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

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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 May 2016, 08:07
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 avg price per person excluding gratuity then

15x+ 15/100(15x)=207
by solving 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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New post 07 May 2016, 10:35
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


Quote:
$207.00, including a 15 percent gratuity for service.


That means 115% = 207

So, 100% = \(\frac{207}{115}*100\) => 180

Further it is given -

Quote:
price of lunch for 15 people was $207.00, including a 15 percent gratuity for service.


So, Price of lunch for 15 people excluding 15 percent gratuity for service = \(180\)

Or, Price of lunch for 15 people excluding 15 percent gratuity for service = \(\frac{180}{15}\) => \(12\)

Hence average price excluding gratuity for service is 12
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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 25 May 2016, 21:46
Attached is a visual that should help.
Attachments

Screen Shot 2016-05-25 at 9.42.14 PM.png
Screen Shot 2016-05-25 at 9.42.14 PM.png [ 51.22 KiB | Viewed 677 times ]


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

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New post 10 Aug 2016, 08:43
Top Contributor
ameyaprabhu wrote:
is this really a 700 question, or is there some error?


No, it's definitely not a 700-level question, in my opinion. I added a "Sub-600 question" tag. Only the original poster of the question can remove tags, as far as I can tell.
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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 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

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

Sent from my Lenovo A6020a46 using GMAT Club Forum mobile app

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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 05 Feb 2017, 21:07
Let the average price per person without gratuity for service be X

Now the overall price would be

X * 15 *{(100+15/100} = 207
--> X * 15*1.15 = 207
--> X = 207/(1.15*15) = 12

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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 28 Aug 2017, 14:24
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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: The price of lunch for 15 people was $207.00, including a 15 [#permalink]

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New post 28 Aug 2017, 19:59
I did this as below:
Given 15 people>207 cost, so avg price=13.8 including the 15%.
so now we can eliminate answers c,d,e..
From a and b, just add 15% to the value and check which one becomes 13.8.
Suppose you take 12, then add its 15% you get 13.8. So ans is 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 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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Re: The price of lunch for 15 people was $207.00, including a 15 [#permalink]

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New post 25 Sep 2017, 22:52
The simple way is no need to calculate for 15 people how much then taking avergae

here 115/100 =207 again to take average we need to divide it by 15 do this operation now only

So it become answer = (207*100/115*15)

then solve

we will get 69*4/23 ..now easily 69/23 equal to 3 so answer should be 3*4 = 12

Can be solved within 1.5 minute
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Re: The price of lunch for 15 people was $207.00, including a 15   [#permalink] 25 Sep 2017, 22:52

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