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

It is currently 18 Nov 2018, 02:54

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
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

A certain bakery sells six different-sized wedding cakes

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

Hide Tags

Senior Manager
Senior Manager
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 475
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
A certain bakery sells six different-sized wedding cakes  [#permalink]

Show Tags

New post 04 Mar 2012, 14:12
1
4
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

79% (02:52) correct 21% (03:13) wrong based on 234 sessions

HideShow timer Statistics

A certain bakery sells six different-sized wedding cakes. Each cake costs x dollars more than the next one below it in size, and the price of the largest cake is $24.50. If the sum of the prices of the six different cakes is $109.50, what is the value of x?
(A) 1.50
(B) 1.75
(C) 2.00
(D) 2.50
(E) 3.00

This is how I am trying to solve this, but got stuck.

Total price = 109.5

Price of each cake i.e. average = \(\frac{109.50}{6}\) = \(18.25\)

Price of the smallest cake = x

Price of the largest cake = 24.5

As this is the evenly spaced set [Price difference of x between any 2 cakes] average of x and 24.5 will be equal to the average 18.25 i.e.

\(\frac{x+24.5}{2}\) = 18.25

x = 12

I am stuck after this. can you please help?

_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50624
Re: Bakery  [#permalink]

Show Tags

New post 04 Mar 2012, 14:49
1
A certain bakery sells six different-sized wedding cakes. Each cake costs x dollars more than the next one below it in size, and the price of the largest cake is $24.50. If the sum of the prices of the six different cakes is $109.50, what is the value of x?
(A) 1.50
(B) 1.75
(C) 2.00
(D) 2.50
(E) 3.00

Since the price of the largest cake (6th) is $24.50, then the price of the smallest cake (1st) is $(24.50-5x). Now, the prices of the cakes are evenly spaced so the sum of the prices is (average price)*(# of cakes)=(first+last)/2*(# of cakes). So, (24.50-5x+24.50)/2*6=109.50 --> x=2.5.

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 16 Feb 2012
Posts: 178
Concentration: Finance, Economics
GMAT ToolKit User
Re: A certain bakery sells six different-sized wedding cakes  [#permalink]

Show Tags

New post 04 Mar 2012, 15:05
1
enigma123 wrote:
A certain bakery sells six different-sized wedding cakes. Each cake costs x dollars more than the next one below it in size, and the price of the largest cake is $24.50. If the sum of the prices of the six different cakes is $109.50, what is the value of x?
(A) 1.50
(B) 1.75
(C) 2.00
(D) 2.50
(E) 3.00

This is how I am trying to solve this, but got stuck.

Total price = 109.5

Price of each cake i.e. average = \(\frac{109.50}{6}\) = \(18.25\)

Price of the smallest cake = x

Price of the largest cake = 24.5

As this is the evenly spaced set [Price difference of x between any 2 cakes] average of x and 24.5 will be equal to the average 18.25 i.e.

\(\frac{x+24.5}{2}\) = 18.25

x = 12

I am stuck after this. can you please help?



Your result isn't the difference between any two cakes. Your result is the price of the first cake.
Let's say that x is the price of the first cake and y is the difference between the cakes, the formula will be: \(x + (x+y) + (x+2y) + (x+3y) + (x+4y) + (x+5y) = 109,5\).
Since you know that x is 12, and you also know that the price of the biggest cake is \(x+5y=24.5\), than just simply calculate the equation.

12 + 5y = 24.5; y = 2.5
_________________

Kudos if you like the post!

Failing to plan is planning to fail.

Director
Director
User avatar
B
Joined: 04 Jun 2016
Posts: 569
GMAT 1: 750 Q49 V43
A certain bakery sells six different-sized wedding cakes  [#permalink]

Show Tags

New post Updated on: 11 Sep 2016, 19:37
1
1
Being simple is the key my friend .
You should not try to be fancy when a simple approach is right in front of your eyes.

This is essentially an algebra problem with two unknown variables.

Let the price of FIRST (ALSO THE SMALLEST) CAKE be Y
Then every other cake will become {Y+X}, {Y+X+X} ......and so on

BASED ON THE INFO, YOU WILL GET:-

First cake price = y
Second cake price = y+x
Third cake price= y+x+x
Fourth cake price = y+x+x+x
Fifth cake price= y+x+x+x+x
sixth cake price = y+x+x+x+x+x

SIXTH CAKE IS LARGEST
y+5x= 24.50

Total price of all cakes =(FIRST $ + SECOND $ + THIRD $....... + SIXTH $) ====> 6y+15x = 109.40

Now you got two unique equation for two unknown variable

WHATS THE PRPBLEM THEN :- SOLVE IT
y+5x=24.50 (Multiply by 3) ...........Eq1
6y+15x=109.40 ............. Eq2
Subtract Eq1 from Eq2

y==>12

put value of y in Eq 1
12+5x=24.50
5x= 12.50
x=\(\frac{12.50}{5}\) ===>2.5 (OPTION D)
ANSWER IS D

ENJOY

enigma123 wrote:
A certain bakery sells six different-sized wedding cakes. Each cake costs x dollars more than the next one below it in size, and the price of the largest cake is $24.50. If the sum of the prices of the six different cakes is $109.50, what is the value of x?
(A) 1.50
(B) 1.75
(C) 2.00
(D) 2.50
(E) 3.00

This is how I am trying to solve this, but got stuck.

