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# A sum of money is divided among three sisters. The first sister receiv

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A sum of money is divided among three sisters. The first sister receiv  [#permalink]

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06 Mar 2020, 03:09
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A sum of money is divided among three sisters. The first sister receives 1/2 of the total, the second receives 1/4 of the total, and the third receives the remaining $10. How many dollars do the three sisters split? (A)$10
(B) $20 (C)$30
(D) $40 (E)$50

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Re: A sum of money is divided among three sisters. The first sister receiv  [#permalink]

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06 Mar 2020, 03:24
Bunuel wrote:
A sum of money is divided among three sisters. The first sister receives 1/2 of the total, the second receives 1/4 of the total, and the third receives the remaining $10. How many dollars do the three sisters split? (A)$10
(B) $20 (C)$30
(D) $40 (E)$50

Let Total = 400x
First = 200x
Second = (1/4)*400x = 100x
Third = 100x = 10

i.e. x = 1/10

i.e. Total = 400x = 400*(1/10 = 40

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Re: A sum of money is divided among three sisters. The first sister receiv  [#permalink]

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06 Mar 2020, 03:33
Bunuel wrote:
A sum of money is divided among three sisters. The first sister receives 1/2 of the total, the second receives 1/4 of the total, and the third receives the remaining $10. How many dollars do the three sisters split? (A)$10
(B) $20 (C)$30
(D) $40 (E)$50

First sister = $$\frac{(1*x)}{2}$$
second sister =$$\frac{(1*x)}{4}$$
third sister = $$\frac{(1*x)}{4}$$ = 10
x = 40
Ans: D
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Re: A sum of money is divided among three sisters. The first sister receiv  [#permalink]

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06 Mar 2020, 05:27
Bunuel wrote:
A sum of money is divided among three sisters. The first sister receives 1/2 of the total, the second receives 1/4 of the total, and the third receives the remaining $10. How many dollars do the three sisters split? (A)$10
(B) $20 (C)$30
(D) $40 (E)$50

let total amount be X
so split would be ; x/2+x/4+ 10 = x
solve we get x= 40
IMO D
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Re: A sum of money is divided among three sisters. The first sister receiv  [#permalink]

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09 Mar 2020, 03:39
Bunuel wrote:
A sum of money is divided among three sisters. The first sister receives 1/2 of the total, the second receives 1/4 of the total, and the third receives the remaining $10. How many dollars do the three sisters split? (A)$10
(B) $20 (C)$30
(D) $40 (E)$50

Letting n = the total number of dollars, we can create the equation:

n/2 + n/4 + 10 = n

Multiplying by 4, we have:

2n + n + 40 = 4n

40 = n

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A sum of money is divided among three sisters. The first sister receiv  [#permalink]

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Updated on: 16 Mar 2020, 00:50
I picked the number from answer choice.

Lets say option C = 30

1st Sister gets 30/2 = 15
2nd Sister gets 30/4 = 7.5 (I'll stop right there as we dont want decimal as per answer choices)
3rd Sister gets 10

Total of these number will exceed 30 anyway

Now try with 40

1st Sis: 40/2 = 20
2nd Sis: 40/4 = 10
3rd Sis: 10

The total is also 40. Thats perfect! Option D
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Originally posted by Farina on 11 Mar 2020, 20:55.
Last edited by Farina on 16 Mar 2020, 00:50, edited 1 time in total.
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Re: A sum of money is divided among three sisters. The first sister receiv  [#permalink]

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14 Mar 2020, 08:59
Bunuel wrote:
A sum of money is divided among three sisters. The first sister receives 1/2 of the total, the second receives 1/4 of the total, and the third receives the remaining $10. How many dollars do the three sisters split? (A)$10
(B) $20 (C)$30
(D) $40 (E)$50

S1 + S2 + S3

x/2 + x/4 + 10 = x
(6x+80)/8 = x
80 = 2x
x = 40

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Re: A sum of money is divided among three sisters. The first sister receiv  [#permalink]

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14 Mar 2020, 15:07
1-(1/2p + 1/4P )
1-3/4P=1/4p =10 ( 10 is the remainder)

D

DONT GIVE UP ON GOD
Re: A sum of money is divided among three sisters. The first sister receiv   [#permalink] 14 Mar 2020, 15:07