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?
A. $600
B. $1000
C. $3800
D. $5300
E. $6200
OA is c
what is wrong with option C in this question? Can you figure the error out too?
Health insurance Plan A requires the insured to pay $1000 or
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Nothing is wrong with C; it is the OA.Roland2rule wrote:what is wrong with option C in this question?
Several solutions are posted here:
https://www.beatthegmat.com/health-insu ... 01243.html
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Here's an algebraic approach:Roland2rule wrote: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?
A. $600
B. $1000
C. $3800
D. $5300
E. $6200
OA is c
what is wrong with option C in this question? Can you figure the error out too?
Let T = TOTAL COST
Plan A: Person pays EITHER $1000 OR 0.5T, whichever is LESS
Plan B: Person pays $300 plus 20% of anything over $300. In other words, the person pays $300 + 0.2(T - 300)
Since Plan A has two different scenarios, we need to test both. That is, create equations that see both plans costing the insured the same amount.
Case #1) 1000 = 300 + 0.2(T - 300).....now SOLVE
Expand: 1000 = 300 + 0.2T - 60
Rearrange: 760 = 0.2T
Solve: T = 3800
Perfect!!
The correct answer is C
Just for "fun" let's check out case #2
Case #2) 0.5T = 300 + 0.2(T - 300).....now SOLVE
Expand: 0.5T = 300 + 0.2T - 60
Rearrange: 0.3T = 240
Solve: T = 800
Hmmm, it seems that if the TOTAL cost were $800, both plans would require the insured to pay the same amount ($400). That said, $800 is not one of the answer choices.
Also notice that the question says, "Which of the following is a cost level for which both insurance plans pay out the same amount?" So, there are two possible correct answers, and the question asks us to find one of them.
Cheers,
Brent
Hi BTGmoderatorRO,
You can get the solution as follows,
Insured payouts:
Plan A --> 1000 or C/2
Plan B --> 300
Insurance payouts:
Plan A --> C - 1000 or C/2
Plan B --> 0.8(C - 300)
We are concerned with the payout made by insurance.
C - 1000 = 0.8 (C - 300)
C = 1000 + 0.8C - 240
0.2C = 760
C = 3800
Hence, the correct answer is the option C.
Regards!
You can get the solution as follows,
Insured payouts:
Plan A --> 1000 or C/2
Plan B --> 300
Insurance payouts:
Plan A --> C - 1000 or C/2
Plan B --> 0.8(C - 300)
We are concerned with the payout made by insurance.
C - 1000 = 0.8 (C - 300)
C = 1000 + 0.8C - 240
0.2C = 760
C = 3800
Hence, the correct answer is the option C.
Regards!
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Hi All,
You can answer this question with Algebra or by TESTing THE ANSWERS. Either way though, you have to pay careful attention to the wording of the prompt.
Since Plan A requires a $1000 payment OR 50% of total cost from the insured - whichever is LOWER - there's a great tactical shortcut here: any total bill that is over $2,000 will require that the insured pay $1,000 through Plan A. Since most of the answers are over $2,000, we can look to see if any of them would require that a total of $1,000 be paid by the insured through Plan B.
I'll start with the smallest option from that sub-group...
Answer C: $3,800
Insurance pays (3800 - 300)(.8) = (3500)(.8) = 2800
Insured pays initial 300 + whatever the insurance does NOT pay (3500 - 2800 = 700).
300 + 700 = 1,000
This is a MATCH for what we're looking for, so this MUST be the answer.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
You can answer this question with Algebra or by TESTing THE ANSWERS. Either way though, you have to pay careful attention to the wording of the prompt.
Since Plan A requires a $1000 payment OR 50% of total cost from the insured - whichever is LOWER - there's a great tactical shortcut here: any total bill that is over $2,000 will require that the insured pay $1,000 through Plan A. Since most of the answers are over $2,000, we can look to see if any of them would require that a total of $1,000 be paid by the insured through Plan B.
I'll start with the smallest option from that sub-group...
Answer C: $3,800
Insurance pays (3800 - 300)(.8) = (3500)(.8) = 2800
Insured pays initial 300 + whatever the insurance does NOT pay (3500 - 2800 = 700).
300 + 700 = 1,000
This is a MATCH for what we're looking for, so this MUST be the answer.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
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since plan A require $1000 payment or 50% of total cost.
Let T= Total cost, plan A=person pays Either $1000 or 0.5T i.e 50% of T. <whichever is lower>
plan B= person pays $300 plus 20% of anything over $300 plus. In other words, the person pays $300+0.2(T-300)
So, therefore
$$1000=300+0.2\left(T-300\right)$$
$$1000=300+0.2T-60$$
$$collect\ like\ term\ and\ rearrange$$
$$1000-300+60=0.2T$$
$$760=0.2T$$
$$T=\frac{760}{0.2}=$3800$$
Let T= Total cost, plan A=person pays Either $1000 or 0.5T i.e 50% of T. <whichever is lower>
plan B= person pays $300 plus 20% of anything over $300 plus. In other words, the person pays $300+0.2(T-300)
So, therefore
$$1000=300+0.2\left(T-300\right)$$
$$1000=300+0.2T-60$$
$$collect\ like\ term\ and\ rearrange$$
$$1000-300+60=0.2T$$
$$760=0.2T$$
$$T=\frac{760}{0.2}=$3800$$
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We can let x = a cost level for which both insurance plans pay out the same amount.BTGmoderatorRO wrote: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?
A. $600
B. $1000
C. $3800
D. $5300
E. $6200
Since 50% of $2000 is $1000, if x > 2000, Plan A will pay out (x - 1000) and Plan B will pay out 0.8(x - 300). Setting them equal, we have:
x - 1000 = 0.8(x - 300)
x - 1000 = 0.8x - 240
0.2x = 760
x = 3,800
Now, if x < 2000, then Plan A will pay out 0.5x and Plan B will still pay out 0.8(x - 300).
0.5x = 0.8(x - 300)
0.5x = 0.8x - 240
240 = 0.3x
800 = x
We see that x could be either 3,800 or 800. However, since the question asks for a cost level (instead of the cost level) and only 3,800 is given, then 3,800 is the correct answer.
Answer: C
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