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

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10 Aug 2016, 07:43

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.
_________________

Harvard grad and 770 GMAT scorer, offering high-quality private GMAT tutoring, both in-person and online via Skype, since 2002.

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?

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.

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

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

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28 Aug 2017, 18:59

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.

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

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23 Oct 2017, 12:30

Bunuel wrote:

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.

Hii.. I don't get why this solution isn't the same as 0.85*207.. Would you please explain this? Thanks..

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.

Hii.. I don't get why this solution isn't the same as 0.85*207.. Would you please explain this? Thanks..

Please read the highlighted part.
_________________

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

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23 Oct 2017, 21:31

[quote="enigma123"]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?

I think the quick way is to believe that most GMAT word problems divide smoothly and pay attention to the numbers, for example, it should be obvious that \(\frac{207}{23} = 9\) i.e \(23(10-1) = 9(23)= 207\)