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Tom collects sports memorabilia from both college and professional tea

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Tom collects sports memorabilia from both college and professional tea  [#permalink]

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New post 17 Oct 2019, 02:30
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Question Stats:

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Tom collects sports memorabilia from both college and professional teams. He currently has 40 Items from college teams and 25 items from professional teams. Without changing the number of his professional team items, what would the least number of college Items in his collection need to be so that the ratio of college items to professional items would be at least 9:2?
A) 73
B) 88
C)103
D)113
E)145

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Re: Tom collects sports memorabilia from both college and professional tea  [#permalink]

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New post 17 Oct 2019, 21:19
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Abhi077 wrote:
Tom collects sports memorabilia from both college and professional teams. He currently has 40 Items from college teams and 25 items from professional teams. Without changing the number of his professional team items, what would the least number of college Items in his collection need to be so that the ratio of college items to professional items would be at least 9:2?
A) 73
B) 88
C)103
D)113
E)145



We are just concerned with initial number of college teams, that is 25, and let the number of professional team be p..
\(9:2=p:25.....2p=25*9=225....p=\frac{225}{2}=112.5\)

Thus, the least teams have to be 113 as the team cannot be 0.5, and it has to be converted to higher integer 1..

D
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Tom collects sports memorabilia from both college and professional tea  [#permalink]

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New post 18 Oct 2019, 06:59
The simplest method will be to go by options. 9/2 is 4.5, and the question mentions it should be at least 4.5 Options A and B can be eliminated as they yield 3.something.

C= 4.1
D=4.5 (roughly)
since option E has a value greater than D, choose D
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Re: Tom collects sports memorabilia from both college and professional tea  [#permalink]

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New post 20 Oct 2019, 13:09
Ratio of sports memorabilia from college and professional team= 40:25

WE want to change the ratio of \(\frac{40}{25}\) to \(\frac{9}{2}\) without changing the denominator of \(\frac{40}{25}\)

Simple way to do that is \(\frac{12.5 * 9}{12.5 * 2}\)
The denominator remains 25 while the numerator is 112.5

So Tom needs 113 trophies

Ans (D)
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Re: Tom collects sports memorabilia from both college and professional tea   [#permalink] 20 Oct 2019, 13:09
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Tom collects sports memorabilia from both college and professional tea

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