Last Updated on May 4, 2023
GMAT OFFICIAL GUIDE PS
Solution:
We can start by creating some variables.
Q = quantity of towels sold
P = price per towel sold
Next we can set up some equations.
We know that at the current price:
PQ = 120
We are next given that if the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120. From this we can say:
(P + 1)(Q – 10) = 120
Since we need to determine the value of P, we should get the second equation in terms of P only. We can do this by manipulating the equation PQ = 120. So we can say:
Q = 120/P
Now we can plug in 120/P for Q in the equation (P + 1)(Q – 10) = 120. We now have:
(P + 1)(120/P – 10) = 120
FOILing this, we get:
120 – 10P + 120/P – 10 = 120
–10P + 120/P – 10 = 0
We can multiply the entire equation by P to get rid of the denominators. This gives us:
–10P^2 + 120 – 10P = 0
10P^2 + 10P – 120 = 0
P^2 + P – 12 = 0
(P + 4)(P – 3) = 0
P = -4 or P = 3
Since P can’t be negative, P = 3.
Answer: C
