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divisibility and remainders -- HELP!

Expert replies
by kn2130 » Tue Mar 09, 2010 10:11 am
I keep running into this type of problem and am unsure about the best approach to solve these questions (all the explanations I find are different, and its getting confusing)

If m and n are positive integers such that m/n = 13.24, which of the floowing could be be the remainder when m is divided by n? a) 12 b)16 c)30 d)48 e)120 answer:B

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 answer:B

Is s and t are positive intergres such that s/t = 64.12, which of the following could be the remainder when s is divided by t? a) 2 b)4 c)8 d)20 e) 45 answer:e

If a and b are positive integers such that a/b = 2.86, which of the following must be a divisor of a?

a)10 b) 13 c) 18 d) 26 e) 50 answer: 13


Thanks so much!
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Source: — Problem Solving |

by papgust » Tue Mar 09, 2010 10:00 pm
Use spoilers when you post the answers.

The concept is pretty simple. All four problems revolve around a single formula,
Dividend = Divisor*quotient + remainder
OR
Dividend/Divisor = quotient + remainder/divisor
Coming to the problems,

The first question should read as,
If m and n are positive integers such that m/n = 13.24, which of the floowing could NOT be the remainder when m is divided by n? a) 12 b)16 c)30 d)48 e)120
m/n = 13.24

0.24 represents the remainder here. Transform this into a fraction and simplify.

m/n = 13 + 24/100

m/n = 13 + 6/25

Here, 6/25 is of the form remainder/divisor.

r/d = 6/25

25*r = 6*d

r must be a multiple of 6 so that remainder evenly divides 6*d. All options except B are multiples of 6. So, its B


Other problems are already discussed in this forum. Also, all these problems are exactly the same as the 1st problem.
https://www.beatthegmat.com/remainder-pr ... 20246.html
https://www.beatthegmat.com/difficult-t15709.html#65825
https://www.beatthegmat.com/divisor-of-a-t37310.html
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by kn2130 » Wed Mar 10, 2010 9:07 am
Thank you so much! This was SO helpful! By the way, how do I use spoilers?
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by papgust » Wed Mar 10, 2010 11:51 pm
Check this!
You do not have the required permissions to view the files attached to this post.
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