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# A certain Social Security recipient will receive an annual b

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Manager
Joined: 10 Feb 2011
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17 Mar 2011, 14:10
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Difficulty:

15% (low)

Question Stats:

85% (01:05) correct 15% (00:50) wrong based on 33 sessions

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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
[Reveal] Spoiler: OA

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Math Forum Moderator
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Re: A certain Social Security recipient will receive an annual b [#permalink]

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17 Mar 2011, 14:15
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;

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]

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19 Mar 2011, 02:18
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]

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19 Mar 2011, 02:39
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]

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22 Jun 2011, 05:29
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

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Re: A certain Social Security recipient will receive an annual b   [#permalink] 22 Jun 2011, 05:29
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