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

It is currently 18 Jul 2018, 19:22

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

Danny spends $360 buying his favorite dolls. If he buys only

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

Hide Tags

Senior Manager
Senior Manager
User avatar
Joined: 21 Oct 2013
Posts: 434
Danny spends $360 buying his favorite dolls. If he buys only [#permalink]

Show Tags

New post 29 Jul 2014, 06:55
4
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

72% (02:25) correct 28% (03:10) wrong based on 161 sessions

HideShow timer Statistics

Danny spends $360 buying his favorite dolls. If he buys only small LemonHead dolls, which are $1 cheaper than the large LemonHead dolls, he could buy 5 more dolls than if he were to buy only large LemonHead dolls. How much does a large LemonHead doll cost?

A. $5
B. $6
C. $7.2
D. $8
E. $9
Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 701
Location: India
GPA: 3.21
WE: Business Development (Other)
Premium Member Reviews Badge
Re: Danny spends $360 buying his favorite dolls. If he buys only [#permalink]

Show Tags

New post 29 Jul 2014, 07:25
2
goodyear2013 wrote:
Danny spends $360 buying his favorite dolls. If he buys only small LemonHead dolls, which are $1 cheaper than the large LemonHead dolls, he could buy 5 more dolls than if he were to buy only large LemonHead dolls. How much does a large LemonHead doll cost?

A. $5
B. $6
C. $7.2
D. $8
E. $9


Let p $ be the price of large lemonhead doll and n be the no. dolls danny can buy

so we have n*p=360

also if price of 1 dollar less then danny can buy 5 more small head dolls so

(p-1)*(n+5)=360=pn..

pn +5p-n-5=pn or 5p= 5+n or \(5p=5+\frac{360}{p}\)

5p^2-360-5p=0

or p^2-p-72=0

p^2-9p+8p-72=0

or p =9 or -8 (price cannot be negative so p =9

note that the problem can be solved by plugging as well..

Starting with D...because C is not great option to start with here

if p=8 then danny can buy 45 large head dolls and p-1=7 $, he can buy \(\frac{360}{7}\neq{Integer}\)So drop this option

Look at p=9 so Large head dolls=40 and for p-1=$8, then he can buy 45 dolls which is exactly what q. stem says..
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47084
Danny spends $360 buying his favorite dolls. If he buys only [#permalink]

Show Tags

New post 29 Jul 2014, 08:58
2
1
goodyear2013 wrote:
Danny spends $360 buying his favorite dolls. If he buys only small LemonHead dolls, which are $1 cheaper than the large LemonHead dolls, he could buy 5 more dolls than if he were to buy only large LemonHead dolls. How much does a large LemonHead doll cost?

A. $5
B. $6
C. $7.2
D. $8
E. $9


I'd plug the options for this question. Usually we start with C but since C is not an integer let's skip it for a while and plug D first.

If large doll costs $8, then he can buy 360/8 = 45 large dolls and 360/7 = 50.something small dolls. The difference is more than 5. Discard.

Now, increase the price of the large doll to decrease the difference.

If large doll costs $9, then he can buy 360/9 = 40 large dolls and 360/8 = 45 small dolls. The difference is 5, which is what we wanted.

Answer: E.
_________________

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

1 KUDOS received
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Danny spends $360 buying his favorite dolls. If he buys only [#permalink]

Show Tags

New post 31 Jul 2014, 23:16
1
Lets say price of big = x

So quantity obtained \(= \frac{360}{x}\) (Total = 360)

So, price of small = x-1

& Qty of small \(= \frac{360}{x} + 5\)

\((x-1)(\frac{360}{x} + 5) = 360\)

\(x^2 - x - 72 = 0\)

x = 9

Answer = E
_________________

Kindly press "+1 Kudos" to appreciate :)

Intern
Intern
User avatar
Joined: 14 Apr 2015
Posts: 7
Re: Danny spends $360 buying his favorite dolls. If he buys only [#permalink]

Show Tags

New post 15 Apr 2015, 03:28
X: Price of small dolls; Y: Price of big dolls.
Y = X +1

360(1/x - 1/y) = 5
<=>x.y = 72
We can make trial: 9x8 = 72.
Choose (E) y = 9.
Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2724
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: Danny spends $360 buying his favorite dolls. If he buys only [#permalink]

Show Tags

New post 30 Jan 2016, 18:06
I didn't want to complicate with the algebra...thus, I just plugged in numbers:
6 is way lower than needed, thus we can right away eliminate A, B - because we need higher price.
C is out because it yields a non-integer number when we check for the price of the small doll (360/6.2 = not integer)
D is out, because 360/7 = non-integer.
thus, we are remained with E.
Current Student
User avatar
B
Status: DONE!
Joined: 05 Sep 2016
Posts: 398
Re: Danny spends $360 buying his favorite dolls. If he buys only [#permalink]

Show Tags

New post 23 Oct 2016, 19:56
S = small doll
L = large doll
D = # of dolls

Use the following formulas:

360/L-1 = D+5
360/L = D

You'll eventually get it down to the following:

5L^2 -5L = 360
(L^2 -L) = 72
L^2 -L -72 = 0
(L+8)(L-9) = 0
L = -8 or 9
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 7293
Premium Member
Re: Danny spends $360 buying his favorite dolls. If he buys only [#permalink]

Show Tags

New post 25 Dec 2017, 19:47
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: Danny spends $360 buying his favorite dolls. If he buys only   [#permalink] 25 Dec 2017, 19:47
Display posts from previous: Sort by

Danny spends $360 buying his favorite dolls. If he buys only

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

Events & Promotions

PREV
NEXT


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®.