategy GPA: 3.9 WE: Analyst (Energy and Utilities) Followers: 0 Kudos [?]: 73 [0], given: 18 Re: A certain salesman's yearly income is determined by a base [#permalink] ### Show Tags 16 Feb 2015, 11:39 Bunuel wrote: devinawilliam83 wrote: Why is the answer to this A and not D? A certain salesman's yearly income is determined by a base salary plus a commission on the sales he makes during the year. Did the salesman's base salary account for more than half of the salesman's yearly income last year? Given: {Income}={salary}+{commission}. Question basically asks: is {salary}>{commission}? (1) If the amount of the commission had been 30 percent higher, the salesman's income would have been 10 percent higher last year --> 1.1({salary}+{commission})={salary}+1.3{commission} --> {salary}=2{commission} --> {salary}>{commission}. Sufficient. (2) The difference between the amount of the salesman's base salary and the amount of the commission was equal to 50 percent of the salesman's base salary last year --> |{salary}-{commission}|=0.5{salary}, notice that {salary}-{commission} is in absolute value sign ||, meaning that we can have two cases: A. {salary}-{commission}=0.5{salary} --> 0.5{salary}={commission} --> {salary}>{commission}, thus the answer would be YES; Or: A. {commission}-{salary}=0.5{salary} --> 1.5{salary}={commission} --> {salary}<{commission}, thus the answer would be No. Not sufficient. Answer: A. Hope it's clear. Dear Bunuel, I'm not sure if you need to consider two cases here based on the question's second statement. It is like stating " if the difference between A and B is 4, I would consider A-B = 4 and not |A-B| =4. The similar question, which you used to merge the topic clearly specifies that the absolute difference between the base salary and the commission is..., there I can understand the two cases but not for the question above, where it does not state anything about the absolute difference. Please correct if I'm wrong. Intern Joined: 15 Feb 2015 Posts: 14 Followers: 0 Kudos [?]: 4 [0], given: 1 A certain salesman's yearly income is determined by a base [#permalink] ### Show Tags 16 Feb 2015, 13:48 My 2 cents from question stem: commission + base = 1 for statement 1, -> 1.3base + commission = 1.1 plus 1base + commission = 1 -> 0.3 base = 0.1 -> base = 33% -> sufficient for statement 2, -> base - commission = 0.5base or -> commission - base = 0.5base -> base is equal 50% or 33% -> not greater than 50% -> not suffificent -> Correct Answer is A JMO, please correct me if there is any logical flaw. Thanks very much! Last edited by cherryli2015 on 16 Feb 2015, 19:37, edited 1 time in total. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 6693 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 289 Kudos [?]: 1971 [0], given: 161 Re: A certain salesman's yearly income is determined by a base [#permalink] ### Show Tags 16 Feb 2015, 18:30 Expert's post Hi santorasantu, The prompt never stated whether the base salary was larger than the commission or the commission was larger than the base salary, so we CANNOT assume that the base salary is bigger just because it was mentioned first in the sentence. The word "difference" implies that one of them IS bigger, but we don't know which one. THAT is why Bunuel addressed it. GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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Re: A certain salesman's yearly income is determined by a base [#permalink]

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31 Jul 2015, 17:38
For statement 1, why can we assume that the base salary stays the same? i.e no percent change associated with base salary. If only the commission had been 30% higher, then the answer would be A, but what if the base salary could be, for example, 20% lower? Wouldn't the answer then be E?

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Re: A certain salesman's yearly income is determined by a base   [#permalink] 31 Jul 2015, 17:38
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