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Problem Solving

by phoenix9801 » Sun May 20, 2012 6:07 pm
Dan has five times as many seashells as Paul, and eight more than Andrew. When Dan gives away 40% of his shells, Paul and Andrew agree to split those shells up evenly, giving Andrew twice as many as Paul. How many shells did Dan start with?

a) 10
b) 15
c) 20
d) 25
e) 30
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by Anurag@Gurome » Sun May 20, 2012 7:21 pm
phoenix9801 wrote:Dan has five times as many seashells as Paul, and eight more than Andrew. When Dan gives away 40% of his shells, Paul and Andrew agree to split those shells up evenly, giving Andrew twice as many as Paul. How many shells did Dan start with?

a) 10
b) 15
c) 20
d) 25
e) 30
D = 5P and D = 8 + A
So, 5P = 8 + A
When Dan gives away 40% of his shells,
40% of Dan's shells = 0.40 * 5P = 2P
Dan has 5P - 2P = 3P shells
Now Paul has P + P = 2P shells
Andrew has A + P = 5P - 8 + P = (6P - 8) shells
Now (6P - 8) = 2(2P)
(6P - 8) = 4P
2P = 8
P = 4

So, initially Dan started with 5P = 5 * 4 = 20 shells

The correct answer is C.
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by bubbliiiiiiii » Mon May 21, 2012 11:44 pm
Hello Anurag Sir,

I am always confused with the term evenly in math problems. I have come across this term mostly while solving factor problems. The wording would be like a number has evenly divided factors ....

Could you please suggest on how to interpret the word evenly?

In this question, I interpreted that 40% of shells given by Dan were split up evenly between Paul and Andrew in the 1:2 whereas after seeing your explanation, I understood that evenly indicated that 40% was divided equally into two and then after adding the equally divided number of shells that Dan gave, the number of shells with A and P were in the ratio 2:1.
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by kullayappayenugula » Tue May 22, 2012 12:02 am
hi Bubliii,

The question says that the 40% of the shells were divided evenly,i.e. they are divided in 1:1 ratio only.

"giving Andrew twice as many as Paul" in the question says that after the shells were distributed evenly Andrew had twice as many as Paul.

Hope it helps.
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by bubbliiiiiiii » Tue May 22, 2012 12:06 am
Hi kullayappayenugula,

Ofcourse it does. :)

I neither question the question nor the explanation. My question is how to interpret the word evenly when it occurs.
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by bubbliiiiiiii » Tue May 22, 2012 12:14 am
Another question which uses the word evenly is:
https://www.beatthegmat.com/divisibility ... tml#474168
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by kullayappayenugula » Tue May 22, 2012 12:52 am
Hi Bublii,

whenver they say evenly => no remiander is left.

Divides evenly => divided without any reminder.
Ex:example the problem in the link you provide.


Distributed evenly => equally distributed without any items left.
Example: the present problem.

Also remember: The distribution is nothing but division.

This is how I approach when I encounter the word "Evenly".


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by GMATGuruNY » Tue May 22, 2012 2:48 am
phoenix9801 wrote:Dan has five times as many seashells as Paul, and eight more than Andrew. When Dan gives away 40% of his shells, Paul and Andrew agree to split those shells up evenly, giving Andrew twice as many as Paul. How many shells did Dan start with?

a) 10
b) 15
c) 20
d) 25
e) 30
To divide evenly means to give everyone the same number.

We can plug in the answers, which represent the number of shells that Dan starts with.

Answer choice C: 20
Since Dan has 5 times as many as Paul, Paul = 20/5 = 4.
Since Dan has 8 more than Andrew, Andrew = 20-8 = 12.
The number split evenly between Paul and Andrew = .4(20) = 8, implying that Paul and Andrew each receive 4 shells.
New Paul = 4+4 = 8.
New Andrew = 12+4 = 16.
Success! Andrew has twice as many as Paul.

The correct answer is C.
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