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A widow received 1/3 of her husband's estate, and each of he

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Director
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A widow received 1/3 of her husband's estate, and each of he [#permalink] New post 27 Mar 2018, 21:55
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78% (01:42) correct 21% (02:26) wrong based on 14 sessions
A widow received \(\frac{1}{3}\) of her husband's estate, and each of her three sons received \(\frac{1}{3}\) of the balance. If the widow and one of her sons received a total of \($120,000\), what was the amount of the estate?

A) $180,000
B) $192,000
C) $216,000
D) $270,000
E) $275,000
[Reveal] Spoiler: OA
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Re: A widow received 1/3 of her husband's estate, and each of he [#permalink] New post 28 Mar 2018, 12:20
Expert's post
I do not know if the answer are precise. However, we could reach the solution as well because the values are fairly apart and not tight.

Now, the widow had 1/3, and 3 sons 1/3 of the rest (balance). So, the widow had 1/3 and each son 1/3 divided by 3 or 2/9.

1/3 + 2/9 = roughly 0.55%.

120,000 = 0.55% of X

C is the answer
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Manager
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Re: A widow received 1/3 of her husband's estate, and each of he [#permalink] New post 14 Dec 2018, 09:54
Carcass wrote:
I do not know if the answer are precise. However, we could reach the solution as well because the values are fairly apart and not tight.

Now, the widow had 1/3, and 3 sons 1/3 of the rest (balance). So, the widow had 1/3 and each son 1/3 divided by 3 or 2/9.

1/3 + 2/9 = roughly 0.55%.

120,000 = 0.55% of X

C is the answer


The answers are indeed precise.

Here is the way I did it.

W = 1/3 H
1 son = 1/3 (2/3 H) = 2/9H

Now 1/3H + 2/9 H = 120000
H = 216000
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Re: A widow received 1/3 of her husband's estate, and each of he [#permalink] New post 14 Dec 2018, 11:56
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Answer: C
1/3 * husband’s estate
What is remained? 2/3* husbands estate
What is the portion for each son? 1/3 * remained = 1/3 * 2/3* husbands estate = 2/9* husband’s estate

Mother + 1 son’s portion = 1/3 * husband’s estate + 2/9* husband’s estate = 5/9 * husband’s estate = 120,000$
Husband’s estate = 120,000$ * 9/5 = 120,000$ * 18/10= 12,0000$ * 18 = 216,000$
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Re: A widow received 1/3 of her husband's estate, and each of he   [#permalink] 14 Dec 2018, 11:56
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