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

It is currently 14 Oct 2019, 04:48

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

The price of lunch for 15 people was $207.00, including a 15

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 13 Mar 2007
Posts: 82
The price of lunch for 15 people was $207 including a 15%  [#permalink]

Show Tags

New post Updated on: 23 Oct 2012, 05:14
4
25
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

65% (01:59) correct 35% (02:08) wrong based on 1657 sessions

HideShow timer Statistics

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

Originally posted by GMAT_700 on 06 Aug 2008, 17:13.
Last edited by Bunuel on 23 Oct 2012, 05:14, edited 1 time in total.
Edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58315
Re: The price of lunch for 15 people was $207.00, including a 15  [#permalink]

Show Tags

New post 28 Feb 2013, 01:50
9
7
Most Helpful Community Reply
Retired Moderator
avatar
Joined: 20 Dec 2010
Posts: 1587
Re: One question from OG 11th ed.  [#permalink]

Show Tags

New post 15 Mar 2011, 08:53
13
7
heygirl wrote:
I keep getting 11.73 as the answer for this one.
Here is what I did:
First I calulated 15% of 207, that is 31.05 and subtracted it from 207. Thus the amount now is 175.95.

175.95/15=11.73.But, OA is B

Anyone knows whaT I'm missing here? :o


Just say the bill was for $x
Including the gratuity of 15% will make the bill amount: 1.15x

1.15x=207
x=180

So; the actual bill without gratuity was 180.

According to you, it should be 175.95, which is not correct.

Think it like this;
Suppose you have 100 dollars, you earn a 15% profit on that. Now you have $115.

If we make a question out of it;
$115 includes a 15% net profit, what was the original amount.

With your method; it would be 115*0.15=17.25
115-17.25 = $97.75. But, you had $100, right?

Thus, you will have to calculate like this;

Suppose you had x dollars;
1.15x = 115
x = 115/1.15 = $100

You initially had $100.
_________________
General Discussion
Intern
Intern
avatar
Joined: 29 Sep 2010
Posts: 12
Schools: IMD '16 (A)
GMAT 1: 730 Q47 V44
Re: One question from OG 11th ed.  [#permalink]

Show Tags

New post 05 Oct 2010, 07:29
4
2
An easier way to solve this is by backcalculating using the answers. Start at the second highest (i.e. 12) so if it turns out to be too high you can eliminate the higher ones and if it's too low you can eliminate the lower ones.

15 people ate. Assuming $12 each without gratuity, then the bill was 15 * 12 = 180

Now add the gratuity: 15% of 180 = 27 (you can quickly see this by doing 10% + 5% = 18 + 9). So 180 + 27 = 207 and the answer is 12.
Senior Manager
Senior Manager
avatar
Joined: 18 Oct 2010
Posts: 369
Reviews Badge
Re: One question from OG 11th ed.  [#permalink]

Show Tags

New post 15 Mar 2011, 08:38
I keep getting 11.73 as the answer for this one.
Here is what I did:
First I calulated 15% of 207, that is 31.05 and subtracted it from 207. Thus the amount now is 175.95.

175.95/15=11.73.But, OA is B

Anyone knows whaT I'm missing here? :o
SVP
SVP
User avatar
P
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1883
GMAT 1: 780 Q51 V48
GRE 1: Q800 V740
Re: Price of lunch  [#permalink]

Show Tags

New post 02 May 2012, 21:23
1
2
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)
_________________
GyanOne [www.gyanone.com]| Premium MBA and MiM Admissions Consulting

Awesome Work | Honest Advise | Outstanding Results

Reach Out, Lets chat!
Email: info at gyanone dot com | +91 98998 31738 | Skype: gyanone.services
Manager
Manager
avatar
Joined: 02 Jun 2011
Posts: 114
Re: Price of lunch  [#permalink]

Show Tags

New post 03 May 2012, 02:48
1
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 ?
Intern
Intern
avatar
Joined: 13 Nov 2010
Posts: 35
Re: The price of lunch for 15 people was $207 including a 15%  [#permalink]

Show Tags

New post 03 May 2012, 07:51
6
3
enigma123 wrote:
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

How come the answer is B?

This is how I solved it and got A, which is incorrect.

$207 includes 15% gratuity so 0.15 * 207 = 31.05

Price EXCLUDING gratuity = 207 - 31.05 = 175.95

Average price per person = 175.95/15 = 11.73




I'll show You perhaps the most easiest way to solve such problem

As it is a percentage problem so just take the initial price before the gratuity is 100 the as the gratuity is calculated on the final price, so as we assumed the final bill before adding gratuity is 100 so gratuity is 15% of 100 is 15 so the total price of meals is 115 so the given amount i.e 207 is for 115 then we have to calculate for 100 here we go

for 115 207
for 100 x

so by cross multiplication we get 115x=100*207 => x=100*207/110 by simplifying we get x as 180 which is the price of lunch before gratuity so the gratuity is 27 so

as the question ask the average price person excluding gratuity is 180/15=12 so our answer is b


hope its concise and clear .

if u satisfied with my effort don't hesitate to give +1 kudos.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58315
Re: Price of lunch  [#permalink]

Show Tags

New post 03 May 2012, 12:56
8
2
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.
_________________
Senior Manager
Senior Manager
avatar
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 423
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Re: The price of lunch for 15 people was $207.00, including a 15  [#permalink]

Show Tags

New post 23 Oct 2012, 01:35
Hi Bunuel,

I took a crazy 4.5 mins to solve this question.

recognizing x+/15x= bill amt took lot of time.. but after that crazy calculation took hell lot of my time.. nos are crazy in thsi Qs like 207, 1.15 .
how to solve questions like these quickly.

