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# A certain Social Security recipient will receive an annual benefit of

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Math Expert
Joined: 02 Sep 2009
Posts: 56307
A certain Social Security recipient will receive an annual benefit of  [#permalink]

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23 Jul 2018, 00:31
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Difficulty:

25% (medium)

Question Stats:

79% (02:05) correct 21% (01:53) wrong based on 28 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

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Joined: 02 Aug 2009
Posts: 7763
Re: A certain Social Security recipient will receive an annual benefit of  [#permalink]

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23 Jul 2018, 01:20
Bunuel 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

We are talking of annual SS benefits..
It is 12000 and reduces by 1 for an increase of 3 above 9360..
50% reduction means 12000/2=6000
And for this the increase in salary is 3*6000=18000

So total annual earnings = 9360+18000=27,360\$

E
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Joined: 16 Apr 2018
Posts: 7
Re: A certain Social Security recipient will receive an annual benefit of  [#permalink]

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23 Jul 2018, 02:53
chetan2u wrote:
Bunuel 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

We are talking of annual SS benefits..
It is 12000 and reduces by 1 for an increase of 3 above 9360..
50% reduction means 12000/2=6000
And for this the increase in salary is 3*6000=18000

So total annual earnings = 9360+18000=27,360\$

E
Hi,
Thanks.

Sent from my vivo 1611 using GMAT Club Forum mobile app
Math Expert
Joined: 02 Aug 2009
Posts: 7763
Re: A certain Social Security recipient will receive an annual benefit of  [#permalink]

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23 Jul 2018, 04:36
Insiya wrote:
chetan2u wrote:
Bunuel 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

We are talking of annual SS benefits..
It is 12000 and reduces by 1 for an increase of 3 above 9360..
50% reduction means 12000/2=6000
And for this the increase in salary is 3*6000=18000

So total annual earnings = 9360+18000=27,360\$

E
Hi,
Thanks.

Sent from my vivo 1611 using GMAT Club Forum mobile app

Hi..

He was loosing 1\$ for an increase of 3\$ above 9360...
Since he lost 6000\$, 50% of 12000, he should have earned 3*6000 above his normal salary of 9360... So 3*6000+9360=18000+9360=27360
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Joined: 18 Jun 2018
Posts: 11
Location: India
Concentration: Technology, Marketing
GPA: 3.98
A certain Social Security recipient will receive an annual benefit of  [#permalink]

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23 Jul 2018, 09:49
1
Bunuel 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

Given: 50% reduction in the Annual Social Security Benefit
Annual Benefit = 12,000\$. So, after 50% reduction, it will be = 6,000\$

Benefit will be reduced by 1\$ for every 3\$
1\$ ----------------------------------------------> 3\$
Therefore, for 6000\$ reduction,
1\$ * 6000\$ ----------------------------------> 3\$ * 6000\$ = 18,000\$

Hence, the total amount will be: 9,360\$ + 18,000\$ = 27,360\$ Option (E)
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Joined: 09 Mar 2017
Posts: 514
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Concentration: Marketing, Organizational Behavior
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Re: A certain Social Security recipient will receive an annual benefit of  [#permalink]

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23 Jul 2018, 09:54
chetan2u wrote:
Bunuel 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

We are talking of annual SS benefits..
It is 12000 and reduces by 1 for an increase of 3 above 9360..
50% reduction means 12000/2=6000
And for this the increase in salary is 3*6000=18000

So total annual earnings = 9360+18000=27,360\$

E

Shouldn't the 50% reduction be done on the total benefit he receives, i.e. [12000 - {\$1(earnings-9360)/3}] as that would be the recipient's annual Social Security benefit ? I am lost at this very part. What am I missing? Thanks for the help.
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Re: A certain Social Security recipient will receive an annual benefit of   [#permalink] 23 Jul 2018, 09:54
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