what is the remainder when 123456...95969798100 is devided by 32??

Question

what is the remainder when 123456...95969798100 is devided by 32??

option:
a) 0
b) 16
c) 8
d) None of these.

Answer 1

i think the solution is based on two elemantary reaction.

FIRST: in the given expression, the numerator is a multiple of 4 but not of 8. hence after cutting both the numerator and the denominator by 4, the above expression can be reduced to (308......25/8)

SECOND:(308......25/8) will give us an odd remainder to the entire question will be an odd multiple of 4. none of first three option is an odd multiple of 4 since 0,16 and 8 are all even multiples of 4,
Hence the answer is 'D'.

Answer 2

D
I think . Either some of yout numbers got cut off... or I don't know what happened.
the answer is none of these....because i guess maths has had an adverse effect on ur mind....please dont stress much...u need some rest.
i think the solution is based on two elemantary reaction.
FIRST: in the given expression, the numerator is a multiple of 4 but not of 8. hence after cutting both the numerator and the denominator by 4, the above expression can be reduced to (308......25/8)
SECOND:(308......25/8) will give us an odd remainder to the entire question will be an odd multiple of 4. none of first three option is an odd multiple of 4 since 0,16 and 8 are all even multiples of 4,
Hence the answer is 'D'.

Answer 3

The remainder of the division by 2^n of any integer number expressed on basis 10 is the same as the remainder of the division by 2^n of the number formed by its n last digits. Since 32 = 2^5, the desired remainder is the remainder of the division of 98100 by 32.

98100 = 32 * 3065 + 20, so the remainder is 20 (d)

EDIT:

I wonder why someone gave me thumbs down.

Answer 4

we know thatb10^5 is divisible by 32 so we need to take last five digits 98100 and devide by 32 to get remainer
20.

But I feel that the number you meant was ,.,, 9596979899100( why the missing 99)
so raminder = 16.

Answer 5

123456...95969798100 / 32
= (123456...95969700000 +98100) / 32
= (123456...959697*100000 +98100) / 32
= 123456...959697*(100000/32) + (98100/ 32)
= 123456...959697*3125 + (98100/ 32)

So the remainder is dependant on the last 5 digits.

98100/32 = 3065 + 20/32
So 20 is the remainder.

Ans: D (None of these)

~~~
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Answer 6

it is 0

Answer 7

Google calc gives 3.85802466 × 10^188

That's all very well, but it doesn't give the remainder!!

Answer 8

the answer is none of these....because i guess maths has had an adverse effect on ur mind....please dont stress much...u need some rest

Answer 9

D...

I think...
Either some of yout numbers got cut off... or I don't know what happened...

Answer 10

none of these