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

This is a  PS Butler Question

Check the links to other Butler Projects:

Data Sufficiency Butler  
  Critical Reasoning Butler

kb26 · Answer

Finding out the cyclicity of remainder when dividing 12n by 15 by putting n = 1,2,3,4...

n value remainder
12 x1 --> 12
12 x2 --> 9
12 x3 --> 6
12 x4 --> 3
12 x5 --> 0
12 x6 --> 12

So, 5 can never be the remainder. Ans is C.

dhart · Answer

12,9,6,3,0 are possible remainders for mulitples diff multiples of 12 except 5

MakB · Answer

Start by putting values for n=1,2,3,4...

When N=1
12x1/15 --- Rem= 12

N=2
12x2/15---Rem=9

N=3--- Rem=6
N=4--- Rem=3
N=5--- Rem=0
N=6--- Rem=12

So, we can see the remainders for this equation repeat in the pattern of 12,9,6,3,0
Hence, any number apart from this pattern is NOT a reminder

Therefore answer is 5, ie, C.

zaturn · Answer

12n = 15a+remainder
remainder = 12n-15a
remainder = 3(4n-5a)

Remainder must be the multiple of 3. The only choice that is not is 5.

Answer: C

Prep Toolkit