Four brothers split a sum of money between them. The first brother received 50% of the total, the second received 25% of

[BTGmoderatorDC]

Four brothers split a sum of money between them. The first brother received 50% of the total, the second received 25% of the total, the third received 20% of the total, and the fourth received the remaining $4. The first brother received how much more money than the third brother received?

(A) $4
(B) $16
(C) $20
(D) $24
(E) $36


OA D

Source: Manhattan Prep

[Jay@ManhattanReview]

Four brothers split a sum of money between them. The first brother received 50% of the total, the second received 25% of the total, the third received 20% of the total, and the fourth received the remaining $4. The first brother received how much more money than the third brother received?

(A) $4
(B) $16
(C) $20
(D) $24
(E) $36

OA D

Source: Manhattan Prep

Given that the first brother received 50% of the total, the second received 25% of the total, the third received 20% of the total, the fourth would receive 100 – 50 – 25 – 20 = 5% of the total

Thus, 5% of the total = $4

=> Total = 4/5% = $80

Of the total, the first brother received 50% – 20% = 30% more of the total than the third brother received.

Thus, 30% of the total = 30% of $80 = $24

The correct answer: D

Hope this helps!

-Jay
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[Scott@TargetTestPrep]

Four brothers split a sum of money between them. The first brother received 50% of the total, the second received 25% of the total, the third received 20% of the total, and the fourth received the remaining $4. The first brother received how much more money than the third brother received?

(A) $4
(B) $16
(C) $20
(D) $24
(E) $36


OA D

Source: Manhattan Prep

Solution:

We see that the fourth brother receives 5% of the total money. Since he received $4 and the third brother received 20% or 4 times his percent share, the third brother received 4 times as much money also, or $16. Similarly, the first brother received 50%, or 10 times, the fourth brother’s percent share, the first brother received 10 times as much money, or $40. Therefore, the first brother received 40 - 16 = $24 more than the third brother received.

Alternate Solution:

Notice that the remaining $4 that the fourth brother receives is 100 - (50 + 25 + 20) = 5% of the total. Thus, the total amount of money that is shared among the brothers is 4/0.05 = $80. Notice also that the difference between the amounts of money received by the 1st and the 3rd brothers corresponds to 50 - 20 = 30% of the total. Thus, the first brother received 80 * 0.3 = $24 more than the third brother.

Answer: D