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Register now and save up to $200 Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code ## Algebra tagged by: Brent@GMATPrepNow This topic has 7 expert replies and 0 member replies marat_isr Newbie | Next Rank: 10 Posts Joined 06 Mar 2014 Posted: 3 messages #### Algebra Tue Feb 28, 2017 8:38 am Elapsed Time: 00:00 • Lap #[LAPCOUNT] ([LAPTIME]) The price of lunch for 15 people was$207.00 including a 15% 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 Why is it wrong to get the price before the gratuity by simply multiplying 207*0.85 ? Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums! ### GMAT/MBA Expert Brent@GMATPrepNow GMAT Instructor Joined 08 Dec 2008 Posted: 10763 messages Followed by: 1212 members Thanked: 5147 times GMAT Score: 770 Tue Feb 28, 2017 9:09 am marat_isr wrote: Why is it wrong to get the price before the gratuity by simply multiplying 207*0.85 ? Your reasoning is 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.

Cheers,
Brent

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### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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Tue Feb 28, 2017 9:11 am
Quote:
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
A fast way to answer this question is by plugging in the answer choices, which I'll leave to you to try.

Here's an algebraic approach:

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.

Answer choice B: $12 per person without gratuity Total price for 15 people = 15*12 = 180. Price + gratuity = 180 + .15(180) = 180+27 = 207. Success! The correct answer is B. _________________ Mitch Hunt GMAT Private Tutor GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "Thank" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert Rich.C@EMPOWERgmat.com Elite Legendary Member Joined 23 Jun 2013 Posted: 8708 messages Followed by: 460 members Thanked: 2733 times GMAT Score: 800 Tue Feb 28, 2017 11:49 am Hi marat_isr, In these types of situations, we have to think about the "timeline" of the math.... Here, we had a bill, THEN the 15% gratuity was added, then we had a total: X + .15X = 207 1.15X = 207 This is the equation that will get us the value of X... X = 207/1.15 At NO POINT was the idea of 85% mentioned, so that should not be in your original calculation. GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert Jay@ManhattanReview GMAT Instructor Joined 22 Aug 2016 Posted: 703 messages Followed by: 17 members Thanked: 332 times Tue Feb 28, 2017 9:24 pm marat_isr wrote: The price of lunch for 15 people was$207.00 including a 15% 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 Why is it wrong to get the price before the gratuity by simply multiplying 207*0.85 ? Hi marat_isr, Let us take a simple example. Say, you dined in a restaurant and the food bill was$100. A gratuity of 15% was charged on it, making the final bill equals to $100 + 100*15% =$115.

Quote:
Now you wish to know only the food bill from the only two information: 1. Bill incl. gratuity = $115 and 2. Percent of gratuity = 15%. If you do the following: Gratuity =$115*15% = 115*0.15 = $17.25. As per this, only the food bill =$115 - $17.25 =$97.75, which is not equal to the correct value $100. you should do the following. Only food bill = (Bill incl gratuity) / (100% + gratuity %) = 115 / (100% + 15%) = 115 / 115% = 115*(100/115) = 100. Hope this makes sense. Relevant book: Manhattan Review GMAT Math Essentials Guide -Jay _________________ Manhattan Review GMAT Prep Locations: New York | Frankfurt | Hong Kong | Zurich | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert Matt@VeritasPrep GMAT Instructor Joined 12 Sep 2012 Posted: 2560 messages Followed by: 113 members Thanked: 581 times Target GMAT Score: V51 GMAT Score: 780 Wed Mar 01, 2017 3:24 pm marat_isr wrote: Why is it wrong to get the price before the gratuity by simply multiplying 207*0.85 ? Because percentages aren't quite the same going up as going down: you're working with different bases. For example, suppose I have a$100 stock. If it goes up 20% today, it's $120. If it then goes down 20% tomorrow, it's$96. So $100 + 20% - 20% doesn't get me back to$100!

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Jeff@TargetTestPrep GMAT Instructor
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Thu Mar 02, 2017 5:18 pm
marat_isr wrote:
The price of lunch for 15 people was $207.00 including a 15% 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
An efficient 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 tip. We use the value 1.15 in the equation below to account for the meal itself plus the gratuity, and x as the individual cost per person for the meal before the gratuity. Thus, we can say:

(1.15)(15)(x) = 207

(115)(15)(x) = 20700

Dividing both sides by 15, we have:

115x = 1380

x = 1380/115

x = 12

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