A number when divided by 5 leaves a remainder 3 , what would be the remainder when the number to the power 100 is divided by 5 ? (a) 5 (b)4 (c)3 (d)2 (e)1

IMO Answer is [spoiler](C)[/spoiler] Explanation : 8 to the power 2 - remainder 4 8 to the power 3 - remainder 2 8 to the power 4 - remainder 1 8 to the power 5 - remainder 3 8 to the power 6 - remainder 4 so after every 4 power the cycle again start 8 to the power 100 meand 25 full cycle of 4 and hence the remainder will be 3

3^100/5 - Remainder -? 3*1= 3 (remainder - 3) 3*3 = 9 (remainder - 4) 3*3*3 = 27 (remainder - 2) 27*3 = 81 (remainder - 1) The pattern repeated every 4 cycles. So 3^100 would end in '1'. Remainder would be '1'. E IMO Marysogh wrote:A number when divided by 5 leaves a remainder 3 , what would be the remainder when the number to the power 100 is divided by 5 ? (a) 5 (b)4 (c)3 (d)2 (e)1

Marysogh wrote:A number when divided by 5 leaves a remainder 3 , what would be the remainder when the number to the power 100 is divided by 5 ? When 3 is divided by 5 the remainder is 3. Hence, we need to find out the remainder when 3^100 is divided by 5. 3^100 = (3^4)^25 = 81^25 = Some large number with units digit 1 Hence, when 81^4 will be divided by 5, the remainder will be either 1 or 6. The correct answer is E.

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