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# The price of lunch for 15 people was $207 including a 15%  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Status: Private GMAT Tutor Joined: 22 Oct 2012 Posts: 119 Location: India Concentration: Economics, Finance Schools: IIMA (A) GMAT 1: 780 Q51 V47 Re: One question from OG 11th ed. [#permalink] ### Show Tags 23 Oct 2012, 19:18 1 1 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? I think the mistake you committed is a fairly common mistake. You calculated 15% gratuity on$207, which is not correct. Let's try to understand this.

These 15 people went for a lunch and ordered some really delicious dishes. They ate to their satisfaction and at last, asked the waiter to bring the bill. The waiter had done a lot in providing a good service to these people and as per the restaurant rules, he deserved 15% gratuity for service.

While the waiter had gone to bring the bill, these 15 guys figured out what all they had eaten till then and using the menu, totaled the amount they would need to pay. However, when the waiter arrived, he had a higher amount on the bill. Why? Because he had included a 15% gratuity also, which these 15 people had ignored in their calculations.

So, while these people calculated their bill amount to be, say, x, the waiter came up with a bill 1.15x.

So, now we are given that 1.15x = 207 =>x=180
Per person cost = 180/15 = 12.

The reason for telling this whole story is that you need to see what is the figure to which apply this 15%. This 15% has to be applied on figure which already existed before applying this 15%; in this case, the total amount of food they ate. The amount they paid was arrived after the application of this 15%; thus this amount existed only after application of 15% on some other number. So, you can't apply 15% to $207 because 15% was originally not applied to this number. A similar issue can be faced in the below problem: A scored 15% more than B. If A's score was 460, what was B's score? Here we can't say that B's score was 460 * (1-15%). That would be incorrect. Why? You can yourself see. What is 460*0.85. It is 391. So, cross checking, Is A 15% more than B? A=b*(1+15%) = 391*1.15 = 449.65, which is not equal to 460. So, where is the problem? The problem is that the question said that A is 15% more than B, not that B is 15% less than A. There's is a difference. (1)If A is 15% more than B, then A = 1.15B =>B=A/1.15 ~ 0.87A (2) If B is 15% less than B, then B = A (1-15%) = 0.85A So, we see that these two expressions are different. So, you have to be cautious when dealing with such statements. It is easier to say here that we limit ourselves to (1) in the question given but how do we do this in complex scenarios just like in the original question given? The common logic, as explained above, is that you need to think if a particular figure existed even before the application of the percentage; if yes, then it is independent of the percentage. For example, in A & B example question, we say that the score of A is 15% more than B. So, there is a score of B and when we increase it by 15%, we get score of A. But score of B exists before the application of percentage. So, coming back to the question, the total amount they paid i.e.$207 existed only after application of 15%, not before. Thus, 15% needs to be applied to some other variable to arrive at $207. I hope my long answer clarifies some doubts. If you have any other queries, please feel free to ask. Cheers, CJ _________________ Intern Joined: 02 May 2013 Posts: 4 Re: The price of lunch for 15 people was$207 including a 15%  [#permalink]

### Show Tags

15 Aug 2013, 22:13
To clear the common misunderstanding of this question, which will still trouble a lot of people out there, even after the solutions. My two cents: Hope it helps.

Most common mistake is multiplying 0.85x to $207 in order to arrive at the cost of the lunch OR to multiply 0.15x * 207 to find the gratuity amount and consecutively subtracting to arrive at the lunch cost. whereas, one should note that gratuity here is 15% of the cost of the lunch (in this question) and not of the total (Lunch cost + gratuity). What the common mistake is people taking the 15% of the total amount (gratuity + cost of lunch), which inflates the gratuity amount than the actual. Manager Joined: 26 Feb 2015 Posts: 115 The price of lunch for 15 people was$207 including a 15%  [#permalink]

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02 May 2015, 08:43
Any suggestions on how to crack this baby on 2 minutes or less?

I mean. $$\frac{207}{1.15}$$ takes a while
Manager
Joined: 19 Mar 2015
Posts: 64

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06 May 2015, 00:03
GMAT_700 wrote:
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 If your long division is weak like mine there is a way involving simpler math to get this. Look at the answer choices and realize that 15*answer choice + 15% is going to need to add up to exactly 207. Based on myself hating to work with decimals my approach was to choose the whole numbers first, luckily for me that meant much less math since the first one I tested was the right answer. 12*15 = 180 180 + (180*0.15)= 207 Senior Manager Joined: 15 Oct 2015 Posts: 319 Concentration: Finance, Strategy GPA: 3.93 WE: Account Management (Education) The price of lunch for 15 people was$207 including a 15%  [#permalink]

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02 Mar 2016, 02:03
GMAT_700 wrote:
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 The gurus, m’aidez please! I said $$15p + \frac{15}{100}$$ of somtin = 207 p being average price Here goes my question. 15% of what? Please answer with succinct explanation. A relentless kudos for your replies. Math Expert Joined: 02 Aug 2009 Posts: 7117 Re: The price of lunch for 15 people was$207 including a 15%  [#permalink]

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02 Mar 2016, 03:32
1
Nez wrote:
GMAT_700 wrote:
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 The gurus, m’aidez please! I said $$15p + \frac{15}{100}$$ of somtin = 207 p being average price Here goes my question. 15% of what? Please answer with succinct explanation. A relentless kudos for your replies. Hi, 15% is of the total amount spent without gratuity. And what is the total amount without gratuity -- 15p.. Since you want an explanation.. say these 15 people had a bill of 150, they had to pay 15% on this amount so total = 1.15*150= 172.5... so 15% gratuity= 172.5-150=22.5.. your equation here is $$15p + \frac{15}{100}$$ of somting = 172.5 what is something here=15p= 150.. $$15p + \frac{15}{100}$$ of somting = 172.5 $$150 + \frac{15}{100}$$ of 150= 172.5.. so :- I said $$15p + \frac{15}{100}$$ of somtin = 207 is $$15p + \frac{15}{100}$$ of 15p = 207 $$15p*(1 + \frac{15}{100})$$ = 207 $$15p*( \frac{115}{100})$$ = 207.. $$p=\frac{(207*100)}{(15*115)}=12$$ _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor VP Joined: 07 Dec 2014 Posts: 1130 The price of lunch for 15 people was$207 including a 15%  [#permalink]

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02 Mar 2016, 14:02
($207/1.15)/15=$12
Senior Manager
Joined: 03 Apr 2013
Posts: 275
Location: India
Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41
GPA: 3
Re: The price of lunch for 15 people was $207 including a 15% [#permalink] ### Show Tags 06 Jul 2016, 09:50 GMAT_700 wrote: 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

One line calculation...

$$\frac{100}{115}*207*\frac{1}{15}$$

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Re: The price of lunch for 15 people was $207 including a 15% [#permalink] ### Show Tags 08 Aug 2018, 06:31 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. _________________ Re: The price of lunch for 15 people was$207 including a 15% &nbs [#permalink] 08 Aug 2018, 06:31

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