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# A one-million dollar inheritance was divided among five

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Intern
Joined: 11 Jan 2007
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Location: United States
Concentration: Marketing, Healthcare
GMAT 1: 600 Q49 V25
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WE: Pharmaceuticals (Consulting)
A one-million dollar inheritance was divided among five  [#permalink]

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21 Jun 2010, 13:06
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Difficulty:

85% (hard)

Question Stats:

55% (02:41) correct 45% (02:45) wrong based on 326 sessions

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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.
Senior Manager
Joined: 25 Feb 2010
Posts: 286

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21 Jun 2010, 14:23
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Take 5 people , A B C D E

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
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28 Jun 2010, 01:31
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.
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Joined: 04 Aug 2013
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Re: A one-million dollar inheritance was divided among five  [#permalink]

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09 Aug 2013, 11:56
1
This is the Manhattan GMAT explanation:
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. Answer: E. _________________ Intern Joined: 10 Jan 2016 Posts: 1 Re: A one-million dollar inheritance was divided among five [#permalink] ### Show Tags 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. Manager Joined: 23 Jun 2009 Posts: 173 Location: Brazil GMAT 1: 470 Q30 V20 GMAT 2: 620 Q42 V33 Re: A one-million dollar inheritance was divided among five [#permalink] ### Show Tags 08 Nov 2016, 05:38 here is my two cents Attachments ineheri.png [ 490.18 KiB | Viewed 21712 times ] Retired Moderator Joined: 05 Jul 2006 Posts: 1456 Re: A one-million dollar inheritance was divided among five [#permalink] ### Show Tags 22 Dec 2016, 11:28 shouldn't 1 specify that (1) Three of the beneficiaries ( EACH) received 80% of the amount received by a fourth beneficiary. GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 935 Re: A one-million dollar inheritance was divided among five [#permalink] ### Show Tags 18 Dec 2018, 14:00 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. $$A \leqslant B \leqslant C \leqslant D \leqslant E\,\,\,\,\,\,\left( \ \right)$$ $$A + B + C + D + E = {10^6}$$ $$A,B,C,D,E\,\,\,\, \leqslant \,\,\,30\% \left( {{{10}^6}} \right)$$ $$? = E$$ $$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {A;B;C;D;E} \right) = \left( {15\% \left( {{{10}^6}} \right);\overbrace {20\% \left( {{{10}^6}} \right);20\% \left( {{{10}^6}} \right);20\% \left( {{{10}^6}} \right);25\% \left( {{{10}^6}} \right)}^{{\rm{statement}}\,\,\left( 1 \right)}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 25\% \left( {{{10}^6}} \right) \hfill \cr \,\,{\rm{Take}}\,\,\left( {A;B;C;D;E} \right) = \left( {\underbrace {17\% \left( {{{10}^6}} \right);17\% \left( {{{10}^6}} \right);17\% \left( {{{10}^6}} \right);21.25\% \left( {{{10}^6}} \right)}_{{\rm{statement}}\,\,\left( 1 \right)};27.75\% \left( {{{10}^6}} \right)} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 27.75\% \left( {{{10}^6}} \right) \hfill \cr} \right.$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 935 Re: A one-million dollar inheritance was divided among five [#permalink] ### Show Tags 18 Dec 2018, 14:11 yezz wrote: shouldn't 1 specify that (1) Three of the beneficiaries ( EACH) received 80% of the amount received by a fourth beneficiary. I believe so! When I started solving this problem, I thought about using the SUM of 3 beneficiaries amounts being equal to 80% ... Fortunately, you will (probably) NOT be put in such uncomfortable situations during your official test! Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net Manager Joined: 29 Sep 2016 Posts: 113 Re: A one-million dollar inheritance was divided among five [#permalink] ### Show Tags 02 May 2019, 17:44 TiredOfStudying wrote: 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.

I feel the wording of statement 1 isn't correct. It should be as below -

(1) Three of the beneficiaries each received 80% of the amount received by a fourth beneficiary.
Re: A one-million dollar inheritance was divided among five   [#permalink] 02 May 2019, 17:44
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