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A certain Social Security recipient will receive an annual b

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A certain Social Security recipient will receive an annual b [#permalink] New post 17 Mar 2011, 13:10
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A certain Social Security recipient will receive an annual benefit of $12,000 provided he has annual earnings of $9,360 or less, but the benefit will be reduced by $1 for every $3 of annual earnings over $9,360. What amount of total annual earnings would result in a 50 percent reduction in the recipient's annual Social Security benefit? (Assume Social Security benefits are not counted as part of annual earnings.)

(A) $15,360
(B) $17,360
(C) $18,000
(D) $21,360
(E) $27,360
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Re: A certain Social Security recipient will receive an annual b [#permalink] New post 17 Mar 2011, 13:15
banksy wrote:
A certain Social Security recipient will receive an annual benefit of $12,000 provided he has annual earnings of $9,360 or less, but the benefit will be reduced by $1 for every $3 of annual earnings over $9,360. What amount of total annual earnings would result in a 50 percent reduction in the recipient's annual Social Security benefit? (Assume Social Security benefits are not counted as part of annual earnings.)

(A) $15,360
(B) $17,360
(C) $18,000
(D) $21,360
(E) $27,360


For every $3 earn above $9360, the recipient loses $1 of benefit.
OR
For every $1 loss in the benefit, the recipient earns $3 above $9360

If earning is; 9360+3x
Benefit = 12000-x
Or the vice versa
If benefit is 12000-x, the earning becomes 9360+3x

He lost 50% of the benefit;

Benefit Received= 12000-1/2*12000 = 12000-6000
x=6000
Earning becomes 9360+3x=9360+3*6000=27360

Ans: "E"
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Re: A certain Social Security recipient will receive an annual b [#permalink] New post 19 Mar 2011, 01:18
Let x - extra income above 9360

reduction in allowance = y

So y/x = 1/3

so y = 6000

=> x = 18000

Hence total income = 9360 + 18000 = 27360
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Re: A certain Social Security recipient will receive an annual b [#permalink] New post 19 Mar 2011, 01:39
subhashghosh wrote:
Let x - extra income above 9360

reduction in allowance = y

So y/x = 1/3

so y = 6000

=> x = 18000

Hence total income = 9360 + 18000 = 27360



How did u calculate y=6000 and x= 18000?
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Re: A certain Social Security recipient will receive an annual b [#permalink] New post 22 Jun 2011, 04:29
For $3 rise in pay $1 is reduced in benefit. For the benefit to be 50% of 12000=6000. Then 6000*3=18000

Total earnings =18000+9360=27360
Re: A certain Social Security recipient will receive an annual b   [#permalink] 22 Jun 2011, 04:29
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