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02 Feb 2024, 02:30
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C
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For a positive integer n, which of the following remainders cannot be obtained when dividing 12n by 15?
A. 0
B. 3
C. 5
D. 6
E. 9
A. 0
B. 3
C. 5
D. 6
E. 9
For a positive integer n, when 12n is divided by 15, which of the following cannot be the remainder?
02 Feb 2024, 03:57
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IMO answer is C
because we get remainders as 0,3,6,9 in multiples of 2,3,4 and 5
because we get remainders as 0,3,6,9 in multiples of 2,3,4 and 5
02 Feb 2024, 12:03
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Correct option should be C
We can try out values to rule out 5 as a remainder but there is a beautiful way to find out that 5 cannot be the remainder when 12n is divided by 15.
We can reduce \(\frac{12n}{15}\) to \(\frac{4n}{5}\) by dividing both numerator and denominator by 3. Now you divide any number by 5, you get 5 remainders which are 0,1,2,3,4.
But Note that these are not the remainders when 12n is divided by 15. We should not forget to multiply these numbers (i.e, 0,1,2,3,4) by 3 because we divided numerator and denominator both by 3. C'mon man you take something in maths you should give something back!!
So, the possible remainders are -> 0,3,6,9,12 (You can check it out with values I won't put my effort to spoil your effort)
Hence, 5 is not a possible remainder.
Hence, correct option should be C
We can try out values to rule out 5 as a remainder but there is a beautiful way to find out that 5 cannot be the remainder when 12n is divided by 15.
We can reduce \(\frac{12n}{15}\) to \(\frac{4n}{5}\) by dividing both numerator and denominator by 3. Now you divide any number by 5, you get 5 remainders which are 0,1,2,3,4.
But Note that these are not the remainders when 12n is divided by 15. We should not forget to multiply these numbers (i.e, 0,1,2,3,4) by 3 because we divided numerator and denominator both by 3. C'mon man you take something in maths you should give something back!!
So, the possible remainders are -> 0,3,6,9,12 (You can check it out with values I won't put my effort to spoil your effort)
Hence, 5 is not a possible remainder.
Hence, correct option should be C
