N is the 36th prime number. N has remainder 1 when it is divided by 3

Question

N is the 36th prime number. N has remainder 1 when it is divided by 3 and it has remainder 1 when it is divided by 5. What is the remainder when N is divided by 2?

A. -1 
B. 0 
C. 1 
D. 2 
E. 3

LevanKhukhunashvili · Accepted Answer

The only even prime number is 2, all other primes are odd, so odd/2 always leaves remainder 1
Note that prime number cant be -ve, kill answer 'A'

Answer: C

pushpitkc · Answer

N%3 = 1 and N%5 = 1
N will be of form 3*5*x + 1 or 15x + 1. 
Various possibilities are 16,31,46,61,76,91,106,121,136,151..

Possibilities of prime numbers are 31,61,151 and any such prime number 
when divided by 2 gives a remainder of  1(Option C)

Tuanguyen248 · Answer

N is prime number. N>2 so probably N=2k+1.

C is the only choice.

chetan2u · Answer

Two things..
1) A prime number>2 will always be ODD, so whatever be its number 36th or 136th, N will always leave 1 as remainder when div by 2..
So C
2) there are no negative remainder so when you say -1, it means 2-1=1
May be choice A should not have been there..

Hero8888 · Answer

Method 1

POE:

1. Reminder can not be greater than divisor (in our case it is 2), so D and E are out.
2. Any prime (except 2) is odd, so B is out
3. There is no negative reminder, so A is out

Method 2

Any prime number can be written as 6n+1 or 6n-1, after dividing it to 2, we get reminder 1.

Answer is C.

MathRevolution · Answer

=>

All prime numbers but 2 are odd integers.
Thus, the remainder when N is divided by 2 is 1.

Therefore, the answer is C.
Answer: C

JeffTargetTestPrep · Answer

Since the 36th prime number must be odd, when divided by 2, the remainder is 1.

Answer: C

ihasan · Answer

This part is given to tell you that it is not the prime number 2 they are talking about - 'N is the 36th prime number'.

This part is given just to confuse you - 'N has remainder 1 when it is divided by 3 and it has remainder 1 when it is divided by 5'.

Every prime number except 2 is odd. Hence any odd number divided by 2 will always give 1 as remainder.

Fisayofalana · Answer

N=3Q+1 also N=5Z+1

Set equal to each other. 3Q=5Z.

Find a number that is equivalent to both. (15).

15/2 leaves a remainder of 1.

N is the 36th prime number. N has remainder 1 when it is divided by 3

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N is the 36th prime number. N has remainder 1 when it is divided by 3

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