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# The price of lunch for 15 people was $207 including a 15%  Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: Manager Joined: 13 Mar 2007 Posts: 101 Followers: 1 Kudos [?]: 6 [1] , given: 0 The price of lunch for 15 people was$207 including a 15% [#permalink]  06 Aug 2008, 16:13
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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, 04:14, edited 1 time in total. Edited the question. VP Joined: 17 Jun 2008 Posts: 1406 Followers: 7 Kudos [?]: 112 [2] , given: 0 Re: One question from OG 11th ed. [#permalink] 06 Aug 2008, 16:36 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 Manager Joined: 15 Jul 2008 Posts: 209 Followers: 3 Kudos [?]: 21 [2] , given: 0 Re: One question from OG 11th ed. [#permalink] 06 Aug 2008, 17:12 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? 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 SVP Joined: 07 Nov 2007 Posts: 1829 Location: New York Followers: 25 Kudos [?]: 439 [0], given: 5 Re: One question from OG 11th ed. [#permalink] 07 Aug 2008, 10:29 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 SVP Joined: 30 Apr 2008 Posts: 1893 Location: Oklahoma City Schools: Hard Knocks Followers: 29 Kudos [?]: 428 [1] , given: 32 Re: One question from OG 11th ed. [#permalink] 07 Aug 2008, 12:12 1 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$$. Get the best GMAT Prep Resources with GMAT Club Premium Membership Manager Status: Will Retake GMAT Joined: 29 Jul 2010 Posts: 137 Location: India Concentration: General Management, Entrepreneurship Schools: Stanford '13 (D) GPA: 3.11 WE: Information Technology (Computer Software) Followers: 3 Kudos [?]: 15 [0], given: 28 Re: One question from OG 11th ed. [#permalink] 05 Oct 2010, 06:22 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.. Intern Joined: 29 Sep 2010 Posts: 13 Schools: IMD '16 (A) GMAT 1: 730 Q47 V44 Followers: 0 Kudos [?]: 5 [0], given: 1 Re: One question from OG 11th ed. [#permalink] 05 Oct 2010, 06:29 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]  15 Mar 2011, 07:38
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]  15 Mar 2011, 07:53
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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. _________________ SVP Joined: 16 Nov 2010 Posts: 1691 Location: United States (IN) Concentration: Strategy, Technology Followers: 30 Kudos [?]: 285 [0], given: 36 Re: One question from OG 11th ed. [#permalink] 15 Mar 2011, 21:27 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) Get the best GMAT Prep Resources with GMAT Club Premium Membership Director Status: GMAT Learner Joined: 14 Jul 2010 Posts: 652 Followers: 34 Kudos [?]: 213 [0], given: 32 Re: One question from OG 11th ed. [#permalink] 16 Mar 2011, 02:00 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 _________________ I am student of everyone-baten 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 Manager Joined: 22 Mar 2011 Posts: 72 Followers: 1 Kudos [?]: 2 [0], given: 10 Re: One question from OG 11th ed. [#permalink] 29 Aug 2011, 03:23 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]  29 Aug 2011, 04:45
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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?

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! Actually, that's the tricky part of the question: When you say 100 is including the 15% gratuity; Upon subtracting 0.15*100 from 100, you won't get the actual value spent for food, excluding gratuity. The reason is that: 0.15*100 is more than 0.15*x(the money spent for food, less than 100 of course) So, you should say x+0.15x=100 And not say 100-0.15x=x Both of these will give different values for x, former being correct. Gratuity of 15% is applied for the food alone. _________________ Manager Joined: 28 Jul 2011 Posts: 213 Followers: 0 Kudos [?]: 26 [0], given: 13 Re: One question from OG 11th ed. [#permalink] 30 Aug 2011, 06:30 let x be the amount before the gratuity So, x + 15%(x) = 270 x + .15x = 270 1.15x = 270 x = 270/1.15 x = 180 for each = 180/15 = 12 = B Director Status: Gonna rock this time!!! Joined: 22 Jul 2012 Posts: 550 Location: India GMAT 1: 640 Q43 V34 GMAT 2: 630 Q47 V29 WE: Information Technology (Computer Software) Followers: 2 Kudos [?]: 27 [0], given: 562 Re: The price of lunch for 15 people was$207.00, including a 15 [#permalink]  23 Oct 2012, 00:35
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] 23 Oct 2012, 04:12 Expert's post 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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Re: The price of lunch for 15 people was $207 including a 15% [#permalink] 23 Oct 2012, 05:19 Thanks a lot Bunuel, Had I known 23* 7 =207 , would have saved lot of time _________________ hope is a good thing, maybe the best of things. And no good thing ever dies. Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595 My GMAT Journey : end-of-my-gmat-journey-149328.html#p1197992 Math Expert Joined: 02 Sep 2009 Posts: 19047 Followers: 3367 Kudos [?]: 24496 [0], given: 2680 Re: The price of lunch for 15 people was$207 including a 15% [#permalink]  23 Oct 2012, 05:22
Expert's post
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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Re: The price of lunch for 15 people was $207 including a 15% [#permalink] 23 Oct 2012, 05:27 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? _________________ hope is a good thing, maybe the best of things. And no good thing ever dies. Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595 My GMAT Journey : end-of-my-gmat-journey-149328.html#p1197992 Math Expert Joined: 02 Sep 2009 Posts: 19047 Followers: 3367 Kudos [?]: 24496 [0], given: 2680 Re: The price of lunch for 15 people was$207 including a 15% [#permalink]  23 Oct 2012, 05:30
Expert's post
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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Re: The price of lunch for 15 people was $207 including a 15% [#permalink] 23 Oct 2012, 05:30 Similar topics Replies Last post Similar Topics: Increasing the original price of an article by 15% and then 3 09 Mar 2013, 20:48 11 The price of lunch for 15 people was$207.00, including a 15 14 02 May 2012, 14:55
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