The positive integer N is not divisible by 2 or 4. What is the sum of

Question

The positive integer N is not divisible by 2 or 4. What is the sum of the possible remainders when N is divided by 8?

(A) 9
(B) 11
(C) 13
(D) 15
(E) 16

D3N0 · Accepted Answer

Ans : E
as number is not divided by 2 and 4 means number can not be even. lets take odd numbers 1,3,5,7,9,11,13
these numbers when divided by 8 leaves reminders= 1,3,5,7,1,3,5,7,1,3..... in cyclic order of 1,3,5,7 so possible reminders gives us sum =16 ans.

doomedcat · Answer

in short question ask is remainder of odd number divided by 8 
rem is cyclic with 3,5,7,1 so sum = 16

gatz · Answer

The general formula for the remainders is \frac{Dividend}{Divisor} =Quotient+ \frac{Remainder}{Divisor}

From the question we have  \frac{N}{8} =Q+ \frac{R}{8}

Nevertheless, we have a condition stating that N is not divided by 2 or 4. In other words, N CAN NOT be a multiple of 2 or 4. 
Please keep in mind that this condition restricts our number of possible remainders when  \frac{N}{8}

The remainders are always smaller than the divisors and in this case ( \frac{N}{8} ) the possible remainders are 7,6,5,4,3,2 and 1.
However, according to the condition 6,4, and 2 do not qualify as a possible remainders when  \frac{N}{8} . Why? Because of the following:

\frac{N}{8} =Q+ \frac{6}{8} 
N=8Q+6 - this means that N will always be a multiple of 2 or 4

\frac{N}{8} =Q+ \frac{4}{8} 
N=8Q+4 - this means that N will always be a multiple of 2 or 4

\frac{N}{8} =Q+ \frac{2}{8} 
N=8Q+2 - this means that N will always be a multiple of 2 or 4

After we disregard 2,4, and 6 we are left with 1,3,5 and 7 as possible remainders. 
For each and every remaining possible remainders (1,3,5, and 7) N will never be a multiple of 2 or 4. Why? We apply the same logic as above:

N=8Q+1 - this means that N will never be a multiple of 2 or 4 
N=8Q+3 - this means that N will never be a multiple of 2 or 4
N=8Q+5 - this means that N will never be a multiple of 2 or 4
N=8Q+7 - this means that N will never be a multiple of 2 or 4

According to the condition, we are left with 1,3,5 and 7 as possible remainders. 
The sum of 1+3+5+7=16

Hence, the right answer is (E) 16

Ksmew · Answer

Simple answer:
remainders are less than 8 (as we are dividing by 8)

N is not multiple of 2 (2, 4, 6 out)
N is not multiple of 4 (4 out)

there4, sum of remainders = 1+3+5+7 = 16

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The positive integer N is not divisible by 2 or 4. What is the sum of

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The positive integer N is not divisible by 2 or 4. What is the sum of

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