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

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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?

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

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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?

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

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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.
_________________

Harvard grad and 770 GMAT scorer, offering high-quality private GMAT tutoring, both in-person and 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, 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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