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

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

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Economist GMAT

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

OA E

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AAPL 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

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Brent Hanneson – Creator of GMATPrepNow.com
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Post
AAPL wrote:
Economist GMAT

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
Since a small doll costs $1 less than a large doll, the answer choices imply the following options for the price of a small doll:
4
5

6.2
7
8
Given that all of the values in the prompt are INTEGERS, the price of a small doll is almost certain to be a factor of 360.
Only the values in blue divide evenly into 360.
Thus, the correct answer is probably A, B or E.
When the correct answer is plugged in, Danny will be able to purchase 5 more large dolls than small dolls.

B: $6 for each large doll, implyinh $5 for each small doll
Number of $6 large dolls that can be purchased for $360 = 360/6 = 60.
Number of $5 small dolls that can be purchased for $360 = 360/5 = 72.
(number of small dolls) - (number of large dolls) = 72-60 = 12.
Since Danny can purchase 12 more small dolls than large dolls, eliminate B.

E: $9 for each large doll, implying $8 for each small doll
Number of $9 large dolls that can be purchased for $360 = 360/9 = 40.
Number of $8 small dolls that can be purchased for $360 = 360/8 = 45.
(number of small dolls) - (number of large dolls) = 45-40 = 5.
Success!

The correct answer is E.

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GMATGuruNY@gmail.com

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Post
AAPL wrote:
Economist GMAT

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

OA E
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



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