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The price of lunch for 15 people was $207.00, including a 15

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The price of lunch for 15 people was $207.00, including a 15 [#permalink]

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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

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Re: The price of lunch for 15 people was $207.00, including a 15 [#permalink]

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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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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.
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Re: The price of lunch for 15 people was $207 including a 15% [#permalink]

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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 .

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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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The price of lunch for 15 people was $207.00, including a [#permalink]

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check the option :

12

12 * 15 = 180

180 + [ 18 + 9 ] ( 15 % of 180) = 207 :wink:

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Re: The price of lunch for 15 people was $207.00, including a 15 [#permalink]

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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]

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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

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! :)

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Re: The price of lunch for 15 people was $207.00, including a 15 [#permalink]

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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
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Re: The price of lunch for 15 people was $207.00, including a 15 [#permalink]

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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

Answer:
[Reveal] Spoiler:
B


Cheers,
Brent
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Re: Price of lunch [#permalink]

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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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The price of lunch for 15 people was $207 including a 15% [#permalink]

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New post 10 May 2012, 03:22
The solution is :

207 * .15 = 31.05 ==> 207 - 31.05 = 175.95==> 175.95 / 15 = 11.73
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Re: The price of lunch for 15 people was $207 including a 15% [#permalink]

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New post 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


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Re: The price of lunch for 15 people was $207.00, including a 15 [#permalink]

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New post 27 Feb 2013, 21:31
Can someone please explain how you compute 207/1.15 under two minutes quickly? I think my division need help
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Re: The price of lunch for 15 people was $207.00, including a 15 [#permalink]

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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]

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New post 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.
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The price of lunch for 15 people was $207.00, including a 15 [#permalink]

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New post 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 :oops: )

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]

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New post 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.. 8-)

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The price of lunch for 15 people was $207.00, including a 15 [#permalink]

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New post 31 Oct 2014, 00:34
Per head without gratuity \(= \frac{207 * 100}{115 * 15} = \frac{900}{75} = 12\)

Answer = B
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Re: The price of lunch for 15 people was $207.00, including a 15 [#permalink]

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New post 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

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Re: The price of lunch for 15 people was $207.00, including a 15   [#permalink] 07 Jan 2015, 13:19

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