Bunuel
The total cost to charter a bus was shared equally by the people who went on a certain trip. If the total cost to charter the bus was $360, how many people went on the trip?
(1) Each person who went on the trip paid $9 to charter the bus.
(2) If 4 fewer people had gone on the trip, each person's share of the total cost to charter the bus would have increased by $1.
DS20420
Given: The total cost to charter the bus was $360. The total cost to charter a bus was shared equally by the people who went on a certain trip. Let N = the number of people that went on the trip.
So, the
price PER PERSON = 360/NTarget question: How many people went on the trip (
in other words, what's the value of N?)
Statement 1: Each person who went on the trip paid $9 to charter the bus. We already know that the
price PER PERSON = 360/NSo, we can now write: 360/N = 9
Solve to get: N = 40
The answer to the target question is
40 people went on the tripSince we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: If 4 fewer people had gone on the trip, each person's share of the total cost to charter the bus would have increased by $1.Let's start by creating a " word equation":
(price per person with 4 fewer people) = (original price per person) + $1In other words:
(price per person with N - 4 people) = (price per person with N people) + 1Substitute values to get: 360/(N - 4) =
360/N + 1
Multiply both sides of the equation by N to get: 360N/(N - 4) = 360 + N
Multiply both sides of the equation by (N - 4) to get: 360N = 360(N - 4) + N(N - 4)
Expand: 360N = 360N - 1440 + N² - 4N
Subtract 360N from both sides: 0 = -1440 + N² - 4N
Rearrange to get: N² - 4N - 1440 = 0
TOUGH ONE TO FACTOR!!!
Fortunately, we don't need two factor this. Here's why:
Since N² - 4N - 1440 = 0, we're looking for two numbers that have a product of -1440
This means one of the possible N-values will be negative, and one will be positive.
Since N cannot be negative, we can be certain that the equation N² - 4N - 1440 = 0 will yield exactly 1 positive value of N.
In other words, upon solving that equation, we will be able to answer the
target question with certainty
Statement 2 is SUFFICIENT
If you're not convinced, let's actually complete the factoring.
We get: (N + 36)(N - 40) = 0
So, EITHER N = -36 OR N = 40
Since N cannot be negative, we can be certain that N = 40
In other words,
40 people went on the tripSince we can answer the
target question with certainty, statement 2 is SUFFICIENT
ASIDE: Factoring N² - 4N - 1440 isn't that hard if we remember our analysis of statement 1 (where we determined that N = 40).
So, when we look for two numbers with a product of -1440, we know that one of those numbers must be 40 (and the other is -36)
Answer: D
Cheers,
Brent