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Bunuel
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A certain Social Security recipient will receive an annual benefit of 23 Jul 2018, 00:31
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25% (medium)

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76% (01:51) correct 24% (02:14) wrong based on 264 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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E
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GMAT Focus 1: 735 Q90 V89 DI81
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A certain Social Security recipient will receive an annual benefit of 23 Jul 2018, 01:20
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Bunuel
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
Show more

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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A certain Social Security recipient will receive an annual benefit of 23 Jul 2018, 02:53
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chetan2u
Bunuel
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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Hi,
Can you please explain the last step of your solution?
Thanks.

Sent from my vivo 1611 using GMAT Club Forum mobile app
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A certain Social Security recipient will receive an annual benefit of 23 Jul 2018, 04:36
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chetan2u
Bunuel
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,
Can you please explain the last step of your solution?
Thanks.

Sent from my vivo 1611 using GMAT Club Forum mobile app
Show more

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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A certain Social Security recipient will receive an annual benefit of 23 Jul 2018, 09:49
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Bunuel
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
Show more

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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A certain Social Security recipient will receive an annual benefit of 23 Jul 2018, 09:54
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chetan2u
Bunuel
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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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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A certain Social Security recipient will receive an annual benefit of 01 Sep 2025, 06:53
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Just need to read the question properly and its not that tough once we understand it. Took me a lot of time as well.

Social Security amount below $9360 = $12,0000.
The reduction of amount is 1 dollar per every 3 dollar increase = (New earnings - 9360)/3.

For this amount to be equal to half the Security deposit we can say=> (New earnings - 9360)/3 = 6000.

From this: New Earnings comes out as: 27,360.

Hence the answer is (E)





Bunuel
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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