An insurance company sells only one type of health and one type of

Question

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.

BrentGMATPrepNow · Answer

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

Skywalker18 · Answer

Let h= number of health insurance policies
 l= number of life insurance policies
 L= monthly premium on a life insurance policies

80 h + Ll = 5000
We need to find the value of L

1.
80h = 4000
Ll = 1000
Not sufficient

2. h=2.5l
80*2.5l +Ll = 5000
=> 200l +Ll = 5000
Not sufficient

Combining 1 and 2, we get
200l=4000
=>l=20

L= 50

Sufficient.
Answer C

mvictor · Answer

1 -> 80H = 4/5 * 5000 or 80H = 4000. H = 50. Can't Find L.
2 -> H = 2.5L
write 2.5L*80 +xL = 5000
20L+xL = 5000
L(20+x) = 5000
don't have X.
both ->
L(20+x) = 5000
H = 50.
2.5L = 50, and L = 20.
now we have 40L = 5000. we can solve for L.
C is the answer.

saikiransomala · Answer

Hi,

Statement 1: We arrive at H = 5000/180 - Not sufficient
Statement 2: Only relation is provided. - Not sufficient

Now using 1 and 2, we arrive at the Value of L.

Option C.

Regards

arhumsid · Answer

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 = 5000

where, 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!

dhruva09 · Answer

Bunuel  can you please address  arhumsid 's doubt. I too believe that is a crucial component,
Or else mention of the values as collection of a particular month.

Bunuel · Answer

Yes, the question should have been phrased more clearly to state that we are dealing with one month’s premiums.

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