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Register now and save up to $200 Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep 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 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 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 Jay@ManhattanReview GMAT Instructor Joined 22 Aug 2016 Posted: 907 messages Followed by: 18 members Upvotes: 470 Top Reply 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: 2640 messages Followed by: 113 members Upvotes: 625 Target GMAT Score: V51 GMAT Score: 780 Top Reply 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!

Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

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Jay@ManhattanReview GMAT Instructor
Joined
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Posted:
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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
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Locations: New York | Frankfurt | Hong Kong | Zurich | and many more...

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Matt@VeritasPrep GMAT Instructor
Joined
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Posted:
2640 messages
Followed by:
113 members
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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! Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! GMAT/MBA Expert Jeff@TargetTestPrep GMAT Instructor Joined 09 Apr 2015 Posted: 506 messages Followed by: 6 members Upvotes: 39 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 Answer: B _________________ Jeffrey Miller Head of GMAT Instruction GMAT/MBA Expert Rich.C@EMPOWERgmat.com Elite Legendary Member Joined 23 Jun 2013 Posted: 8954 messages Followed by: 468 members Upvotes: 2867 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 GMATGuruNY GMAT Instructor Joined 25 May 2010 Posted: 13608 messages Followed by: 1796 members Upvotes: 13060 GMAT Score: 790 Tue Feb 28, 2017 9:15 am marat_isr wrote: Why is it wrong to get the price before the gratuity by simply multiplying 207*0.85 ? X is 15% greater than Y does NOT imply that Y is 15% less than X or that Y is 85% of X. In the problem above, let P = the final price with gratuity and C = the total cost for 15 people without gratuity. Since the final price is 15% greater than the cost without gratuity, we get: P = (115/100)C P = (23/20)C C = (20/23)P. Thus, the cost without gratuity is equal to 20/23 -- not 85% -- of the final price with gratuity. Since P = 207, we get: C = (20/23)(207) = 180. Since there are 15 people, the cost per person without gratuity = 180/15 = 12. Alternate approach: We can PLUG IN THE ANSWERS, which represent the cost per person. Given that the total cost is an INTEGER, the correct answer is almost certainly an integer itself. Answer choice D is too great, since 15 people paying$14 each = 15*14 = 210 -- a value beyond the total cost of 207.

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!

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