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Insurance Plan A requires the patient to pay up to the first
[#permalink]
18 May 2020, 05:37

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Question Stats:

Insurance Plan A requires the patient to pay up to the first $1,600 of any hospital bill plus 12% of the remainder of the bill. Insurance Plan B requires the patient to pay the entire amount of any hospital bill under $2,000; for hospital bills of at least $2,000 , the patient pays $2,000 plus another 8% of the entire amount.

The patient would pay the same under either insurance plan for hospital bills of which of the following amounts?

Indicate all such hospital bill amounts.

❑ $1,280

❑ $1.600

❑ $1,840

❑ $2,000

❑ $6,800

❑ $9,900

❑ $14,800

_________________

The patient would pay the same under either insurance plan for hospital bills of which of the following amounts?

Indicate all such hospital bill amounts.

❑ $1,280

❑ $1.600

❑ $1,840

❑ $2,000

❑ $6,800

❑ $9,900

❑ $14,800

_________________

Re: Insurance Plan A requires the patient to pay up to the first
[#permalink]
18 May 2020, 05:37

Expert Reply

Post A Detailed Correct Solution For The Above Questions And Get A Kudos.

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Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!

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Re: Insurance Plan A requires the patient to pay up to the first
[#permalink]
21 May 2020, 06:35

Please describe in detail the answer

Re: Insurance Plan A requires the patient to pay up to the first
[#permalink]
21 May 2020, 13:28

1

It looks like there are some formatting issues in the question and answer options

Re: Insurance Plan A requires the patient to pay up to the first
[#permalink]
21 May 2020, 13:39

1

Expert Reply

Fixed. Thank you for pointing out

_________________

_________________

Re: Insurance Plan A requires the patient to pay up to the first
[#permalink]
21 May 2020, 14:08

3

First thing I did was set up 2 equations for each insurance when the bill exceeds the minimum payment requirement

A = 1600 + 0.12(x-1600)

B = 2000 + 0.08(x)

We know that under plan A the patient pays the full amount if it's under or = 1600, same goes for B if the total is under 2000, so instantly options A and B are valid.

I ruled out C because plan B would pay the full 1840, whereas A would pay less (just by glancing at the earlier equation, the actual value A would pay is 1628.8)

Once you hit 2000 on plan B, you have to pay 2000+0.08(total) [this is where word problems get tricky], so I knew that D wasn't a valid option because plan B would pay more than 2000 and A would pay less than 2000

From there, I plugged options E, F, and G into the earlier equations to get my final answer of A,B, and G.

I'm willing to bet there's a quicker way to solve this problem, this was just how I set it up

A = 1600 + 0.12(x-1600)

B = 2000 + 0.08(x)

We know that under plan A the patient pays the full amount if it's under or = 1600, same goes for B if the total is under 2000, so instantly options A and B are valid.

I ruled out C because plan B would pay the full 1840, whereas A would pay less (just by glancing at the earlier equation, the actual value A would pay is 1628.8)

Once you hit 2000 on plan B, you have to pay 2000+0.08(total) [this is where word problems get tricky], so I knew that D wasn't a valid option because plan B would pay more than 2000 and A would pay less than 2000

From there, I plugged options E, F, and G into the earlier equations to get my final answer of A,B, and G.

I'm willing to bet there's a quicker way to solve this problem, this was just how I set it up

Re: Insurance Plan A requires the patient to pay up to the first
[#permalink]
18 Aug 2020, 05:08

2

To complete the previous answer, especially to show that 14,800 is the answer:

For any amount less than 1600 you know you will pay the same amount under both plans. Because they require you to pay your bill basically.

Then, let's look at an amount x between 1600 and 2000, 1600 < x <= 2000

Under plan A you pay 1600 + (x-1600)x0.12.

Under plan B you will always pay x

When are those things equal? Only when x=1600 (but it's not in the range we're considering).

Now let's look at an amount x > 2000

Then under plan A you pay

1600 + 0.12(x-1600)

Under plan B you pay

2000 + 0.08 x

When are those things equal?

1600 + 0.12(x-1600)=2000 + 0.08x

0.04 x = 400 + 0.12x1600

x=14,800

So we can tick any box below (less than or equal) 1600 and equal to 14,800.

For any amount less than 1600 you know you will pay the same amount under both plans. Because they require you to pay your bill basically.

Then, let's look at an amount x between 1600 and 2000, 1600 < x <= 2000

Under plan A you pay 1600 + (x-1600)x0.12.

Under plan B you will always pay x

When are those things equal? Only when x=1600 (but it's not in the range we're considering).

Now let's look at an amount x > 2000

Then under plan A you pay

1600 + 0.12(x-1600)

Under plan B you pay

2000 + 0.08 x

When are those things equal?

1600 + 0.12(x-1600)=2000 + 0.08x

0.04 x = 400 + 0.12x1600

x=14,800

So we can tick any box below (less than or equal) 1600 and equal to 14,800.

Re: Insurance Plan A requires the patient to pay up to the first
[#permalink]
22 Sep 2021, 07:27

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

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