a and b are two positive integers that are not divisible by : PS Archive
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# a and b are two positive integers that are not divisible by

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a and b are two positive integers that are not divisible by [#permalink]

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24 Sep 2006, 14:03
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a and b are two positive integers that are not divisible by 10, and the sum of the digits of the product of a and b is 1. Which of the following cannot be the remainder when |a-b| is divided by 10?

(I) 5
(II) 9
(III) 0

(A) I only (B) I and III only (C) III only (D) II and III only (E) I, II and III
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24 Sep 2006, 20:22
Sum of the digits of the product of a and b is 1 so a*b=10^n ( n is integer)
In addition, a and b are two positive integers that are not divisible by 10
=> a=2^n and b=5^n
The remainder when 5^n diveded by 10 is always 5
The remainder when 2^n divided by 10 could be 2;4;6;8
So the remainder when |a-b| is divided by 10 could be 3;1;9;7
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