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10aK + P is divisible by 81. If K,P, a and b are positive integers, is

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10aK + P is divisible by 81. If K,P, a and b are positive integers, is  [#permalink]

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New post 10 Oct 2018, 11:43
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\(10^aK + P\) is divisible by 81. If K,P, a and b are positive integers, is \(10^bK + P\)divisible by 15?

(1) P is the lowest prime which can be expressed in the form of 6n-1, where n is a positive integer.
(2) K is one less than P
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Re: 10aK + P is divisible by 81. If K,P, a and b are positive integers, is  [#permalink]

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New post 10 Oct 2018, 18:40
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\(10^aK + P\) is divisible by 81. If K,P, a and b are positive integers, is \(10^bK + P\)divisible by 15?
Since a is a positive integer it means the sum of K and P is divisible by 3 and 9
Now \(10^bK + P\) too will be divisible by 3 and if P is divisible by 5, it will be divisible by 15

(1) P is the lowest prime which can be expressed in the form of 6n-1, where n is a positive integer.
When n=1, 6n-1=6*1-1=5, so P is 5..
Ans is Yes
Sufficient

(2) K is one less than P
There can be various combinations fitting in..
\(10^aK + P=10^ak+k+1\) let k=22 and a=b=1, 220+23=243 div by 81 but not by 15
\(10^aK + P=10^ak+k+1\) let k=4 and a=b=2, 400+5=405, div by both 81 and 15
Insufficient

A
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


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Re: 10aK + P is divisible by 81. If K,P, a and b are positive integers, is   [#permalink] 10 Oct 2018, 18:40
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10aK + P is divisible by 81. If K,P, a and b are positive integers, is

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