BTGModeratorVI wrote: ↑

Sun Aug 02, 2020 7:02 am

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

Answer: E
Source: Economist GMAT

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