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06 Aug 2008, 17:13
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62% (01:19) correct 38% (01:17) wrong based on 756 sessions

The price of lunch for 15 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity? A. 11.73 B. 12 C. 13.8 D. 14 E. 15.87 [Reveal] Spoiler: OA Last edited by Bunuel on 23 Oct 2012, 05:14, edited 1 time in total. Edited the question. Kudos [?]: 38 [3], given: 0 VP Joined: 17 Jun 2008 Posts: 1374 Kudos [?]: 426 [2], given: 0 Re: One question from OG 11th ed. [#permalink] ### Show Tags 06 Aug 2008, 17:36 2 This post received KUDOS GMAT_700 wrote: The price of lunch for 15 people was$207.00, including a 15 percent gratuity for service. What was the average price per person,excluding the gratuity?
a) $11.73 b)$12.00
c) $13.80 d)$14.00
e) $15.87 Here what I did: 207 * .15 = 31.05 207 - 31.05 = 175.95 175.95 / 15 = 11.73 However the correct answer is B. Can you explain the correct answer? Clearly B is the answer I used POE here Lets consider option (E) say 15*15=225 => > 207 which is including 15% gratutity => not possible (D) 15*14=210 > 207 not possible (C)15*13.8 = 207 not possible (B) 15*12= 180 now 180(115/100)=207 => possible ANSWER IMO B _________________ cheers Its Now Or Never Kudos [?]: 426 [2], given: 0 Manager Joined: 15 Jul 2008 Posts: 205 Kudos [?]: 71 [3], given: 0 Re: One question from OG 11th ed. [#permalink] ### Show Tags 06 Aug 2008, 18:12 3 This post received KUDOS GMAT_700 wrote: The price of lunch for 15 people was$207.00, including a 15 percent gratuity for service. What was the average price per person,excluding the gratuity?
a) $11.73 b)$12.00
c) $13.80 d)$14.00
e) $15.87 Here what I did: 207 * .15 = 31.05 207 - 31.05 = 175.95 175.95 / 15 = 11.73 However the correct answer is B. Can you explain the correct answer? 207*.15 is where u r wrong. it should have been 207=1.15x where x is the bill without the tips. Note that 207 is the amount including tips, not excluding. solve 207=1.15x and divide by 15 to get 12 Kudos [?]: 71 [3], given: 0 SVP Joined: 07 Nov 2007 Posts: 1790 Kudos [?]: 1089 [0], given: 5 Location: New York Re: One question from OG 11th ed. [#permalink] ### Show Tags 07 Aug 2008, 11:29 GMAT_700 wrote: The price of lunch for 15 people was$207.00, including a 15 percent gratuity for service. What was the average price per person,excluding the gratuity?
a) $11.73 b)$12.00
c) $13.80 d)$14.00
e) $15.87 Here what I did: 207 * .15 = 31.05 207 - 31.05 = 175.95 175.95 / 15 = 11.73 However the correct answer is B. Can you explain the correct answer? say total bill b 207 = b (1+15/100) = b 1.1.5 average = 207 / (1.15 *15) =12 _________________ Your attitude determines your altitude Smiling wins more friends than frowning Kudos [?]: 1089 [0], given: 5 SVP Joined: 30 Apr 2008 Posts: 1863 Kudos [?]: 624 [3], given: 32 Location: Oklahoma City Schools: Hard Knocks Re: One question from OG 11th ed. [#permalink] ### Show Tags 07 Aug 2008, 13:12 3 This post received KUDOS Another way you can set it up if it's hard to thinkg of 1.15 x = 207 is this: x = how much you paid. x + 15% of x = total amount of bill 1x + .15x = 207 1.15x = 207. Gets you to the same thing, but helps you think of it as if you were there at the table calculating the amount rather than working backwards from 207. It might be easier for some people to do it this way. It takes a little longer, but sometimes the right answer is worth a few extra seconds. _________________ ------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$. GMAT Club Premium Membership - big benefits and savings Kudos [?]: 624 [3], given: 32 Manager Status: Will Retake GMAT Joined: 30 Jul 2010 Posts: 129 Kudos [?]: 15 [0], given: 28 Location: India Concentration: General Management, Entrepreneurship Schools: Stanford '13 (D) GPA: 3.11 WE: Information Technology (Computer Software) Re: One question from OG 11th ed. [#permalink] ### Show Tags 05 Oct 2010, 07:22 GMAT_700 wrote: The price of lunch for 15 people was$207.00, including a 15 percent gratuity for service. What was the average price per person,excluding the gratuity?
a) $11.73 b)$12.00
c) $13.80 d)$14.00
e) $15.87 Here what I did: 207 * .15 = 31.05 207 - 31.05 = 175.95 175.95 / 15 = 11.73 However the correct answer is B. Can you explain the correct answer? Answer will be B clearly. You went wrong at -> 207 * .15 = 31.05 207 includes the tip. _________________ Re-taking GMAT. Hope the charm works this time.. Kudos [?]: 15 [0], given: 28 Intern Joined: 29 Sep 2010 Posts: 13 Kudos [?]: 11 [4], given: 1 Schools: IMD '16 (A) GMAT 1: 730 Q47 V44 Re: One question from OG 11th ed. [#permalink] ### Show Tags 05 Oct 2010, 07:29 4 This post received KUDOS 1 This post was BOOKMARKED An easier way to solve this is by backcalculating using the answers. Start at the second highest (i.e. 12) so if it turns out to be too high you can eliminate the higher ones and if it's too low you can eliminate the lower ones. 15 people ate. Assuming$12 each without gratuity, then the bill was 15 * 12 = 180

