GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Oct 2018, 14:18

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Twenty people had dinner together at a restaurant. The cost of the mea

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50058
Twenty people had dinner together at a restaurant. The cost of the mea  [#permalink]

Show Tags

01 Apr 2018, 10:34
00:00

Difficulty:

25% (medium)

Question Stats:

72% (02:17) correct 28% (02:42) wrong based on 41 sessions

HideShow timer Statistics

Twenty people had dinner together at a restaurant. The cost of the meal plus an automatic gratuity of 18% for a large party was $531.00, before sales tax was added. What was the average price of the meal per person NOT INCLUDING the gratuity or sales tax? (A)$21.77
(B) $22.50 (C)$26.55
(D) $30.50 (E)$36.55

_________________
Intern
Joined: 20 Dec 2014
Posts: 37
Twenty people had dinner together at a restaurant. The cost of the mea  [#permalink]

Show Tags

01 Apr 2018, 11:07
Bunuel wrote:
Twenty people had dinner together at a restaurant. The cost of the meal plus an automatic gratuity of 18% for a large party was $531.00, before sales tax was added. What was the average price of the meal per person NOT INCLUDING the gratuity or sales tax? (A)$21.77
(B) $22.50 (C)$26.55
(D) $30.50 (E)$36.55

Given:
20 people,
Total cost + 18 % Gratuity = 531

Need to find per person cost excluding the gratuity...
Method 1: Normal Calculations

average total cost will be less than average of total Cost + 18% Gratuity
=> average of total cost + Gratuity = 531/20
=> $$total cost < 531/20$$
=> total cost < 26.55
eliminate option C, D and E

Gratuity is little less than 20%
so for ease of calculation lets take gratuity as 20%

=> Average Total cost * 1.20 (20% gratuity) = Average (total cost + Gratuity)
=> $$Average total cost = 26.55/1.20$$
Approx = 22
as we increased the denominator from 1.18 to 1.2 the answer should be greater than 22 hence Option B

Method 2: Use the options

Pick the mid value -> 26.55
if that is the average cost than overall cost = 26.55 * 20 = 513.00,
Now 18% gratuity will result in an amount that is more than 531 hence all options equal to or greater than 26.55 are disqualified

move on to the next number 22.50
22.50 * 20 = 450
increase by 18% = 450 *1.18 = 531
this is what we were looking for hence answer is B

_________________

Kindly press "+1 Kudos" to appreciate

Senior SC Moderator
Joined: 22 May 2016
Posts: 2040
Twenty people had dinner together at a restaurant. The cost of the mea  [#permalink]

Show Tags

01 Apr 2018, 15:59
Bunuel wrote:
Twenty people had dinner together at a restaurant. The cost of the meal plus an automatic gratuity of 18% for a large party was $531.00, before sales tax was added. What was the average price of the meal per person NOT INCLUDING the gratuity or sales tax? (A)$21.77
(B) $22.50 (C)$26.55
(D) $30.50 (E)$36.55

D) $30.50 each? Round to$30
Total before gratuity is already too great.
$$\frac{30}{person}* 20(persons) = 600$$ - REJECT

Per person cost must be lower. Answers A, B, and C remain. Choose the round number, B.

Either B is too low and the answer is C; B is too high and the answer is A; or B is the answer.

B) $22.50 each? $$22.50 = 22\frac{1}{2}=\frac{45}{2}$$ Total before gratuity: $$\frac{45}{2}*20=450$$ Total with gratuity? Find 18% of$450, add it to $450 $$(\frac{18}{100}*450)=(\frac{9}{50}*450)=81$$ $$(81 + 450) = 531$$ MATCH Answer B Algebra Let $$x$$ = total cost of dinner without gratuity$531 includes a tip of 18% on original total, $$x$$

$$531 = 1.18x$$
$$x = \frac{531}{1.18}$$

$$1.18=1\frac{18}{100}=1\frac{9}{50}=\frac{59}{50}$$

$$x =\frac{531}{(\frac{59}{50})}=531*\frac{50}{59}$$

$$x=(531*\frac{50}{59})=(9*50)=450$$

Per person cost? $$(\frac{450}{20})=(\frac{45}{2})=22.50$$

_________________

___________________________________________________________________
For what are we born if not to aid one another?
-- Ernest Hemingway

CEO
Joined: 08 Jul 2010
Posts: 2576
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: Twenty people had dinner together at a restaurant. The cost of the mea  [#permalink]

Show Tags

01 Apr 2018, 22:32
Bunuel wrote:
Twenty people had dinner together at a restaurant. The cost of the meal plus an automatic gratuity of 18% for a large party was $531.00, before sales tax was added. What was the average price of the meal per person NOT INCLUDING the gratuity or sales tax? (A)$21.77
(B) $22.50 (C)$26.55
(D) $30.50 (E)$36.55

Cost + Gratuity @18% = 531

i.e. C+ (18/100)*C = 531

i.e. 1.18 C = 531

i.e. C = 531/1.18 = 450

The cost is shared by 20 people hence Cost per person = C/20 = 450/20 = 22.5

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Re: Twenty people had dinner together at a restaurant. The cost of the mea &nbs [#permalink] 01 Apr 2018, 22:32
Display posts from previous: Sort by