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02 May 2012, 15:55
5
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Difficulty:

55% (hard)

Question Stats:

65% (01:31) correct 35% (01:39) wrong based on 1512 sessions

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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

[Reveal] Spoiler:
How come the answer is B?

This is how I solved it and got A, which is incorrect.

$207 includes 15% gratuity so 0.15 * 207 = 31.05 Price EXCLUDING gratuity = 207 - 31.05 = 175.95 Average price per person = 175.95/15 = 11.73 [Reveal] Spoiler: OA _________________ Best Regards, E. MGMAT 1 --> 530 MGMAT 2--> 640 MGMAT 3 ---> 610 GMAT ==> 730 Kudos [?]: 4115 [5], given: 217 Math Expert Joined: 02 Sep 2009 Posts: 41873 Kudos [?]: 128619 [7], given: 12180 Re: The price of lunch for 15 people was$207.00, including a 15 [#permalink]

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28 Feb 2013, 01:50
7
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Expert's post
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DelSingh wrote:
Can someone please explain how you compute 207/1.15 under two minutes quickly? I think my division need help

Transform decimal into fraction: $$1.15=1\frac{15}{100}=1\frac{3}{20}=\frac{23}{20}$$.

$$Bill*1.15=207$$ --> $$Bill*\frac{23}{20}=207$$ --> $$Bill*\frac{23}{20}=9*23$$ --> $$\frac{Bill}{20}=9$$ --> $$Bill=180$$.

Hope it helps.
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03 May 2012, 12:56
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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. _________________ Kudos [?]: 128619 [4], given: 12180 Intern Joined: 13 Nov 2010 Posts: 42 Kudos [?]: 26 [3], given: 2 Re: The price of lunch for 15 people was$207 including a 15% [#permalink]

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03 May 2012, 07:51
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enigma123 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 How come the answer is B? This is how I solved it and got A, which is incorrect.$207 includes 15% gratuity so 0.15 * 207 = 31.05

Price EXCLUDING gratuity = 207 - 31.05 = 175.95

Average price per person = 175.95/15 = 11.73

I'll show You perhaps the most easiest way to solve such problem

As it is a percentage problem so just take the initial price before the gratuity is 100 the as the gratuity is calculated on the final price, so as we assumed the final bill before adding gratuity is 100 so gratuity is 15% of 100 is 15 so the total price of meals is 115 so the given amount i.e 207 is for 115 then we have to calculate for 100 here we go

for 115 207
for 100 x

so by cross multiplication we get 115x=100*207 => x=100*207/110 by simplifying we get x as 180 which is the price of lunch before gratuity so the gratuity is 27 so

as the question ask the average price person excluding gratuity is 180/15=12 so our answer is b

hope its concise and clear .

if u satisfied with my effort don't hesitate to give +1 kudos.

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02 May 2012, 21:23
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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)
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20 Feb 2013, 14:14
1
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let the price before gratuity = x
that means that (115/100)x = 207

Solving for x we get 180. 180/15 = 12. Answer B.

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The price of lunch for 15 people was $207 including a 15% [#permalink] ### Show Tags 12 May 2014, 02:55 1 This post received KUDOS 1 This post was BOOKMARKED 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

here is my trouble:

the answer is B, because people say that the "15%" means 15% of the real amount, by say real amount, I mean the amounts these guys paid for what they ate.
but what puzzled me is that,
the subject of the sentence is "the price", which equals to $207, so, in my opinion, the following "15%" is to modify "the price", which is$207. if so, the gratuity must be $207*15%, and in this way, answer is A. so could anybody explain this to me? am i wrong? thanks a lot! Kudos [?]: 1 [1], given: 0 Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 1634 Kudos [?]: 837 [1], given: 2 Location: United States (CA) Re: The price of lunch for 15 people was$207.00, including a 15 [#permalink]

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03 May 2016, 11:38
1
KUDOS
Expert's post
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

[Reveal] Spoiler:
How come the answer is B?

This is how I solved it and got A, which is incorrect.

