Three people have $32, $72, and $98, respectively. If they pool their

Question

Three people have $32, $72, and $98, respectively. If they pool their money then redistribute it among them, what is the maximum value for the median amount of money?

(A) $72 
(B) $85 
(C) $98 
(D) $101 
(E) $202

GMATinsight · Accepted Answer

CONCEPT: The Median will be HIGHEST if the terms other than Median are SMALLEST

Total Money = 32 + 72 + 98 = 202

The money has to distributed among three parts
Let's say A, B and C
where A < B < C i.e. Median is B

i.e. Smallest amount that anyone of those three can have i.e. A = $0

Remaining Money = $202-$0 = $202 = B+C

Now the Since C has to be minimised and still C >B therefore (C)_min = 101  and  (B)_max = 101

Answer: Option  D

asfandabid · Answer

the question says that the money was redistributed among the three people. How does $0 count as redistributing? Shouldn't it be atleast 1?

reto · Answer

Add all the values $32 + $72 + $98. Sum = $202
The median is maximised if the first person receives 0 and the total amount is equally distributed between the remaining two people. Median = 202/2=101

balamoon · Answer

Solution - 
Total money distributed is $202. In order to maximize median, one person has to accept $0 and remaining two people share $101 each. Hence median is $101.

ANS D

bluesquare · Answer

Together the total would be $32+$72+98=$202. If they redistribute it, the median will be the middle amount. The lowest amount can be $0, leaving $202 for the other two. If the remaining $202 is split, then the median will be $101, answer choice D.

Bunuel · Answer

The pool of money is $32 + $72 + $98 = $202. After the redistribution, each person will have an amount between $0 and $202, inclusive. Let's call the amounts L, M, and H (low, median, high). To maximize M, we must minimize L and H. https://gmatclub.com/forum/download/file.php?id=27040 Minimum L = $0 Minimum H = M Maximum M = Total pool of money - Minimum L- Minimum H M = $202 – $0 – M 2M = $202 M = $101 The correct answer is D. 2015-06-22_1800.png

vegetate · Answer

I thought the smallest number should be 1.
hence，I worked out 100. not listed.
picked 101，anyway.

ScottTargetTestPrep · Answer

The total number of dollars is 32 + 72 + 98 = 202.

The first person could have 0 dollars, the next person 101 dollars, and the next person 101 dollars.

Thus, the maximum value of the median is 101.

Answer: D

srishti246 · Answer

If one person can get 0$ then why not the third person? It could be that only 1 person among the 3 takes all money making median 202$?

Hovkial · Answer

It is not possible for two people to get $0 because then you cannot arrange the three amounts in ascending order to have the largest possible median amount. You will have $0, $0 and $202 in ascending order. This sequence will not produce the largest possible median.

This question in incorrectly written. You cannot say that you have distributed a quantity among some people if at least one person does not get any part of that quantity. The question should have clearly specified that it is possible for at least one person not to receive anything. Official GMAT questions will be clearly written.

Sandrine · Answer

Weird and unclear question. Redistributing means that everybody should receive something.

MathRevolution · Answer

Sum of money = 32 + 72 + 98 = 202.

Median is central value so two of them cannot be 0 each and the third one gets all 202, otherwise the median will be '0'.

Maximum median =  \frac{202 }{ 2} = 101  .

Answer D

ShoSho3 · Answer

So when sum of the money is $202, then how come someone gets $202 and the other $101?!

Regor60 · Answer

That's not what he's saying.

He's saying that if someone gets 202, the other two get 0 and then the median would be 0. But that would not maximize the median.

Posted from my mobile device

ThatDudeKnows · Answer

Do math if you want. Or reason your way through these types of questions.

If we take the $32 and give it to the person with $72, we'd have a distribution of
$0
$98
$104

Answer choices A and B are proven wrong, and E sure isn't going to make sense. That leaves C and D. C is what we have in the distribution above, but we can see (without doing the math) that we can do better than that. There's only one answer choice remaining that's better than C. Answer choice D. No math (okay, okay, we added the 32 and 72...so barely any math). Use the answer choices, guys!

Oh, and nitpicking the question wording doesn't get you any additional points...there are ambiguities in some of the OG questions, too...just get it right...you're trying to go to master the GMAT so you can go to b-school, not studying for the LSAT to become a nit-picky lawyer type.

Vibhatu · Answer

C will not be the correct answer  because, question doesn't tell the money should be integer value.  Money can be $0.5, $101, $101.5
Answer: D

Xiaolin2021 · Answer

not really a good question as it can be confusing with the statement saying that the pooled money was distributed among 3 people. If 1 person receives $0, it means the money was only distributed within 2 people, instead of 3, IMO. Hence, not a well-designed question.

Three people have $32, $72, and $98, respectively. If they pool their

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Three people have $32, $72, and $98, respectively. If they pool their

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