Marcab wrote:
For each order, a certain company charges a delivery fee d that depends on the total price x of the merchandise in the order, where d and x are in dollars and
d = 3, if 0<x<=100
d = 3 + (x-100)/100, if 100<x<=500
d = 7, if x>500
If George placed two separate orders with the company, was the total price of the merchandise in the two orders greater than $499?
(1) The delivery fee for one of the two orders was $3.
(2) The sum of the delivery fees for the two orders was $10.
We need to determine whether the total price of the merchandise in two separate orders is greater than $499 or not.
Statement One Alone:
The delivery fee for one of the two orders was $3.
Thus we know price of one of the orders is at least $1 and at most $100. However, since we don’t know anything about the other order, we can’t answer the question. Statement one alone is not sufficient.
Statement Two Alone:
The sum of the delivery fees for the two orders was $10.
If the sum of the delivery fees was $10, it is possible that one order is at most $100 (thus has a delivery fee of $3) and the other order is at least $501 (thus has a delivery fee of $7). In this case the total price of the two orders will be greater than $499 since one of them is already greater than $499.
However, it is also possible that each of the orders has a price that is more than $100 but no more than $500.
So let’s let a = price of the one order and b = price of the other order where both a and b are more than $100 but no more than $500. We can create the following equation:
3 + (a - 100)/100 + 3 + (b - 100)/100 = 10
(a - 100)/100 + (b - 100)/100 = 4
(a - 100) + (b - 100) = 400
a + b = 600
We can see that if each order is more than $100 but no more than $500, then the total price of the two orders is always $600, which is greater than $499.
Answer: B