POE mentioned above is good though.
Regards,
Sachin
_________________
hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : http://gmatclub.com/forum/end-of-my-gmat-journey-149328.html#p1197992
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58315
Re: The price of lunch for 15 people was $207.00, including a 15  [#permalink]

Show Tags

New post 23 Oct 2012, 05:12
sachindia wrote:
Hi Bunuel,

I took a crazy 4.5 mins to solve this question.

recognizing x+/15x= bill amt took lot of time.. but after that crazy calculation took hell lot of my time.. nos are crazy in thsi Qs like 207, 1.15 .
how to solve questions like these quickly.

POE mentioned above is good though.
Regards,
Sachin


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

First note that 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.

\(Bill*1.15=207=23*9\) --> \(Bill*\frac{115}{100}=23*9\) --> \(Bill*\frac{23}{20}=23*9\) --> \(Bill=20*9=180\) --> the price per person is \(\frac{180}{15}=12\).

Answer: B.
_________________
Senior Manager
Senior Manager
avatar
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 423
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Re: The price of lunch for 15 people was $207 including a 15%  [#permalink]

Show Tags

New post 23 Oct 2012, 06:19
Thanks a lot Bunuel,

Had I known 23* 7 =207 , would have saved lot of time :lol:
_________________
hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : http://gmatclub.com/forum/end-of-my-gmat-journey-149328.html#p1197992
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58315
Re: The price of lunch for 15 people was $207 including a 15%  [#permalink]

Show Tags

New post 23 Oct 2012, 06:22
GMAT Tutor
User avatar
G
Status: Private GMAT Tutor
Joined: 22 Oct 2012
Posts: 142
Location: India
Concentration: Economics, Finance
Schools: IIMA (A)
GMAT 1: 780 Q51 V47
Re: One question from OG 11th ed.  [#permalink]

Show Tags

New post 23 Oct 2012, 20:18
1
1
heygirl wrote:
I keep getting 11.73 as the answer for this one.
Here is what I did:
First I calulated 15% of 207, that is 31.05 and subtracted it from 207. Thus the amount now is 175.95.

175.95/15=11.73.But, OA is B

Anyone knows whaT I'm missing here? :o


I think the mistake you committed is a fairly common mistake. You calculated 15% gratuity on $207, which is not correct. Let's try to understand this.

These 15 people went for a lunch and ordered some really delicious dishes. They ate to their satisfaction and at last, asked the waiter to bring the bill. The waiter had done a lot in providing a good service to these people and as per the restaurant rules, he deserved 15% gratuity for service.

While the waiter had gone to bring the bill, these 15 guys figured out what all they had eaten till then and using the menu, totaled the amount they would need to pay. However, when the waiter arrived, he had a higher amount on the bill. Why? Because he had included a 15% gratuity also, which these 15 people had ignored in their calculations.

So, while these people calculated their bill amount to be, say, x, the waiter came up with a bill 1.15x.

So, now we are given that 1.15x = 207 =>x=180
Per person cost = 180/15 = 12.

The reason for telling this whole story is that you need to see what is the figure to which apply this 15%. This 15% has to be applied on figure which already existed before applying this 15%; in this case, the total amount of food they ate. The amount they paid was arrived after the application of this 15%; thus this amount existed only after application of 15% on some other number. So, you can't apply 15% to $207 because 15% was originally not applied to this number.

A similar issue can be faced in the below problem:
A scored 15% more than B. If A's score was 460, what was B's score?
Here we can't say that B's score was 460 * (1-15%). That would be incorrect. Why? You can yourself see. What is 460*0.85. It is 391. So, cross checking, Is A 15% more than B?

A=b*(1+15%) = 391*1.15 = 449.65, which is not equal to 460.

So, where is the problem? The problem is that the question said that A is 15% more than B, not that B is 15% less than A. There's is a difference.

(1)If A is 15% more than B, then A = 1.15B =>B=A/1.15 ~ 0.87A
(2) If B is 15% less than B, then B = A (1-15%) = 0.85A

So, we see that these two expressions are different. So, you have to be cautious when dealing with such statements.

It is easier to say here that we limit ourselves to (1) in the question given but how do we do this in complex scenarios just like in the original question given?

The common logic, as explained above, is that you need to think if a particular figure existed even before the application of the percentage; if yes, then it is independent of the percentage. For example, in A & B example question, we say that the score of A is 15% more than B. So, there is a score of B and when we increase it by 15%, we get score of A. But score of B exists before the application of percentage.