Now add the gratuity: 15% of 180 = 27 (you can quickly see this by doing 10% + 5% = 18 + 9). So 180 + 27 = 207 and the answer is 12.

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Re: One question from OG 11th ed. [#permalink]

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15 Mar 2011, 08:38
I keep getting 11.73 as the answer for this one.
Here is what I did:
First I calulated 15% of 207, that is 31.05 and subtracted it from 207. Thus the amount now is 175.95.

175.95/15=11.73.But, OA is B

Anyone knows whaT I'm missing here?

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Re: One question from OG 11th ed. [#permalink]

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15 Mar 2011, 08:53
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heygirl wrote:
I keep getting 11.73 as the answer for this one.
Here is what I did:
First I calulated 15% of 207, that is 31.05 and subtracted it from 207. Thus the amount now is 175.95.

175.95/15=11.73.But, OA is B

Anyone knows whaT I'm missing here?

Just say the bill was for $x Including the gratuity of 15% will make the bill amount: 1.15x 1.15x=207 x=180 So; the actual bill without gratuity was 180. According to you, it should be 175.95, which is not correct. Think it like this; Suppose you have 100 dollars, you earn a 15% profit on that. Now you have$115.

If we make a question out of it;
$115 includes a 15% net profit, what was the original amount. With your method; it would be 115*0.15=17.25 115-17.25 =$97.75. But, you had $100, right? Thus, you will have to calculate like this; Suppose you had x dollars; 1.15x = 115 x = 115/1.15 =$100

