mgmat question

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mirantdon: Master | Next Rank: 500 Posts; Posts: 135; Joined: Thu May 05, 2011 9:00 amFollowed by: 1 member; Thanked: 4 times; GMAT Score:700

by mirantdon » Mon May 30, 2011 8:54 am

Health insurance Plan A requires the insured to pay $1000 or 50% of total cost, whichever is lower. Plan B requires the insured to pay the initial $300, but then pays 80% of the cost over $300. Which of the following is a cost level for which both insurance plans pay out the same amount?
$600
$1000
$3800
$5300
$6200

oa is c. but not satisfied with explanation .can anyone help .
thanks

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Source: Beat The GMAT — Problem Solving | Mon May 30, 2011 8:54 am

SoCan: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Sun May 15, 2011 9:19 amFollowed by: 1 member; Thanked: 18 times

by SoCan » Mon May 30, 2011 9:16 am

The wording is a little tricky because it's easy to confuse which party is paying what. Also, the question starts out by explaining what the insured customer pays, and then asks for the level in which the insurance COMPANY pays the same.

Insurance company payments
1) A: $300 (insured pays 50% of 600), B: $240 (insured pays first $300, company pays 80% of remaining $300)
2) A: $500 (insured pays 50% of 1000), B: $560 (insured pays first $300, company pays 80% of remaining $700)
3) A: $2800 (insured pays $1000, company pays remaining $2800), B: $2800 (insured pays first $300, company pays 80% of remaining $3500)

You can solve all the answers until you get to the right one. This worked out nicely because the first question where the insured is capped at $1000 proved to be the right one. However, this may not always be the case, so if you realize that the insured is capped at $1000 in the remaining questions, you can solve for x (where x is the cost level) with the equation:
x-1000=0.8(x-300)
x/5=760
x=3800

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sivaelectric: Master | Next Rank: 500 Posts; Posts: 439; Joined: Sat Aug 09, 2008 8:32 amFollowed by: 28 members; Location: India; Thanked: 34 times

by sivaelectric » Mon May 30, 2011 9:24 am

Nice explanation

If I am wrong correct me

, If my post helped let me know by clicking the Thanks button

.

Chitra Sivasankar Arunagiri

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[email protected]: Legendary Member; Posts: 934; Joined: Tue Nov 09, 2010 5:16 amFollowed by: 14 members; Location: AAMCHI MUMBAI LOCAL; Thanked: 63 times

by [email protected] » Mon Jun 13, 2011 3:05 am

good explanation!!!

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newgmattest: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Wed May 18, 2011 8:48 pm; Thanked: 4 times

by newgmattest » Mon Jun 13, 2011 5:19 am

Hi GMAT Experts,

Apart from testing the answer choices, how to go about actual solution please? I can see one solution, but I don't understand.

Thanks

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Mon Jun 13, 2011 5:36 am

newgmattest wrote: Apart from testing the answer choices, how to go about actual solution please? I can see one solution, but I don't understand.

Thanks

Hi,
As you have said you understood the plug-in , I will try to explain the other method that you are looking for.
Let x be the total cost.
As the payment of 'A' depends on the lower of 0.5x and 1000, we have two cases: 0.5x<1000 and 0.5x>1000 i.e x<2000 and x>2000
case-1: x<2000
A will play 0.5x. So, the remaining 0.5x will be paid by the insurance company
B will pay 300$. So, the insurance company will pay (0.8)*(x-300)
For them to be equal: 0.5x = 0.8*(x-300) => x=800

case-2: x>2000
A will play 1000$. So, the remaining (x-1000) will be paid by the insurance company
B will pay 300$. So, the insurance company will pay (0.8)*(x-300)
For them to be equal: x-1000 = (0.8)*(x-300) => 0.2x = 760 =>x=3800.

Cheers!

Things are not what they appear to be... nor are they otherwise

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newgmattest: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Wed May 18, 2011 8:48 pm; Thanked: 4 times

by newgmattest » Mon Jun 13, 2011 5:41 am

So it means that we can have two values of x. But solution first proposed have only one final value of x. Can you elaborate please....

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finites: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Thu Jun 02, 2011 7:21 am

by finites » Tue Jun 14, 2011 11:08 am

x be the total amount to be paid..

Incase of A
A pays either 1000 or x/2
Insurance pays either x -1000 or x/2..

Incase of B
x = 300 + (x -300) * 80/100 + (x -300) *20/100
B pays 300 + (x - 300) *20/100

objective A and B shud pay same amount..

case 1:
x/2 = 300 + (x -300)/5
solve for x
5x/2 = 1500 + x - 300
5x/2 -x = 1200
5x -2x = 1200 *2
3x = 2400
x = 800

case 2:
1000 = 300 + (x - 300)/5
slove for x
700 = (x - 300)/5
3500 = x -300
x = 3800

let me if i have done anything wrong..i believe in this case amount payed by A and B can be same in 2 cases. Just that 3800 is in the option.

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gmatdriller: Master | Next Rank: 500 Posts; Posts: 418; Joined: Sun Jul 04, 2010 12:48 pmFollowed by: 3 members; Thanked: 6 times

by gmatdriller » Mon Nov 21, 2011 1:37 pm

key is in understanding the wordings of the question:
plan B requires the insurer to pay..., but then pays 80%...
subject - verb.
it was the plan that pays 80%; there I lost my steam under the heat of the test.

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