For a positive integer n, which of the following remainders cannot be

Question

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

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For a positive integer n, when 12n is divided by 15, which of the following cannot be the remainder?

sood1596 · Answer

IMO answer is C

because we get remainders as 0,3,6,9 in multiples of 2,3,4 and 5

Shubhradeep · Answer

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

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

PranavVyas · Answer

Number 15 divisible by 5 , others not have such possible remainder.

IMO-C "5"

VivekSri · Answer

For a positive integer n, which of the following remainders cannot be

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GMAT Problem Solving (PS) Questions

For a positive integer n, which of the following remainders cannot be

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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745 with Only Self-Prep and GMAT Club

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Perfect 805 Score Debrief by Julia

My Rewards