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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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10 Oct 2018, 11:43
3
00:00

Difficulty:

85% (hard)

Question Stats:

48% (01:48) correct 52% (02:50) wrong based on 27 sessions

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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
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: 10aK + P is divisible by 81. If K,P, a and b are positive integers, is  [#permalink]

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10 Oct 2018, 18:40
1
$$10^aK + P$$ 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
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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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