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GMAT Instructor
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a and b are two positive integers that are not divisible by [#permalink]
 06 Mar 2007, 01:31
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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) II only (C) III only (D) II and III only (E) I, II and III
Last edited by kevincan on 06 Mar 2007, 11:06, edited 1 time in total.
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Intern
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Re: PS: Remainder of Special Product [#permalink]
06 Mar 2007, 03:55
According to me the answer should be (B).
a*b = 10^n as the sum of the digits is 1.
=> a*b = (5^n) * (2^n)
=> |a-b| is odd but not divisible by 5.
=> the answer is (B).
is the answer and explanation correct?
~newbie here...
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Manager
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There are three numbers 1, 10, 100 can be product of a and b, and the sum of digits would be 1. Beyond 100 one of the numbers has to be divisible by 10.
1 = 1*1
10 = 2*5
100= 4*25
|1-1| = 0, remainder=0, when divided by 10
|2-5| = 3, remainder=3, when divided by 10
|4-25| = 21, remainder=1, when divided by 10
so the answer is (I) and (II). But do not see the choice with (I) and (II). Am I doing something wrong?
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Senior Manager
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I go with B.
rdg,
You can try 100 = 5* 20 and then rule out 1.
I solved this similar to how you did it.
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Director
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the product of a and b would be :
1 = 1*1 remainder is zero
10= 5*2 remainder is 3
100 = 25*4 remainder is 1
1000 = 125*8 remainder is 7
10000 = 625*16 remainder is 9
100000 = 3125*32 remainder is 3
and so on......
'A' seems to be the answer.
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Manager
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Thanks. I should have considered with more numbers.
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Senior Manager
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Kevincan question seems to be wrong then...as all three can be remainder.
And there is no option that says 'none'
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close
