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Integer Properties - DS

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by Brent@GMATPrepNow » Fri Jan 31, 2014 7:27 am
nadiva171987 wrote:Is the rule for adding the sum of the digits and the sum being able to be divided by a specific number evenly only apply to the number 9? Or could this be for all numbers? I'm assuming only 9 because in the case of 11 the sum of the digits is 2 but 11 is not divisible by 2 evenly.
The rule applies to divisibility by 3 and by 9.
Other numbers have different rules.
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by vijayngmat » Wed Sep 24, 2014 12:23 pm
Answer is B :)

A number to be divisible by 9, the sum of numbers should add to 9.
With J = 1 , we don't need to look at K , as 8*10^k , will always be 8. With J = 1 , we know
8*10^K + 1 , the sum will always be = 9.
Hence B alone helps to determine the answer.
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by jaspreetsra » Sat Sep 27, 2014 11:44 pm
will go with D
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by jaspreetsra » Sat Sep 27, 2014 11:46 pm
will go with D
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by SachetMittal » Mon Nov 17, 2014 6:13 am
B.
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by Mathsbuddy » Wed Nov 19, 2014 8:30 am
If j and k are positive integers, what is the remainder when (8 * 10^k) + j is divided by 9?
(1) k = 13
(2) j = 1

Statement 1 gives [80000000000000+j]/9; as j is undefined, INSUFFICIENT
Statement 2 gives [80000...+1]/9; As the sum of the digits of the dividend equal 9, then there is no remainder, SUFFICIENT
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by Vyking » Sun Dec 14, 2014 1:52 am
IMO B. Only the value of J matters.
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by akash singhal » Thu Apr 30, 2015 9:01 am
For this question of data sufficiency:-
firstly, 8 * (whatever to the power)10
= 800.....
if we add 1 to it (as j=1)
then the value becomes- 81,801,8001,80001 etc
and we know that the sum of such numbers whatsoever be is (8+1)9 thus it will
be divisible by 9 and remainder is zero.
we do not need the value of k.....
so answer is option 2 is alone sufficient no need of option 1
i Hope i am right.....
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by pethkarninad » Sat Jul 04, 2015 4:48 am
If j and k are positive integers, what is the remainder when (8 * 10^k) + j is divided by 9?
(1) k = 13
(2) j = 1


In case one forget divisibility by 9 rule & want to save the time;
(8 * 10^k) + j /9

statement 1 : k=13 . certainly it is insufficient as value of remainder will be dependent on "j"
statement 2 : j=1 . here we dont know value of k. so check if for j=1 and k=0,1,2 (test cases) whether we get same remainder or not.

case 1 : j=1 , k=0
--> [( 8 * 10 ^0) + 1 ]/9 = 9/9=0

case 2 : j=1 , k=1
--> [( 8 * 10 ^1) + 1 ]/9 = 81/9=0

Thus Answer=(B)
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by hitesh.arora2 » Mon Mar 20, 2017 11:05 pm
since reminder will depend upon j only ,stat2 is suff.
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by dexter » Sun Apr 30, 2017 12:41 am
B.
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by deepak4mba » Fri Feb 23, 2018 1:00 am
B
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by kaziselim » Wed Feb 28, 2018 1:06 am
If j and k and positive integers, what is the remainder then 8*10^k + j is divided by 9?

1. k = 13
2. j = 1

in this question , k and j are variables. to answer this kind of questions, we have to analyse the 8*10^k + j. Remember that 10^k always gives us extra zero , nothing else. thus regardless of the power of K, we will get 10,100,10000 etc. if we then multiply by 8 it yields 80, 800, 8000 etc. thus J is crucial as we know a number is divisible by 9 if its sum of digits divisible by 9.

1. k=13.
the power of k is inferior here as we don't know the value of j, crucial one for this question.
2. j=1
we have already determined that regardless of the power of K we will get 80,800,800000 etc. now add 1 to these numbers. it looks like 801, 8001, 80001, 8000001 etc. sum of the digits is 9. thus , statement 2 is enough. Answer is B.
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