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Integer Properties - DS
B looks correct to me .
for j = 1 given in 2.
the equation can 81, 801, 8001, 80001.... so on. what ever be the value of 'k' the expression is divisible by 9(sum of the digits always remain 9)
with only k = 13 we cannot be sure.
for j = 1 given in 2.
the equation can 81, 801, 8001, 80001.... so on. what ever be the value of 'k' the expression is divisible by 9(sum of the digits always remain 9)
with only k = 13 we cannot be sure.
Good question. I misread the question as 8*10^(k+j). Were I immediately concluded the answer would be D.
So, lesson learned: Avoid careless errors by reading stem carefully.
Here's the break down
A - Insufficient becuase can't determine the value 8*10^13 + j given that j is unkown.
B - Sufficient becasue we know that 8*10^k +1 will alway yield a number that is divisble by 9,
C - N/A given that be is true
D - N/A given that be is true
E - N/A given that be is true
Answer is B
So, lesson learned: Avoid careless errors by reading stem carefully.
Here's the break down
A - Insufficient becuase can't determine the value 8*10^13 + j given that j is unkown.
B - Sufficient becasue we know that 8*10^k +1 will alway yield a number that is divisble by 9,
C - N/A given that be is true
D - N/A given that be is true
E - N/A given that be is true
Answer is B
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jainnikhil02
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IMO B
Nikhil K Jain
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if sum of digits of a number is divisible by 9, then that no. is divisible by 9.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
8*10^k + j has sum of digits = 8+j
a)k=13; the remainder depends on j
insufficient
b)j=1
sum=9, thus no. divisible by 9.
remainder=0
Sufficient
IMO B
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Brent@GMATPrepNow
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Your question about difficulty level is difficult to answercmmancin wrote:What level question would you say this is?
It pretty much comes down to whether or not one realizes that, with statement 2, the number will be of the form 8000....01 and that the sum of the digits will be 9
That said, I'd say the question is of above-average difficulty (650+)
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lawri wrote:Good question. I misread the question as 8*10^(k+j). Were I immediately concluded the answer would be D.
So, lesson learned: Avoid careless errors by reading stem carefully.
Here's the break down
A - Insufficient becuase can't determine the value 8*10^13 + j given that j is unkown.
B - Sufficient becasue we know that 8*10^k +1 will alway yield a number that is divisble by 9,
C - N/A given that be is true
D - N/A given that be is true
E - N/A given that be is true
Answer is B
Similar thing with me but not the same
I took (8.10^k+j)/9
Substituted values
1) k=13..
If k=1 ,80/9 = 8
If k=2, 800/9 = 8
So k=13, (8.10^13)/9=8
But forgot about j....So concluded A will satisfy
2) (8.10^k+1)/9
If k=1 ,81/9 = 0
If k=2, 801/9 = 0
So k=13, (8.10^13+1)/9=0
So B will satisfy
Therefore chose D....
But correct ans. is B
Takeaway for me : when solving fastly, watch out not to miss any variable carelessly.
Takeaway for others : when solving problems like these, it is much more easy to pick smart numbers because you cannot depend upon standard formulaes at all places in GMAT.
I solved this in less than 60 secs.
a 8*10^13+ j where j can have any value. for j=0 remainder = 0, for j=1 remainder = 1.
not sufficient.
b remainder = 0 as 8+1 = 9/9 = 1 remainder =0 always.
B it is.
not sufficient.
b remainder = 0 as 8+1 = 9/9 = 1 remainder =0 always.
B it is.
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The question, I think, may be in the low 600 range question. Just need a little knowledge in number theory. Statement 1 is not sufficient because J is still unknown. Statement 2 allows us to come to a conclusion that the numerator will be a multiple of 9. K is positive integer, thus K must be greater than 0. 0 is an integer, but not positive nor negative. When J is 1, the numerator will be 1 greater than 8x10^k. The division rule of 9 is when the sum of all numbers in a given integer is multiple of 9, the integer is a multiple of 9, or 9 is a factor/divisor of the given integer. For example, if K=1, then the numerator will be 81. If K=2, numerator will be 801. There will be k-1 number of zeros in-between 8 and 1. Add the sum of all numbers in the numerator: 8+1=9, so no remainder. Question can be answered with statement 2. Pick B.
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akhilsuhag
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Here:
(8*10^k+j)/9 = (8*10^k)/9 + j/9
Now (8*10^k)/9 will always give a remainder of 0.8 for any value of k. So if we are supplied a value of k then it is insufficient. We would need the value of j to find the answer
Therefore, statement A is INSUFFICIENT.
and statement B is SUFFICIENT.
Please tell me if this way is correct or not..
Thanks
(8*10^k+j)/9 = (8*10^k)/9 + j/9
Now (8*10^k)/9 will always give a remainder of 0.8 for any value of k. So if we are supplied a value of k then it is insufficient. We would need the value of j to find the answer
Therefore, statement A is INSUFFICIENT.
and statement B is SUFFICIENT.
Please tell me if this way is correct or not..
Thanks
