GMATPrepNow wrote:

Bunuel wrote:

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.

Kudos for a correct solution.

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 = 5000Target 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 = 1000Since

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 = 5000Since

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 = 5000pL = 1000Subtract the bottom equation from the top equation to get: 200L = 4000, which means

L = 20Now that we know L = 20 and pL = 1000, we can see that

p = 50Since we can answer the

target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,

Brent

Hi,

I have a doubt in the explanations provided. I see all have arrived at C with only taking these three variables into account

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

But what about the number of months? Should that not be considered?

The question says that

"If the insurance company took in a total $5000 in premiums".

But in how many months?? (How can we assume that this total is for one month?)

Therefore,

80H will represent premium collected from H policies for 1 month and not for

all the months. Similarly Lp.

IMO, the equation should be something like this-

80*H*M1 + L*p*M2 = 5000where, M1=number of months for which premium was collected for health insurance policies

M2=number of months for which premium was collected for life insurance policies

Please help me, what am i missing??

Thanks!

_________________

One Kudos for an everlasting piece of knowledge is not a bad deal at all...

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