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

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An insurance company sells only one type of health and one type of [#permalink]

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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.


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Re: An insurance company sells only one type of health and one type of [#permalink]

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New post 01 Nov 2015, 09:26
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 = 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
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Re: An insurance company sells only one type of health and one type of [#permalink]

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New post 01 Nov 2015, 11:32
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
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Re: An insurance company sells only one type of health and one type of [#permalink]

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New post 01 Nov 2015, 12:43
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.
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Re: An insurance company sells only one type of health and one type of [#permalink]

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New post 01 Nov 2015, 22:57
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.

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Re: An insurance company sells only one type of health and one type of [#permalink]

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New post 03 Nov 2015, 22:28
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 = 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


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!
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Re: An insurance company sells only one type of health and one type of [#permalink]

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New post 31 Mar 2017, 04:53
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Re: An insurance company sells only one type of health and one type of   [#permalink] 31 Mar 2017, 04:53
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