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The price of lunch for 15 people was $207 including a 15%

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The price of lunch for 15 people was $207 including a 15% [#permalink] New post 06 Aug 2008, 16:13
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Oct 2012, 04:14, edited 1 time in total.
Edited the question.
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Re: One question from OG 11th ed. [#permalink] New post 06 Aug 2008, 16:36
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GMAT_700 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

Here what I did:
207 * .15 = 31.05
207 - 31.05 = 175.95

175.95 / 15 = 11.73
However the correct answer is B.

Can you explain the correct answer?


Clearly B is the answer
I used POE here

Lets consider option (E) say 15*15=225 => > 207 which is including 15% gratutity => not possible
(D) 15*14=210 > 207 not possible
(C)15*13.8 = 207 not possible
(B) 15*12= 180 now 180(115/100)=207 => possible ANSWER IMO B
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Re: One question from OG 11th ed. [#permalink] New post 06 Aug 2008, 17:12
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GMAT_700 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

Here what I did:
207 * .15 = 31.05
207 - 31.05 = 175.95

175.95 / 15 = 11.73
However the correct answer is B.

Can you explain the correct answer?


207*.15 is where u r wrong. it should have been 207=1.15x where x is the bill without the tips. Note that 207 is the amount including tips, not excluding.

solve 207=1.15x and divide by 15 to get 12
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Re: One question from OG 11th ed. [#permalink] New post 07 Aug 2008, 10:29
GMAT_700 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

Here what I did:
207 * .15 = 31.05
207 - 31.05 = 175.95

175.95 / 15 = 11.73
However the correct answer is B.

Can you explain the correct answer?


say total bill b

207 = b (1+15/100) = b 1.1.5

average = 207 / (1.15 *15) =12
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Re: One question from OG 11th ed. [#permalink] New post 07 Aug 2008, 12:12
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Another way you can set it up if it's hard to thinkg of 1.15 x = 207 is this:

x = how much you paid.

x + 15% of x = total amount of bill

1x + .15x = 207
1.15x = 207.

Gets you to the same thing, but helps you think of it as if you were there at the table calculating the amount rather than working backwards from 207. It might be easier for some people to do it this way. It takes a little longer, but sometimes the right answer is worth a few extra seconds.
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Re: One question from OG 11th ed. [#permalink] New post 05 Oct 2010, 06:22
GMAT_700 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

Here what I did:
207 * .15 = 31.05
207 - 31.05 = 175.95

175.95 / 15 = 11.73
However the correct answer is B.

Can you explain the correct answer?


Answer will be B clearly.

You went wrong at -> 207 * .15 = 31.05
207 includes the tip.
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Re: One question from OG 11th ed. [#permalink] New post 05 Oct 2010, 06:29
An easier way to solve this is by backcalculating using the answers. Start at the second highest (i.e. 12) so if it turns out to be too high you can eliminate the higher ones and if it's too low you can eliminate the lower ones.

15 people ate. Assuming $12 each without gratuity, then the bill was 15 * 12 = 180

Now add the gratuity: 15% of 180 = 27 (you can quickly see this by doing 10% + 5% = 18 + 9). So 180 + 27 = 207 and the answer is 12.
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Re: One question from OG 11th ed. [#permalink] New post 15 Mar 2011, 07:38
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? :o
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Re: One question from OG 11th ed. [#permalink] New post 15 Mar 2011, 07:53
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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? :o


Just say the bill was for $x
Including the gratuity of 15% will make the bill amount: 1.15x

1.15x=207
x=180

So; the actual bill without gratuity was 180.

According to you, it should be 175.95, which is not correct.

Think it like this;
Suppose you have 100 dollars, you earn a 15% profit on that. Now you have $115.

If we make a question out of it;
$115 includes a 15% net profit, what was the original amount.

With your method; it would be 115*0.15=17.25
115-17.25 = $97.75. But, you had $100, right?

Thus, you will have to calculate like this;

Suppose you had x dollars;
1.15x = 115
x = 115/1.15 = $100

You initially had $100.
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Re: One question from OG 11th ed. [#permalink] New post 15 Mar 2011, 21:27
x -> Price without Gratuity

207 = x + 0.15x

=> x = 207/1.15 = 180

So average price per person,excluding the gratuity = 180/15 = 12

The answer is B.
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Re: One question from OG 11th ed. [#permalink] New post 16 Mar 2011, 02:00
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? :o




15%=100+15=115

with gratuity 115 without 100
so if 207 = (100/115)*207= 180/15=12

Ans. B
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Re: One question from OG 11th ed. [#permalink] New post 29 Aug 2011, 03:23
Quote:
207*.15 is where u r wrong. it should have been 207=1.15x where x is the bill without the tips. Note that 207 is the amount including tips, not excluding.

solve 207=1.15x and divide by 15 to get 12


Sorry I still don't get one part in the solution - multiplying by 1.15. The Q asks what was the average price per person, EXCLUDING the gratuity?

