Data Sufficiency

AAPL wrote:Princeton Review

An insurance company sells only one type of health and one type of life insurance policy. The monthly premium for a health insurance policy is $80. If the insurance company took in a total $5000 in premiums, what was the monthly premium of a life insurance policy?

(1) The total revenue from health insurance premiums was 4/5 of the total revenue the company received from premiums.
(2) The insurance company sold 2.5 times as many health insurance policies as life insurance policies.

OA C.

Let H = the number of health insurance policies
Let L = the number of life insurance policies
Let p = the monthly premium on a life insurance policy

So, 80H + pL = 5000

Target question: What is the value of p?

Statement 1: The total revenue from health insurance premiums was 4/5 of the total revenue the company received from premiums.
Total revenue = $5000
(4/5)($5000) = $4000
So, 80H = $4000.
Take 80H + pL = 5000 and replace 80H with $4000 to get 4000 + pL = 5000, which simplifies to pL = 1000
Since there are many possible values for p that satisfy this equation, statement 1 is NOT SUFFICIENT

Statement 2: The insurance company sold 2.5 times as many health insurance policies as life insurance policies.
In other words, H = 2.5L
Take 80H + pL = 5000 and replace H with 2.5L to get 80(2.5L) + pL = 5000, which simplifies to be 200L + pL = 5000
Since there are many possible values for p that satisfy this equation, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
From the two statements we get two equations:
200L + pL = 5000
pL = 1000
Subtract the bottom equation from the top equation to get: 200L = 4000, which means L = 20
Now that we know L = 20 and pL = 1000, we can see that p = 50
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent