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A certain Social Security recipient will receive an annual benefit of

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

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New post 22 Jul 2018, 23:31
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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 benefit of  [#permalink]

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New post 23 Jul 2018, 00:20
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: A certain Social Security recipient will receive an annual benefit of  [#permalink]

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New post 23 Jul 2018, 01:53
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,
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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Re: A certain Social Security recipient will receive an annual benefit of  [#permalink]

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New post 23 Jul 2018, 03:36
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,
Can you please explain the last step of your solution?
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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

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New post 23 Jul 2018, 08:49
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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Re: A certain Social Security recipient will receive an annual benefit of  [#permalink]

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New post 23 Jul 2018, 08:54
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 &nbs [#permalink] 23 Jul 2018, 08:54
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