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29 Jul 2014, 06:55
5
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Difficulty:

45% (medium)

Question Stats:

72% (02:28) correct 28% (03:14) wrong based on 154 sessions

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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 [Reveal] Spoiler: OA Director Joined: 25 Apr 2012 Posts: 704 Location: India GPA: 3.21 WE: Business Development (Other) Re: Danny spends$360 buying his favorite dolls. If he buys only [#permalink]

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29 Jul 2014, 07:25
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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..
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Danny spends $360 buying his favorite dolls. If he buys only [#permalink] ### Show Tags 29 Jul 2014, 08:58 2 This post received KUDOS Expert's post 1 This post was BOOKMARKED 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.

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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.
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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
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Re: Danny spends $360 buying his favorite dolls. If he buys only [#permalink] ### Show Tags 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. _________________ Re: Danny spends$360 buying his favorite dolls. If he buys only   [#permalink] 25 Dec 2017, 19:47
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