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Difficulty:   55% (hard)

Question Stats: 71% (02:54) correct 29% (02:46) wrong based on 141 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 Director  Joined: 25 Apr 2012 Posts: 660 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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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 3 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.

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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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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 Top Contributor 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 L = cost of 1 LARGE LemonHead doll
So L-1 = cost of 1 SMALL LemonHead doll

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. Let's first write a "word equation": (# of LARGE dolls for$360) = (# of SMALL dolls for $360) - 5 Substitute values to get:$360/L = $360/(L-1) - 5 ASIDE: At this point, it might be faster to just TEST THE ANSWER CHOICES to see which one satisfies the above equation. Or we can just solve the equation for L. Let's do that. Multiply both sides by L to get: 360 = 360L/(L-1) - 5L Multiply both sides by (L-1) to get: 360(L-1) = 360L - 5L(L-1) Expand to get: 360L - 360 = 360L - 5L² + 5L Subtract 360L from both sides to get: -360 = -5L² + 5L Rearrange to get: 5L² - 5L - 360 = 0 Divide both sided by 5 to get: L² - L - 72 = 0 Factor to get: (L - 9)(L + 8) = 0 So, EITHER L = 9 OR L = -8 Since L cannot be negative, it must be the case that L = 9 Answer: E Cheers, Brent _________________ Target Test Prep Representative D Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 8117 Location: United States (CA) Re: Danny spends$360 buying his favorite dolls. If he buys only  [#permalink]

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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 We can let the cost of a large doll = d and thus the cost of a small doll = d - 1. We can let q = the number of large dolls that can be purchased with$360, and thus q + 5 = the number of small dolls that can be purchased with $360. We can create the equations: 360 = (d - 1)(q + 5) 360 = dq - q + 5d - 5 and 360 = dq 360/d = q Substituting, we have: 360 = d(360/d) - 360/d + 5d - 5 360 = 360 - 360/d + 5d - 5 0 = -360/d + 5d - 5 Multiplying the equation by d, we have: 0 = -360 + 5d^2 - 5d d^2 - d - 72 = 0 (d - 9)(d + 8) = 0 d = 9 or d = -8 Since d can’t be negative, d = 9. Answer: E _________________ Scott Woodbury-Stewart Founder and CEO Scott@TargetTestPrep.com 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. Re: Danny spends$360 buying his favorite dolls. If he buys only   [#permalink] 19 Mar 2019, 19:11
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