Equation

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[email protected]: Master | Next Rank: 500 Posts; Posts: 429; Joined: Wed Sep 19, 2012 11:38 pmFollowed by: 4 members; Thanked: 6 times

by [email protected] » Sun Nov 03, 2013 4:48 am

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.

Last edited by [email protected] on Sun Nov 03, 2013 5:49 am, edited 1 time in total.

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Source: Beat The GMAT — Data Sufficiency | Sun Nov 03, 2013 4:48 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Nov 03, 2013 5:44 am

[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

Brent Hanneson - Creator of GMATPrepNow.com

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Sun Nov 03, 2013 5:45 am

[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.

Is something missing in the question?

R A H U L

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[email protected]: Master | Next Rank: 500 Posts; Posts: 429; Joined: Wed Sep 19, 2012 11:38 pmFollowed by: 4 members; Thanked: 6 times

by [email protected] » Sun Nov 03, 2013 5:50 am

have made the changes! Its actually 4/5

Brent@GMATPrepNow wrote:
[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

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Sun Nov 03, 2013 6:03 am

Health Policy(HP) & Life Policy(LP)
HP, x = 80
LP, y = A
Total = 5000

80(x) + (A)(y) = 5000 -(1)

TO find: A

Statement 1:
80(x) = 4/5 (5000) = 4000
Ay = 1000 --(2)
We can have multiple values of A & y .
INSUFFICIENT

Statement 2:
x = 2.5(y)
80(2.5y) + (A)(y) = 5000
INSUFFICIENT

Combining...
80(X) = 1000
Also, x = 2.5y--> we can get "y"
By putting the value of (y) in (2) we can get A
SUFFICIENT

Is it Answer [spoiler]{C}[/spoiler]?

R A H U L

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Nov 03, 2013 6:34 am

[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

Brent Hanneson - Creator of GMATPrepNow.com

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[email protected]: Master | Next Rank: 500 Posts; Posts: 429; Joined: Wed Sep 19, 2012 11:38 pmFollowed by: 4 members; Thanked: 6 times

by [email protected] » Sun Nov 03, 2013 6:57 am

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

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Nov 03, 2013 7:06 am

[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

Brent Hanneson - Creator of GMATPrepNow.com

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