Total price = 109.5

Price of each cake i.e. average = \(\frac{109.50}{6}\) = \(18.25\)

Price of the smallest cake = x

Price of the largest cake = 24.5

As this is the evenly spaced set [Price difference of x between any 2 cakes] average of x and 24.5 will be equal to the average 18.25 i.e.

\(\frac{x+24.5}{2}\) = 18.25

x = 12

I am stuck after this. can you please help?

_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.


Originally posted by LogicGuru1 on 03 Jul 2016, 06:15.
Last edited by LogicGuru1 on 11 Sep 2016, 19:37, edited 1 time in total.
Intern
Intern
User avatar
Joined: 20 Jan 2016
Posts: 45
GMAT 1: 600 Q47 V26
Re: A certain bakery sells six different-sized wedding cakes  [#permalink]

Show Tags

New post 03 Jul 2016, 09:52
109.5= 24.5x6 - 15X
X=2.5


Sent from my iPhone using GMAT Club Forum mobile app
Intern
Intern
avatar
Joined: 25 Jun 2015
Posts: 8
Location: Portugal
GMAT 1: 370 Q37 V37
GPA: 2.92
GMAT ToolKit User
Re: A certain bakery sells six different-sized wedding cakes  [#permalink]

Show Tags

New post 11 Sep 2016, 08:13
rohitrawat9990 wrote:
109.5= 24.5x6 - 15X
X=2.5


Sent from my iPhone using GMAT Club Forum mobile app



How did you came up with 15X?
Board of Directors
User avatar
V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3614
Premium Member Reviews Badge
Re: A certain bakery sells six different-sized wedding cakes  [#permalink]

Show Tags

New post 11 Sep 2016, 08:23
arturportugal wrote:
rohitrawat9990 wrote:
109.5= 24.5x6 - 15X
X=2.5


Sent from my iPhone using GMAT Club Forum mobile app



How did you came up with 15X?


Let L6 represents the price of largest and L1 represents the smallest.

We are given that L6 = 24.5

L5 = 24.5-x ( each smaller sized is x less than its immediate larger)

L4 = 24.5 - 2x

L3 = 24.5 - 3x

L2 = 24.5 - 4x

L1 = 24.5 - 5x

Now, the sum of all prices = 109.5

So, L6 to L1, you will get

109.5= 24.5x6 - 15x

or x = 2.5
_________________

My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place
Blog: Subscribe to Question of the Day Blog
GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.

Current Student
User avatar
B
Status: DONE!
Joined: 05 Sep 2016
Posts: 378
Re: A certain bakery sells six different-sized wedding cakes  [#permalink]

Show Tags

New post 18 Oct 2016, 15:26
From the question we can derive the following equation:

(24.50-5x) + (24.50-4x)+... = 109.50

simplifies to... 24.50(6)-15x=109.50

Solve for x.

x=2.5
Current Student
avatar
B
Joined: 26 Jan 2016
Posts: 105
Location: United States
GPA: 3.37
Re: A certain bakery sells six different-sized wedding cakes  [#permalink]

Show Tags

New post 18 Oct 2016, 15:55
I first saw what 25*6 is just to give a ball park number and it was 150. I then realized that the numbers had to decrease by the "biggest" answer values.

I first started with D just b/c it ended in a .50. Once you start to go down the numbers you'll see that in order to end with a .50 (109.5) you need to have an amount taken away that ends in .50. B,C, and E are out. D worked.
Manager
Manager
User avatar
S
Status: Math Tutor
Joined: 12 Aug 2017
Posts: 73
GMAT 1: 750 Q50 V42
WE: Education (Education)
Re: A certain bakery sells six different-sized wedding cakes  [#permalink]

Show Tags

New post 29 Oct 2017, 12:37
Since the price of each cake is reducing by a constant value all the time, the prices will from Arithmetic Series
Average of 6 terms in Arithmetic is average of 3rd and 4th term. Thus now using options
Option C
4th term is 24.5 - 2*2 = 20.5
3rd term is 20.5-2 = 18.5
Average is 19.5
Total price of all 6 is 19.5*6 = 19*6+0.5*6 = 117
But since we need answer less than 117 (109.5) average value is less than 19.5.
Thus moving down to option D
4th term = 24.5-2*2.5 = 19.5
3rd term = 19.5 - 2.5 = 17
Average = 18.25
Total price = 18.25*6 = 18*6+0.25*6 = 108+1.5 = 109.5
Matching with question
Thus answer is option D
_________________

Abhishek Parikh
Math Tutor
Whatsapp- +919983944321
Mobile- +971568653827
Website: http://www.holamaven.com

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4170
Location: United States (CA)
Re: A certain bakery sells six different-sized wedding cakes  [#permalink]

Show Tags

New post 31 Oct 2017, 15:41
enigma123 wrote:
A certain bakery sells six different-sized wedding cakes. Each cake costs x dollars more than the next one below it in size, and the price of the largest cake is $24.50. If the sum of the prices of the six different cakes is $109.50, what is the value of x?
(A) 1.50
(B) 1.75
(C) 2.00
(D) 2.50
(E) 3.00


We can create the following equation:

(24.50) + (24.50 - x) + (24.50 - 2x) + (24.50 - 3x) + (24.50 - 4x) + (24.50 - 5x) = 109.50

6(24.50) - 15x = 109.50

147 - 15x = 109.5

37.5 = 15x

2.50 = x

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

GMAT Club Bot
Re: A certain bakery sells six different-sized wedding cakes &nbs [#permalink] 31 Oct 2017, 15:41
Display posts from previous: Sort by

A certain bakery sells six different-sized wedding cakes

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.