Five Heirs: A one-million dollar inheritance...

[ahay.hba2006]

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.


This question is very confusing. I chose E correctly, but I believe (1) is phrased too vaguely to be reliably interpreted. I assumed that 3 of the beneficiaries received 80% of the amount, COMBINED, that ONE beneficiary got (ie. if one beneficiary got $300,000, then the total received by 3 others was $240,000). With this in mind, 1 and 2 actually CONFLICT, which is of course not possible on the GMAT.

Can we expect phrasing this vague on the GMAT? I have not seen anything like this in the question banks yet.

[saurav.raaj]

I understand the confusion, but if then the devil is with the wordings in any word problem, and GMAT may want to trap test-takers.

However, if you try to evaluate this, you would notice that the share of 3 cannot be combined as you mentioned.

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)

[JonathanSchneider]

It's an excellent point, Saurav. However, the GMAT would probably not rely on your proving that in order to understand the question. I agree that the question might sound confusing. There ARE some published questions that do sound a bit confusing, but in general the quality control for this test is very good. As such, I'd agree with ahay that this question might be better phrased if it said "each."

[alisonlu007]

Is there a quick way to do this one? I see from the answer in the question bank that they tested cases--I just don't know if I would immediately test the correct ones.

[RonPurewal]

Is there a quick way to do this one? I see from the answer in the question bank that they tested cases--I just don't know if I would immediately test the correct ones.

There may not necessarily be a single set of "correct" cases; it's possible that you could establish the answer in many different specific ways.

In any case, the point is to impose organization on the process.
If you feel as though you're picking cases completely at random, that's not good. If you get into that kind of place, try various forms of organization.
- If there's an inherent order to something, then try cases in that order. (For instance, if you need a number that gives a remainder 1 on division by 5, it's better to try numbers in the order 6, 11, 16, 21, ... than to try randoms.)
"- If there are binaries / things that can be separated into discrete cases (odd, even, positive, negative, etc.), try to make a complete list of all such cases, and then run through the list (excluding any cases that don't satisfy the criteria of the problem).
"- Think about the biggest and smallest possible values.

Here, it's pretty clear that the first two don't apply, but the third could. Did you try making various things as big as you could? and then turn around and try to make them as small as you could?
If not, that's a good way to go. (There are "greater"s and "less"s all over this problem"”"”a big hint that such an approach might be productive.)

[AngelaH887]

Can someone explain to me why my logic is wrong(assuming its wrong since it wasnt marked as correct)

lets assume one of the beneficiaries gets max:300,000.


700000 is left over to split among 4.

We know three of the beneficiaries each get .8 the amount of one of the beneficiaries.

so 700000 = X + 3(.8X)

X=205882 (4th person)
X(.8) = 164705 (1st , 2nd, 3rd)

[RonPurewal]

Can someone explain to me why my logic is wrong(assuming its wrong since it wasnt marked as correct)

lets assume one of the beneficiaries gets max:300,000.


700000 is left over to split among 4.

We know three of the beneficiaries each get .8 the amount of one of the beneficiaries.

so 700000 = X + 3(.8X)

X=205882 (4th person)
X(.8) = 164705 (1st , 2nd, 3rd)

You seem to have forgotten that this is a data sufficiency problem.

The point is not to come up with one possible answer. (At least one possible answer will always exist.)

The point is to see whether you can find another possible answer. (If you can, then "not sufficient".)

[AngelaH887]

Hrmm, then I still don't understand. I did not forget I was doing a DS question. The questions asked: "If no beneficiary received more than 30% of the inheritance, what was the greatest amount received by any one of the beneficiaries?"


The greatest amount is 300,000. No other value, just this one value. I don't really care what the others received., that wasn't asked, I was simply showing that receiving the max, $300,000 is possible. Hence, wouldn't #1 and #2 be sufficient? ie the greatest amount received by any one beneficiary is 300,000

[tim]

You have only shown (correctly) that it is *possible* for someone to get 300,000. As Ron pointed out, since this is data sufficiency, showing that one answer is possible is not what you need to do. You need to either show that it is also possible that the greatest number is less than 300,000 (this would make the information insufficient), or that NO MATTER WHAT someone HAS to get 300,000 (this would make the information sufficient). The latter scenario is not the case here; given any combination of the statements it is always possible to find (at least) two different options for how much the highest inheritance is.

[RonPurewal]

^^ That.

In simpler terms, "no value is over ____" does not mean that one of the values IS "____".

For instance, if the four people in a room are 24, 27, 33, and 40 years old, then "No one in the room is over 50" is still a true statement. You don't need to have a 50-year-old present to say that.

[LucasM827]

I admit that I agree with the original poster. The question asks what is the "GREATEST" amount received. By definition, is there not only one "greatest" amount. So, by the terms of the question - why wouldn't it be reasonable to take the constraints to determine the "greatest." In this instance, the parameters listed in 1 & 2 do not constrain the maximum possible value, which is identified to be 300k. But I'm a lawyer and a GMAT novice so I could be way off.

You have only shown (correctly) that it is *possible* for someone to get 300,000. As Ron pointed out, since this is data sufficiency, showing that one answer is possible is not what you need to do. You need to either show that it is also possible that the greatest number is less than 300,000 (this would make the information insufficient), or that NO MATTER WHAT someone HAS to get 300,000 (this would make the information sufficient). The latter scenario is not the case here; given any combination of the statements it is always possible to find (at least) two different options for how much the highest inheritance is.

[Sage Pearce-Higgins]

I don't think that this is a GMAT-specific point. The question lays out some constraints, one of which is that "no beneficiary received more than 30% of the inheritance". However, that's different from stating that somebody actually received 30%. Perhaps a simpler analogy would work:

"All humans are shorter than 30 feet in height. What's the tallest human in the world?" It would be absurd to reply: "well, you've already told me that the tallest person is 30 feet tall."

[LucasM827]

Right, that makes sense. I think that just by the way the question is worded it teases you into driving towards the goal of confirming a 30k gift to one of the children.

[Sage Pearce-Higgins]

Yes! The GMAT is designed to do that! Specifically, on DS problems mixing up what you're told and what you're asked for is the classic confusion.