A one-million dollar inheritance was divided among five

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)=235. 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.
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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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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.

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.

The correct answer is E.

...............
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

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

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.
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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.
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This shows the maximum amount that anyone can receive given the conditions of the problem.

here is my two cents

shouldn't 1 specify that
(1) Three of the beneficiaries ( EACH) received 80% of the amount received by a fourth beneficiary.

\(A \leqslant B \leqslant C \leqslant D \leqslant E\,\,\,\,\,\,\left( \$ \right)\)

\(A + B + C + D + E = {10^6}\)

\(A,B,C,D,E\,\,\,\, \leqslant \,\,\,30\% \left( {{{10}^6}} \right)\)

\(? = E\)

\(\left( {1 + 2} \right)\,\,\,\left\{ \matrix{\\
\,{\rm{Take}}\,\,\left( {A;B;C;D;E} \right) = \left( {15\% \left( {{{10}^6}} \right);\overbrace {20\% \left( {{{10}^6}} \right);20\% \left( {{{10}^6}} \right);20\% \left( {{{10}^6}} \right);25\% \left( {{{10}^6}} \right)}^{{\rm{statement}}\,\,\left( 1 \right)}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 25\% \left( {{{10}^6}} \right) \hfill \cr \\
\,\,{\rm{Take}}\,\,\left( {A;B;C;D;E} \right) = \left( {\underbrace {17\% \left( {{{10}^6}} \right);17\% \left( {{{10}^6}} \right);17\% \left( {{{10}^6}} \right);21.25\% \left( {{{10}^6}} \right)}_{{\rm{statement}}\,\,\left( 1 \right)};27.75\% \left( {{{10}^6}} \right)} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 27.75\% \left( {{{10}^6}} \right) \hfill \cr} \right.\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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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.
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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.

(1) Three of the beneficiaries received 80% of the amount received by a fourth beneficiary.
We are required to find the greatest amount from five beneficiary, BUT from this condition, we need to identify the greatest amount from B4 or B5 only

Say B1 or B2 or B3 = 80% * B4, means: B1=B2=B3= 4/5 * B4
Say the total of (B1 to B5) is 1000, then: 1000 = 3 * (4/5 * B4) + B4 + B5 = 17/5*B4 + B5
Result: 1000 = 17/5*B4 + B5
Let's test by simple numbers:
B4=250 --> B5= 150 --> the greatest amount is 250
B4=220 --> B5= 252 --> the greatest amount is 252

Conclusion: insufficient.

(2) No beneficiary received less than 10% of the total inheritance.
Clear: insufficient.

(1) and (2): Clear: insufficient.

Answer: E

word each is missing in statement A