So lets say the price was $100 including 15% gratuity. So excluding the gratuity should be 100 - (100*.15) = 85? (If I multiply 100* 1.15 then i get 115).

Please clarify why do we need 1.15 instead of .15 in the original Q. thanks!
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Re: One question from OG 11th ed. [#permalink] New post 29 Aug 2011, 04:45
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melguy wrote:
Quote:
207*.15 is where u r wrong. it should have been 207=1.15x where x is the bill without the tips. Note that 207 is the amount including tips, not excluding.

solve 207=1.15x and divide by 15 to get 12


Sorry I still don't get one part in the solution - multiplying by 1.15. The Q asks what was the average price per person, EXCLUDING the gratuity?

So lets say the price was $100 including 15% gratuity. So excluding the gratuity should be 100 - (100*.15) = 85? (If I multiply 100* 1.15 then i get 115).

Please clarify why do we need 1.15 instead of .15 in the original Q. thanks!


Actually, that's the tricky part of the question:

When you say 100 is including the 15% gratuity; Upon subtracting 0.15*100 from 100, you won't get the actual value spent for food, excluding gratuity.

The reason is that:
0.15*100 is more than 0.15*x(the money spent for food, less than 100 of course)

So,
you should say
x+0.15x=100

And not say
100-0.15x=x

Both of these will give different values for x, former being correct. Gratuity of 15% is applied for the food alone.
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Re: One question from OG 11th ed. [#permalink] New post 30 Aug 2011, 06:30
let x be the amount before the gratuity

So,

x + 15%(x) = 270

x + .15x = 270
1.15x = 270
x = 270/1.15
x = 180

for each = 180/15 = 12 = B
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Re: The price of lunch for 15 people was $207.00, including a 15 [#permalink] New post 23 Oct 2012, 00:35
Hi Bunuel,

I took a crazy 4.5 mins to solve this question.

recognizing x+/15x= bill amt took lot of time.. but after that crazy calculation took hell lot of my time.. nos are crazy in thsi Qs like 207, 1.15 .
how to solve questions like these quickly.

POE mentioned above is good though.
Regards,
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Re: The price of lunch for 15 people was $207.00, including a 15 [#permalink] New post 23 Oct 2012, 04:12
Expert's post
sachindia wrote:
Hi Bunuel,

I took a crazy 4.5 mins to solve this question.

recognizing x+/15x= bill amt took lot of time.. but after that crazy calculation took hell lot of my time.. nos are crazy in thsi Qs like 207, 1.15 .
how to solve questions like these quickly.

POE mentioned above is good though.
Regards,
Sachin


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

First note that 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.

Bill*1.15=207=23*9 --> Bill*\frac{115}{100}=23*9 --> Bill*\frac{23}{20}=23*9 --> Bill=20*9=180 --> the price per person is \frac{180}{15}=12.

Answer: B.
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Re: The price of lunch for 15 people was $207 including a 15% [#permalink] New post 23 Oct 2012, 05:19
Thanks a lot Bunuel,

Had I known 23* 7 =207 , would have saved lot of time :lol:
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Re: The price of lunch for 15 people was $207 including a 15% [#permalink] New post 23 Oct 2012, 05:22
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sachindia wrote:
Thanks a lot Bunuel,

Had I known 23* 7 =207 , would have saved lot of time :lol:


Actually it's 23*9=207. Factorizing 207 is good strategy and one could spot that it's divisible by 9 since the sum of the digits of 207 is divisible by 9.
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Re: The price of lunch for 15 people was $207 including a 15% [#permalink] New post 23 Oct 2012, 05:27
Thanks a lot. I was dividing it by 3 since the sum is divisible by 3 as well.
not i gotto keep this in mind to check for the divisibility of 9 along with 3 as this could save lot of time. .

do u think memorizing tables till 30 will do any good? :shock:
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Re: The price of lunch for 15 people was $207 including a 15% [#permalink] New post 23 Oct 2012, 05:30
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sachindia wrote:
Thanks a lot. I was dividing it by 3 since the sum is divisible by 3 as well.
not i gotto keep this in mind to check for the divisibility of 9 along with 3 as this could save lot of time. .

do u think memorizing tables till 30 will do any good? :shock:


Check divisibility rules worth memorizing here: math-number-theory-88376.html (Divisibility Rules chapter)

Hope it helps.
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Re: The price of lunch for 15 people was $207 including a 15%   [#permalink] 23 Oct 2012, 05:30
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