BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 1223
Joined: Sat Feb 15, 2020 2:23 pm
Followed by:1 members

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

by BTGModeratorVI » Wed Jul 29, 2020 2:54 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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.

Answer: C
Source: Princeton Review
Top
Source: — Data Sufficiency |
User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

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

by Brent@GMATPrepNow » Thu Jul 30, 2020 7:32 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

BTGModeratorVI wrote: ↑
Wed Jul 29, 2020 2:54 pm
 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.

Answer: C
Source: Princeton Review
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
Image
Top
Legendary Member
Posts: 2214
Joined: Fri Mar 02, 2018 2:22 pm
Followed by:5 members

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

by deloitte247 » Fri Jul 31, 2020 2:07 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Let the no. of insurance policy = x
Let the no. of life policy = y
Let the no. of a monthly premium of a life insurance policy = z
Let the no. of a monthly premium of a health insurance policy = $80

Target question: What was the monthly premium of a life insurance policy?
Given that 80x + zy = 5000; find the value of z.

Statement 1: The total revenue from health insurance premiums was 4/5 of the total revenue the company received from premiums.
Total revenue = 5000
Health insurance policy premiums = 80 * x = 80x
$$Therefore,\ 80x=\frac{4}{5}\cdot5000$$
$$80x=4000$$
From the question stem, 80x + zy = 5000; where 80x = 4000
Therefore, 4000 + zy = 5000
zy = 5000 - 4000 = 1000

Here, the exact value of z and y is unknown. So, the target question cannot be answered with a definite value because there are so many variations of integers that satisfy zy=1000. Therefore, statement 1 is NOT SUFFICIENT.

Statement 2: The insurance company sold 2.5 times as many health insurance policies as life insurance policies.
Therefore, x = 2.5 of y
From question stem , 80x + zy = 5000
80 (2.5y) + zy = 5000
200y + zy =5000
The exact value of z and y is unknown and as such, the target question cannot be answered with certainty. Hence, statement 2 is NOT SUFFICIENT.

Combining both statements together
From statement 1; zy = 1000 eqn (1)
From statement 2; 200y + zy = 5000 eqn (2)
Subtracting equation 1 from equation 2
200y + zy = 5000
- zy = 1000
We have,
200y = 4000
$$y=\frac{4000}{200}=20$$
From eqn (1), zy = 1000, where y=20
20z = 1000
$$z=\frac{1000}{20}=$50$$
Comclusively, both statements combined together ARE SUFFICIENT.
Answer = Option C
Top
Post new topic Post Reply
• Page 1 of 1