$207 includes 15% gratuity so 0.15 * 207 = 31.05 Price EXCLUDING gratuity = 207 - 31.05 = 175.95 Average price per person = 175.95/15 = 11.73 Solution: An easy way to solve this problem is to translate what is provided in the question into a mathematical equation. We know that the total bill for 15 people was 207 dollars, including the 15 percent gratuity. We use the value 1.15 in the equation below to account for the meal itself plus the gratuity. We can use x as the average cost per person for the meal without the gratuity. Thus, we can say: (1.15)(15)(x) = 207 (115/100)(15)(x) = 207 (115)(15)(x) = (207)(100) We can divide the entire equation by 3. Doing so gives us: (115)(5)(x) = (69)(100) We can divide the entire equation by 5 and we get: (115)x = (69)(20) We can again divide the entire equation by 5 and we get: (23)x = (69)(4) We can again divide the entire equation by 23 and we get: x = (3)(4) x = 12 Answer B _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Kudos [?]: 837 [1], given: 2 SVP Joined: 12 Sep 2015 Posts: 1794 Kudos [?]: 2446 [1], given: 356 Location: Canada Re: The price of lunch for 15 people was$207.00, including a 15 [#permalink]

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28 Aug 2017, 14:24
1
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Expert's post
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

[Reveal] Spoiler:
B

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

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03 May 2012, 02:48
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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 ?

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14 May 2012, 06:10
enigma123 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 How come the answer is B? This is how I solved it and got A, which is incorrect.$207 includes 15% gratuity so 0.15 * 207 = 31.05

Price EXCLUDING gratuity = 207 - 31.05 = 175.95

Average price per person = 175.95/15 = 11.73

Hello
here is my approach

so let x be the sum of the 15 lunch WITHOUT the 15 %
1.15 X = 207
X = 207/ 1.15
X= 180

so 180 is for 15 people
the average price be 180 /15= 12

HENCE B

HOPE THIS HELP

BEST REGARDS

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07 May 2014, 15:06
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For those who are intimidated by the division I found back solving to be very efficient for this problem.

I started with D $14.00 14*15 = 210 210>207 and that doesn't even have the gratuity added. So I know right there that D and E are out and a 20 cent deduction on choice C is probably still going to be too high. Went to answer choice B.$12.00

12*15=180 15% of 180=27 180+72=207.00

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Re: The price of lunch for 15 people was $207 including a 15% [#permalink] ### Show Tags 12 May 2014, 03:00 MY42 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

here is my trouble:

the answer is B, because people say that the "15%" means 15% of the real amount, by say real amount, I mean the amounts these guys paid for what they ate.
but what puzzled me is that,
the subject of the sentence is "the price", which equals to $207, so, in my opinion, the following "15%" is to modify "the price", which is$207. if so, the gratuity must be $207*15%, and in this way, answer is A. so could anybody explain this to me? am i wrong? thanks a lot! Merging similar topics. please refer to the discussion above. As for your question, I think it's addressed here: the-price-of-lunch-for-15-people-was-207-00-including-a-131794.html#p1081531 Hope it helps. _________________ Kudos [?]: 128619 [0], given: 12180 Intern Joined: 25 Jul 2014 Posts: 18 Kudos [?]: 37 [0], given: 52 Concentration: Finance, General Management GPA: 3.54 WE: Asset Management (Venture Capital) The price of lunch for 15 people was$207.00, including a 15 [#permalink]

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24 Aug 2014, 15:04
DelSingh wrote:
Can someone please explain how you compute 207/1.15 under two minutes quickly? I think my division need help

I TOTALLY agree with you. The problem is easy except for the 207/1.15 (well, the division is not hard, just time consuming). I got the right answer in 2:12, so my concern is also how to perform the division in 30 seconds?

Here is my thought (after thinking again and again )

First, 207/1.15 would be alot easier if it become 230/1.15 = 200, so the actual result will be less than 200... but how much less??
Then I think, i need to add 23 more from 207 to get 230, so it would be a little bit less than 23 from 200 since we divide the number to 1.15 (a little more than1)... my best guess is 20 (just because it's a round number), so the result is 180.

Not sure if it works in another problem with different numbers. I will keep this in mind for my next try.

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Re: The price of lunch for 15 people was $207.00, including a 15 [#permalink] ### Show Tags 12 Sep 2014, 06:42 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 [Reveal] Spoiler: How come the answer is B? This is how I solved it and got A, which is incorrect.$207 includes 15% gratuity so 0.15 * 207 = 31.05

Price EXCLUDING gratuity = 207 - 31.05 = 175.95

Average price per person = 175.95/15 = 11.73

let x be the total without gratuity.. then we shall form

x+0.15x = 207
1.15x=207
x=207/1.15

x=180.

x/15 for each person then 180/15 = 12..

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07 Jan 2015, 13:19
The price included a gratuity of 15% on top of the original bill, hence $207.00 represents 115% of bill$x.yz

$207.00 ------- 115%$x.yz ---------- 100%

x = $180.00 Bill per person:$180.00 : 15 = $12.00 Kudos [?]: 20 [0], given: 13 Re: The price of lunch for 15 people was$207.00, including a 15   [#permalink] 07 Jan 2015, 13:19

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