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number problem

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Junior | Next Rank: 30 Posts
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by asigheartau » Sun Jun 29, 2008 8:57 pm
When two numbers 34041 and 32506 are divided by the 3 digit number N the reminder is the same. What is this 3 digit number?
A) 297
B) 307
C) 367
D) 407
E) 453
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Junior | Next Rank: 30 Posts
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by asigheartau » Sun Jun 29, 2008 9:12 pm
I`m having problems assigning notation for this problem.
say -x- is the three digit number
R is remainder
a=result for the first division
b=result for the second

34041/x=a+ R =>34041=x(a+R)

32506/x=b+R so 32506=x(b+R)

1535=xa+xR-xb-xR
1535=x(a-b)

I was a little confused here, expecting for something more specific. In conclusion, I checked the possible answers to see whichever of the numbers could be divided evenly by 1535.

It took melonger than 2 minutes, however.
Please let me know if you find out an easier way.
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Master | Next Rank: 500 Posts
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by gmataug08 » Sun Jun 29, 2008 10:05 pm
answer : B

Got the difference between the two numbers .

34041 - 32506 = 1535

checked which of the answer choices multiplied by 5 gives 1535 (as the unit digits are 7 & 3 )

last 2 choices are out of question as the leading digit is 4 and will result in 20+ result when multiplied by 5.

multiplied the rest 3 choices to get the possible answer.
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