So, coming back to the question, the total amount they paid i.e. $207 existed only after application of 15%, not before. Thus, 15% needs to be applied to some other variable to arrive at $207.

I hope my long answer clarifies some doubts. If you have any other queries, please feel free to ask.

Cheers,
CJ
_________________
Manager
Manager
avatar
Joined: 25 Jul 2012
Posts: 65
Location: United States
Re: The price of lunch for 15 people was $207.00, including a 15  [#permalink]

Show Tags

New post 27 Feb 2013, 21:31
Can someone please explain how you compute 207/1.15 under two minutes quickly? I think my division need help
_________________
If my post has contributed to your learning or teaching in any way, feel free to hit the kudos button ^_^
Intern
Intern
avatar
Joined: 30 Apr 2014
Posts: 2
GMAT ToolKit User
Re: The price of lunch for 15 people was $207.00, including a 15  [#permalink]

Show Tags

New post 07 May 2014, 15:06
1
1
For those who are intimidated by the division I found back solving to be very efficient for this problem.

I started with D $14.00

14*15 = 210 210>207 and that doesn't even have the gratuity added.

So I know right there that D and E are out and a 20 cent deduction on choice C is probably still going to be too high.


Went to answer choice B. $12.00

12*15=180 15% of 180=27 180+72=207.00
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8040
Location: United States (CA)
Re: The price of lunch for 15 people was $207.00, including a 15  [#permalink]

Show Tags

New post 03 May 2016, 11:38
2
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?

(A) $11.73
(B) $12.00
(C) $13.80
(D) $14.00
(E) $15.87

How come the answer is B?

This is how I solved it and got A, which is incorrect.

$207 includes 15% gratuity so 0.15 * 207 = 31.05

Price EXCLUDING gratuity = 207 - 31.05 = 175.95

Average price per person = 175.95/15 = 11.73


Solution:

An easy 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 gratuity. We use the value 1.15 in the equation below to account for the meal itself plus the gratuity. We can use x as the average cost per person for the meal without the gratuity. Thus, we can say:

(1.15)(15)(x) = 207

(115/100)(15)(x) = 207

(115)(15)(x) = (207)(100)

We can divide the entire equation by 3. Doing so gives us:

(115)(5)(x) = (69)(100)

We can divide the entire equation by 5 and we get:

(115)x = (69)(20)

We can again divide the entire equation by 5 and we get:

(23)x = (69)(4)

We can again divide the entire equation by 23 and we get:

x = (3)(4)

x = 12

Answer B
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4750
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Re: The price of lunch for 15 people was $207.00, including a 15  [#permalink]

Show Tags

New post 07 May 2016, 10:35
1
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?

(A) $11.73
(B) $12.00
(C) $13.80
(D) $14.00
(E) $15.87

How come the answer is B?

This is how I solved it and got A, which is incorrect.

$207 includes 15% gratuity so 0.15 * 207 = 31.05

Price EXCLUDING gratuity = 207 - 31.05 = 175.95

Average price per person = 175.95/15 = 11.73


Quote:
$207.00, including a 15 percent gratuity for service.


That means 115% = 207

So, 100% = \(\frac{207}{115}*100\) => 180

Further it is given -

Quote:
price of lunch for 15 people was $207.00, including a 15 percent gratuity for service.


So, Price of lunch for 15 people excluding 15 percent gratuity for service = \(180\)

Or, Price of lunch for 15 people excluding 15 percent gratuity for service = \(\frac{180}{15}\) => \(12\)

Hence average price excluding gratuity for service is 12
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Director
Director
User avatar
P
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 706
Location: United States (CA)
Age: 39
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47
GMAT 3: 750 Q50 V42
GRE 1: Q168 V169
WE: Education (Education)
Re: The price of lunch for 15 people was $207.00, including a 15  [#permalink]

Show Tags

New post 25 May 2016, 21:46
Attached is a visual that should help.
Attachments

Screen Shot 2016-05-25 at 9.42.14 PM.png
Screen Shot 2016-05-25 at 9.42.14 PM.png [ 51.22 KiB | Viewed 1948 times ]


_________________
Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching worldwide since 2002.

One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V.

You can download my official test-taker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y7knw7bt Date of Birth: 09 December 1979.

GMAT Action Plan and Free E-Book - McElroy Tutoring

Contact: mcelroy@post.harvard.edu (I do not respond to PMs on GMAT Club) or find me on reddit: http://www.reddit.com/r/GMATpreparation
CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3990
Location: Canada
Re: The price of lunch for 15 people was $207.00, including a 15  [#permalink]

Show Tags

New post 28 Aug 2017, 14:24
1
Top Contributor
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?

(A) $11.73
(B) $12.00
(C) $13.80
(D) $14.00
(E) $15.87



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.

I wrote an article about this misconception: http://www.gmatprepnow.com/articles/com ... 93-part-ii

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

Answer:

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
GMAT Club Bot
Re: The price of lunch for 15 people was $207.00, including a 15   [#permalink] 28 Aug 2017, 14:24

Go to page    1   2    Next  [ 21 posts ] 

Display posts from previous: Sort by

The price of lunch for 15 people was $207.00, including a 15

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne