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Divisibility

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by selango » Wed May 26, 2010 12:49 am
When positive integer x is divided by positive integer y,the remainder is 9. If x/y=96.12,what is the value of y?

A)96

B)75

C)48

D)25

E)12

OA B
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by liferocks » Wed May 26, 2010 12:52 am
x=ky+9 so x/y=k+9/y=96.12 =96 3/25= 96 9/75 =96+9/75

hence [spoiler]y=75..ans option B[/spoiler]
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by frank1 » Wed May 26, 2010 2:48 am
B
My working
extra is 0.12 here
which is equal to 9
so 9/0.12=75 (make it 900/12=300/4=75....)
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by gmatjedi » Wed May 26, 2010 3:50 am
key to solving:

x/y=quotient + remainder/y

focus on decimal =12/100

in this case 9/y=12/100 and my must be an integer

solve for y=75
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by selango » Wed May 26, 2010 4:26 am
A bit elaborate approach for understanding(same as liferocks)


x=ky+9

-->x/y=k+9/y

96.12=k+9/y

92+0.12=k+9/y


-->9/y=0.12

y=75
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by vikramveer » Wed May 26, 2010 5:34 am
in this question let .12t = 9

or t = 9/.12 which equals to 75..

Hence B
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by Patrick_GMATFix » Wed May 26, 2010 12:46 pm
vikramveer, your solution seems very fast! would you try to explain the logic behind it? What does t represent? Why do you set .12t=9?


This is OG12 #106. Two Solutions and a Take-Away lesson are attached. Answer is B
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by vikramveer » Wed May 26, 2010 7:08 pm
Actually .12 represents 9 here since that is the remainder... so any arbitrary t,z,e taken for understanding 9/.12 without any t would also help.... of course the steps mentioned above are also helpful...
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by Patrick_GMATFix » Thu May 27, 2010 4:52 am
Thank you. I get it :-)
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