Data Sufficiency

[email protected] wrote:An insurance company sells only one type of health insurance policy and only 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 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.

I think you're missing part of the question (in red)

Cheers,
Brent

[email protected] wrote:An insurance company sells only one type of health insurance policy and only 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.

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

[email protected] wrote:But why cant we take 1/5 as the part for life insurance, aren't we already given 5000 as the total value?

We are considering this information.
Statement 1 essentially tells us that the company collected $1000 in Life Insurance policies.
In other words, pL = 1000.
HOWEVER, this doesn't tell us the value of p (the life insurance premium)
Consider these two conflicting cases:
case a: L = 100 and p = 10
case b: L = 10 and p = 100

Cheers,
Brent