You initially had $100. _________________ Kudos [?]: 2102 [8], given: 376 TOEFL Forum Moderator Joined: 16 Nov 2010 Posts: 1602 Kudos [?]: 601 [0], given: 40 Location: United States (IN) Concentration: Strategy, Technology Re: One question from OG 11th ed. [#permalink] ### Show Tags 15 Mar 2011, 22:27 x -> Price without Gratuity 207 = x + 0.15x => x = 207/1.15 = 180 So average price per person,excluding the gratuity = 180/15 = 12 The answer is B. _________________ Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership - big benefits and savings Kudos [?]: 601 [0], given: 40 Director Status: No dream is too large, no dreamer is too small Joined: 14 Jul 2010 Posts: 608 Kudos [?]: 1154 [1], given: 39 Re: One question from OG 11th ed. [#permalink] ### Show Tags 16 Mar 2011, 03:00 1 This post received KUDOS heygirl wrote: I keep getting 11.73 as the answer for this one. Here is what I did: First I calulated 15% of 207, that is 31.05 and subtracted it from 207. Thus the amount now is 175.95. 175.95/15=11.73.But, OA is B Anyone knows whaT I'm missing here? 15%=100+15=115 with gratuity 115 without 100 so if 207 = (100/115)*207= 180/15=12 Ans. B _________________ Collections:- PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html 100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html Kudos [?]: 1154 [1], given: 39 Manager Joined: 22 Mar 2011 Posts: 65 Kudos [?]: 16 [0], given: 10 Re: One question from OG 11th ed. [#permalink] ### Show Tags 29 Aug 2011, 04:23 Quote: 207*.15 is where u r wrong. it should have been 207=1.15x where x is the bill without the tips. Note that 207 is the amount including tips, not excluding. solve 207=1.15x and divide by 15 to get 12 Sorry I still don't get one part in the solution - multiplying by 1.15. The Q asks what was the average price per person, EXCLUDING the gratuity? So lets say the price was$100 including 15% gratuity. So excluding the gratuity should be 100 - (100*.15) = 85? (If I multiply 100* 1.15 then i get 115).

Please clarify why do we need 1.15 instead of .15 in the original Q. thanks!

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Re: One question from OG 11th ed. [#permalink]

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29 Aug 2011, 05:45
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melguy wrote:
Quote:
207*.15 is where u r wrong. it should have been 207=1.15x where x is the bill without the tips. Note that 207 is the amount including tips, not excluding.

solve 207=1.15x and divide by 15 to get 12

Sorry I still don't get one part in the solution - multiplying by 1.15. The Q asks what was the average price per person, EXCLUDING the gratuity?

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23 Oct 2012, 01:35
Hi Bunuel,

I took a crazy 4.5 mins to solve this question.

recognizing x+/15x= bill amt took lot of time.. but after that crazy calculation took hell lot of my time.. nos are crazy in thsi Qs like 207, 1.15 .
how to solve questions like these quickly.

POE mentioned above is good though.
Regards,
Sachin
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Re: The price of lunch for 15 people was $207.00, including a 15 [#permalink] ### Show Tags 23 Oct 2012, 05:12 Expert's post 3 This post was BOOKMARKED sachindia wrote: Hi Bunuel, I took a crazy 4.5 mins to solve this question. recognizing x+/15x= bill amt took lot of time.. but after that crazy calculation took hell lot of my time.. nos are crazy in thsi Qs like 207, 1.15 . how to solve questions like these quickly. POE mentioned above is good though. Regards, Sachin The price of lunch for 15 people was$207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity?

A. 11.73
B. 12
C. 13.8
D. 14
E. 15.87

First note that tip is charged on the bill. Consider this: the bill is $100 and tip is 15% means that total amount paid is 100+15=$115.

$$Bill*1.15=207=23*9$$ --> $$Bill*\frac{115}{100}=23*9$$ --> $$Bill*\frac{23}{20}=23*9$$ --> $$Bill=20*9=180$$ --> the price per person is $$\frac{180}{15}=12$$.

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23 Oct 2012, 06:22
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sachindia wrote:
Thanks a lot Bunuel,

Had I known 23* 7 =207 , would have saved lot of time

Actually it's 23*9=207. Factorizing 207 is good strategy and one could spot that it's divisible by 9 since the sum of the digits of 207 is divisible by 9.
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23 Oct 2012, 06:30
sachindia wrote:
Thanks a lot. I was dividing it by 3 since the sum is divisible by 3 as well.
not i gotto keep this in mind to check for the divisibility of 9 along with 3 as this could save lot of time. .

do u think memorizing tables till 30 will do any good?

Check divisibility rules worth memorizing here: math-number-theory-88376.html (Divisibility Rules chapter)

Hope it helps.
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