morya003 wrote:
If S is the infinite sequence: S1=9, S2=99, S3=999, ..., SK = 10^K-1, ..., is every term in S divisible by the prime number p?
(1) p is greater than 2.
(2) At least one term in sequence S is divisible by p.
I think with statement 2 - if P is 3 then all the terms in the sequence are divisible by P
So my answer is B
Please advise.
Question is tricky and seems very tough in the first instance. Though I understood that every term is not divisible by p, but I marked C option due to my understanding that every term is not divisible by p (I did a mistake here... Every term is divisible by 3 and not by 11 as correctly suggested by @bunuel). So, the reading and understanding the language of the question in such problems is very important.
So, finally the solution goes like this.
Given : infinite sequence: S1=9, S2=99, S3=999, ..., SK = 10^K-1
DS: is S1, S2, S3, ......, SK divisible by the prime number p.
Statement 1 : P>2. So, p can be 3,5,7,11,.....
We can clearly see that every term is divisible by 3 but not by 5,7,11.....
NOT SUFFICIENTStatement 2 : At least one term in sequence S is divisible by p. So, we can see that 9 is divisble by 3 and 99 is divisible by 11.
Here again every term is divisible by 3
But every term is not divisible by 11.
NOT SUFFICIENTCombined : p>2 and At least one term in sequence S is divisible by p. So, p can be 3 or 11 or...
Its clear that every term is divisible by 3, but every term is not divisible by 11.
NOT SUFFICIENTAnswer E _________________
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