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A one-million dollar inheritance was divided among five [#permalink]

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21 Jun 2010, 13:06

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A one-million dollar inheritance was divided among five beneficiaries. If no beneficiary received more than 30% of the inheritance, what was the greatest amount received by any one of the beneficiaries?

(1) Three of the beneficiaries received 80% of the amount received by a fourth beneficiary. (2) No beneficiary received less than 10% of the total inheritance.

Say, of 100 units, D gets 30 (max any one can receive). Then A + B + C = 24. Hence E should get 100 - (30+24) = 46 which is not possible. (any beneficiary can receive up to a max of 30 units)

E _________________

GGG (Gym / GMAT / Girl) -- Be Serious

Its your duty to post OA afterwards; some one must be waiting for that...

Given, 5 participants, each receiving less than 30% of something.

(i) 3 participants received 80% of 4th's share. 4th cud be 29, 28... hence, 3 participants cud have received variable amount (80%x29 OR 80%x28) based on 4th's share. These 4 participant's shares are variable hence 5ht is also variable. Multiple solutions. NOT SUFFICIENT.

(ii) {1,2,3,4,5}'s share > 10%. Multiple solutions possible. NOT SUFFICIENT.

Re: A one-million dollar inheritance was divided among five [#permalink]

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09 Aug 2013, 11:56

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This is the Manhattan GMAT explanation: The question stem tells us that there were 5 beneficiaries and that no beneficiary received more than $300,000. We are asked to determine the greatest amount received by any of the beneficiaries.

(1) INSUFFICIENT: There are many possible scenarios. For example, it's possible that one beneficiary received $250,000, three beneficiaries received 80% of that amount or $200,000 each, and the fifth beneficiary received the balance of $150,000. In this scenario the greatest amount awarded is $250,000. Alternatively, it is possible that one beneficiary received $225,000, three beneficiaries received 80% of that amount or $180,000, and the fifth beneficiary received the balance of $235,000. In this scenario the greatest amount awarded is $235,000.

(2) INSUFFICIENT: This provides a range for the dollar amount received by each beneficiary from $100,000 to $300,000 (10% to 30%) but does not provide any way to determine the greatest amount received by any of the beneficiaries.

(1) AND (2) INSUFFICIENT: Both statements together still allow for multiple scenarios. The two scenarios outlined in the discussion of statement (1) still hold even when adding the information in statement (2). Since there is still more than one possible value for the greatest amount received by any beneficiary, both statements together are not sufficient.

Re: A one-million dollar inheritance was divided among five [#permalink]

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10 Aug 2013, 01:56

shaneforu wrote:

A one-million dollar inheritance was divided among five beneficiaries. If no beneficiary received more than 30% of the inheritance, what was the greatest amount received by any one of the beneficiaries?

(1) Three of the beneficiaries received 80% of the amount received by a fourth beneficiary. (2) No beneficiary received less than 10% of the total inheritance.

............... st1, say fourth beneficiary received = x but its not possible now to evaluate the value of x from st1. st2 is nothing that can fix the problem. so E _________________

Re: A one-million dollar inheritance was divided among five [#permalink]

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16 Oct 2013, 18:16

shaneforu wrote:

A one-million dollar inheritance was divided among five beneficiaries. If no beneficiary received more than 30% of the inheritance, what was the greatest amount received by any one of the beneficiaries?

(1) Three of the beneficiaries received 80% of the amount received by a fourth beneficiary. (2) No beneficiary received less than 10% of the total inheritance.

Any nice and straightforward approach for solving this one Bunuel? Or anyone if you dare! Much appreciated Cheers J

Re: A one-million dollar inheritance was divided among five [#permalink]

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17 Oct 2013, 03:21

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Expert's post

A one-million dollar inheritance was divided among five beneficiaries. If no beneficiary received more than 30% of the inheritance, what was the greatest amount received by any one of the beneficiaries?

Say the inheritance was $1,000. We are told that no one received more than $300.

(1) Three of the beneficiaries received 80% of the amount received by a fourth beneficiary. This implies that 3 of he beneficiaries received an equal amount, which was 80% of the amount received by a 4th.

Now, if that 4th received $250, then 3 received $200 each and 5th received 1,000-(250+3*200)=150. The greatest amount received is $250. But if that 4th received $225, then 3 received $180 each and 5th received 1,000-(225+3*180)=2350. The greatest amount received is $235.

(2) No beneficiary received less than 10% of the total inheritance. Consider the same examples. Not sufficient.

(1)+(2) Consider the same examples. Not sufficient.

Re: A one-million dollar inheritance was divided among five [#permalink]

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08 Dec 2015, 10:01

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Re: A one-million dollar inheritance was divided among five [#permalink]

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11 Jan 2016, 00:04

There isn't enough information. However, you can find what the highest possible amount is if you use 10% as the lowest amount received.

Beneficiary 4 receives $264,705.88.

$264,705.88 x 80% is $211,764.70 rounded to the nearest cent. Beneficiaries 1, 2, and 3 receive this amount.

$211,764.70(3) = $635,294.11

$635,294.11 $264,705.88 +___________ $899,999.99

This leaves $100,000.00 for Beneficiary 5 with an extra penny due to rounding. * * * This Doesn't work the other way around. Beneficiary 4 cannot receive 30% because that is %300,000.00 $300,000.00 x 80% = $240,000.00 $240,000(3) = $720,000 $720,000 + 300,000 = $1,200,000.00 leaving beneficiary 5 $20,000.00 in debt rather than getting at least 10 percent. * * * This shows the maximum amount that anyone can receive given the conditions of the problem.

gmatclubot

Re: A one-million dollar inheritance was divided among five
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11 Jan 2016, 00:04

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