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

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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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?

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 ?

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.

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.

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.

Thanks a lot Bunuel,

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

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.

I think the mistake you committed is a fairly common mistake. You calculated 15% gratuity on $207, which is not correct. Let's try to understand this.

These 15 people went for a lunch and ordered some really delicious dishes. They ate to their satisfaction and at last, asked the waiter to bring the bill. The waiter had done a lot in providing a good service to these people and as per the restaurant rules, he deserved 15% gratuity for service.

While the waiter had gone to bring the bill, these 15 guys figured out what all they had eaten till then and using the menu, totaled the amount they would need to pay. However, when the waiter arrived, he had a higher amount on the bill. Why? Because he had included a 15% gratuity also, which these 15 people had ignored in their calculations.

So, while these people calculated their bill amount to be, say, x, the waiter came up with a bill 1.15x.

So, now we are given that 1.15x = 207 =>x=180
Per person cost = 180/15 = 12.

The reason for telling this whole story is that you need to see what is the figure to which apply this 15%. This 15% has to be applied on figure which already existed before applying this 15%; in this case, the total amount of food they ate. The amount they paid was arrived after the application of this 15%; thus this amount existed only after application of 15% on some other number. So, you can't apply 15% to $207 because 15% was originally not applied to this number.

A similar issue can be faced in the below problem:
A scored 15% more than B. If A's score was 460, what was B's score?
Here we can't say that B's score was 460 * (1-15%). That would be incorrect. Why? You can yourself see. What is 460*0.85. It is 391. So, cross checking, Is A 15% more than B?

A=b*(1+15%) = 391*1.15 = 449.65, which is not equal to 460.

So, where is the problem? The problem is that the question said that A is 15% more than B, not that B is 15% less than A. There's is a difference.

(1)If A is 15% more than B, then A = 1.15B =>B=A/1.15 ~ 0.87A
(2) If B is 15% less than B, then B = A (1-15%) = 0.85A

So, we see that these two expressions are different. So, you have to be cautious when dealing with such statements.

It is easier to say here that we limit ourselves to (1) in the question given but how do we do this in complex scenarios just like in the original question given?

The common logic, as explained above, is that you need to think if a particular figure existed even before the application of the percentage; if yes, then it is independent of the percentage. For example, in A & B example question, we say that the score of A is 15% more than B. So, there is a score of B and when we increase it by 15%, we get score of A. But score of B exists before the application of percentage.

So, coming back to the question, the total amount they paid i.e. $207 existed only after application of 15%, not before. Thus, 15% needs to be applied to some other variable to arrive at $207.

I hope my long answer clarifies some doubts. If you have any other queries, please feel free to ask.

Cheers,
CJ

Can someone please explain how you compute 207/1.15 under two minutes quickly? I think my division need help

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

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

Attached is a visual that should help.

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: https://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:

Cheers,
Brent