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25 May 2016, 21:46
Attached is a visual that should help.
Attachments

Screen Shot 2016-05-25 at 9.42.14 PM.png [ 51.22 KiB | Viewed 1344 times ]

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10 Aug 2016, 12:27
let "X" be the cost of the meal excluding the 15% tax.

Now

> x+ 15% of x = 207
> 115x/100 = 207
> x = $180 No of people = 15 Cost per person =$180/15 = $12 Intern Joined: 21 Jan 2017 Posts: 10 Re: The price of lunch for 15 people was$207.00, including a 15  [#permalink]

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23 Jan 2017, 19:55
X+15%ofX=207
23X/20=207
X=180
180/15=12

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28 Aug 2017, 14:24
1
Top Contributor
enigma123 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

Many students will incorrectly reason that, since $207 is 15% GREATER than the pre-tip total, then the pre-tip total must be 15% LESS than$207 (i.e., pre-tip total = 85% of $207) This is a common misconception that goes something like this: If A is k percent greater than B, then B must be k percent less than A. The truth of the matter is as follows: If A is k percent greater than B, then B is NOT k percent less than A. I wrote an article about this misconception: http://www.gmatprepnow.com/articles/com ... 93-part-ii MY SOLUTION: Let x = the total BEFORE the gratuity. A 15% gratuity = 0.15x So, the TOTAL cost = x + 0.15x In other words, the TOTAL cost = 1.15x So, we can write 1.15x = 207 So, x = 207/1.15 NOTE: The GMAT often rewards people for using fractions rather than decimals. The reason for this is that most people are very uncomfortable working with fractions. So...... 207/1.15 = 207/(1 3/20) [I converted the decimal to a fraction] = 207/(23/20) = 207 x (20/23) IMPORTANT: At this point, the calculation looks very hard. But first notice that (23)(10) = 230. In other words, 230 = the sum of ten 23's Also notice that 207 is 23 less than 230 So, 207 = the sum of nine 23's In other words 207 = (23)(9) So, we have . . . = (23)(9) x (20/23) = 9 x 20 [the 23's cancel out] = 180 Yes, these calculations look cumbersome, but that's only because I added a lot of extra information. In reality, students with strong fraction skills can perform most (if not all) of these calculations in their heads. Since the total PRE-GRATUITY price =$180, the price PER PERSON = 180/15 = 12

Cheers,
Brent
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09 Sep 2017, 01:30
Can be solved with equations--
15*1.15x= $207 -->x=207*100/15*115 --> x=$12
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23 Oct 2017, 13:30
Bunuel wrote:
kashishh wrote:
GyanOne wrote:
The mistake you have made is that you have calculated the gratuity on the final amount, instead of finding the amount on which gratuity was charged to get the final amount.

If the amount spent excluding the gratuity was x, then x(1.15) = 207
=> x = 207/1.15 = 180

Then the average price per person = 180/15 = 12

Option (B)

gratuity is charged on final amount then is it not obvious to calculate such as!

just wish to have clarification on the two :
1.) 270 - 15% of 270 = 175.95/ 15 = 11.73

2.) if 115 is 270 then 100 = 180 and 180/15 = 12

is it not the same thing ?

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.

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 Bill*1.15=$207 --> Bill=$180 --> per person=$180/15=$12. Answer: B. Hii.. I don't get why this solution isn't the same as 0.85*207.. Would you please explain this? Thanks.. Math Expert Joined: 02 Sep 2009 Posts: 55609 Re: The price of lunch for 15 people was$207.00, including a 15  [#permalink]

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23 Oct 2017, 21:13
reemel3bd wrote:
Bunuel wrote:
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.

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 Bill*1.15=$207 --> Bill=$180 --> per person=$180/15=$12. Answer: B. Hii.. I don't get why this solution isn't the same as 0.85*207.. Would you please explain this? Thanks.. Please read the highlighted part. _________________ Manager Joined: 03 May 2017 Posts: 91 The price of lunch for 15 people was$207.00, including a 15  [#permalink]

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23 Oct 2017, 22:31
[quote="enigma123"]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
$$Here: 207 * \frac{20}{23} * \frac{1}{15}$$ =$$9 * \frac{4}{3} = 12... B$$

I think the quick way is to believe that most GMAT word problems divide smoothly and pay attention to the numbers, for example, it should be obvious that $$\frac{207}{23} = 9$$
i.e $$23(10-1) = 9(23)= 207$$
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Re: The price of lunch for 15 people was $207.00, including a 15 [#permalink] ### Show Tags 26 Nov 2018, 12:07 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$207.00, including a 15   [#permalink] 26 Nov 2018, 12:07

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