Latest Elitmus Aptitude Question SOLUTION: 999^x-999^y when divided by 1000 will give some remainder.How many such remainders will be possible? options: a) 3 b) 8 c) 99 d) more than 99

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(#M40030042) ELITMUS question elitmus quant asked in 10th nov,2013 Keep an EYE

999^x-999^y when divided by 1000 will give some remainder.How many such remainders will be possible?
options:
a) 3
b) 8
c) 99
d) more than 99

Asked In Elitmus Amardip Gautam (10 years ago)

Unsolved Read Solution (5)

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kharak  (10 years ago)

we can write the equation like this
[(999^x)/1000]-[(999^y)/1000]
which is a form of [(a^x)/(a+1)]-[(a^y)/(a+1)]
and we know [(a^n)/(a+1)] gives remainder "1" whn n is even and gives remainder "a" when n is odd.by taking even odd combination of x and y only 2 remainder are possible .so ans is 3(as question was including zero).

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Anurag Verma  (10 years ago)

A)3
999^x/1000=(-1)^x
Similarly 999^y=(-1)^y
hence we get [(-1)^x]+[(-1)^y] which can result in 3 combinations-0,2,-2

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Jeevana  (10 years ago)

0,7 and 8 are possible solutions.
so answer is 3.

Is this solution Helpfull? Yes (1) | No (1)  

Ankit Goyal  (10 years ago)

999^x - 999^y = (1000-1)^x - (1000-1)^y
Depending on the value of X and Y being even or odd we will get

x = even & y = even remainder = 0
x = odd & y = even remainder = -2
x = even & y = odd remainder = 2
x = odd & y = odd remainder = 0

so there can be total 3 possible remainders

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Amardip Gautam  (10 years ago)

given x>y>0

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