E IMO.

10^(m or n) will have sum of the digits as 1.

Possible remainders when divided by 3, are 0,1 and 2.

Statement 1:

m > n, notice when m=5 and n=2, both expressions are divisible by 3. We can increase m=6, remainder becomes 1. So different possibilities - Insufficient.

Statement 2:

n=6, we dont know 'm' here, cannot be determined.

Even combining, we can have different remainders for the expression. (say n=6 and m=9 will have same remainder, whereas m can take value of 10 when remainder changes)

E IMO

shankar.ashwin wrote:E IMO.

10^(m or n) will have sum of the digits as 1.

Possible remainders when divided by 3, are 0,1 and 2.

Statement 1:

m > n, notice when m=5 and n=2, both expressions are divisible by 3. We can increase m=6, remainder becomes 1. So different possibilities - Insufficient.

Statement 2:

n=6, we dont know 'm' here, cannot be determined.

Even combining, we can have different remainders for the expression. (say n=6 and m=9 will have same remainder, whereas m can take value of 10 when remainder changes)

E IMO

i also agree with u but I donno why I wrote on my note that the answer is B.. but there is a point u missed for stat 2
when n=6, whatever m is the remainder will be 1
but for 10^6 +m we ca not say bcuz the important figure here (for divisibility by 3) is the number added to 10^whatever

the question asks if remainder (n+1)/3 > remainder (m+1)/3?
note: the tens will be divided by 3 with the remainder of 1 added to either n or m.
st(1) m>n, if we divide both sides by 3 and add 1/3 (consider given m,n=positive integers) the sign won't change, hence m/3 +1/3 > n/3 +1/3. We can answer No to the original question, Sufficient.
st(2) n/3=2 translates into n=6, but we don't know anything about m. Not Sufficient.

a

after solving this q. I have noticed the poster to come up with agreement about ans. E, what's the source and is E OA?

mehrasa wrote:if m and n are positive integers. is remainder of [10^m)+n]/3 larger than remainder [(10^n)+m]/3?
1)m>n
2) n/3=2

plz provide ur explanation
thnx

pemdas wrote:the question asks if remainder (n+1)/3 > remainder (m+1)/3?
note: the tens will be divided by 3 with the remainder of 1 added to either n or m.
st(1) m>n, if we divide both sides by 3 and add 1/3 (consider given m,n=positive integers) the sign won't change, hence m/3 +1/3 > n/3 +1/3. We can answer No to the original question, Sufficient.
st(2) n/3=2 translates into n=6, but we don't know anything about m. Not Sufficient.

a

after solving this q. I have noticed the poster to come up with agreement about ans. E, what's the source and is E OA?

mehrasa wrote:if m and n are positive integers. is remainder of [10^m)+n]/3 larger than remainder [(10^n)+m]/3?
1)m>n
2) n/3=2

plz provide ur explanation
thnx

hey pemdas
if u read the Q stem again, it is (10^m)+n/3 and (10^n)+m/3 NOT simply (n+1)+3

thnx

mehrasa wrote:if m and n are positive integers. is remainder of [10^m)+n]/3 larger than remainder [(10^n)+m]/3?
1)m>n
2) n/3=2

plz provide ur explanation
thnx

+1 for E

stmnt 1 is insuff, because m could be 3 , n=2 then the remainder of [(10^n)+m]/3 is 0, and the remainder of [10^m)+n]/3 is 2. so [10^m)+n]/3 is larger than [(10^n)+m]/3. but if m=2 , n=1
the situation will change.

stmnt 2 says that n= 6. since we have no info about m, this stmnt is insuff

both stmnt- assume that n=6 (from stmnt 2) and m=7(from stmnt 1 that m must be greater than n), then the remainder of [(10^n)+m]/3 is greater than that of [10^m)+n]/3 .but lets suppose that n=6 and m =9, then the remainders are equal

so ,the answ is E

@mehrasa, i've read the question before posting reply - no worries
i hope you don't revise the question's text from original

is remainder of [10^m)+n]/3 larger than remainder [(10^n)+m]/3

to just entered

(10^m)+n/3 and (10^n)+m/3

now the click here is that when i say (n+1)/3 i mean (n+1)/3 which has the same remainder as [(10^m)+n]/3. Please check m=1, positive integer -> (10^1+n)/3 should be equivalent to 3 1/3 +n/3, hence we have remainder 1 (besides the whole part 3) and number n divided by 3.

You can try the fate with m=2,3,4,100,etc. it's all the same matter -> (n+1)/3

Having said about n, i also mean (m+1)/3 for m BUT not

simply (n+1)+3

i hope we are learning from our posts and not burlesquing each other

do me favor, plz reread my post

mehrasa wrote:

pemdas wrote:the question asks if remainder (n+1)/3 > remainder (m+1)/3?
note: the tens will be divided by 3 with the remainder of 1 added to either n or m.
st(1) m>n, if we divide both sides by 3 and add 1/3 (consider given m,n=positive integers) the sign won't change, hence m/3 +1/3 > n/3 +1/3. We can answer No to the original question, Sufficient.
st(2) n/3=2 translates into n=6, but we don't know anything about m. Not Sufficient.

a

after solving this q. I have noticed the poster to come up with agreement about ans. E, what's the source and is E OA?

mehrasa wrote:if m and n are positive integers. is remainder of [10^m)+n]/3 larger than remainder [(10^n)+m]/3?
1)m>n
2) n/3=2

plz provide ur explanation
thnx

hey pemdas
if u read the Q stem again, it is (10^m)+n/3 and (10^n)+m/3 NOT simply (n+1)+3

thnx

thnx pemdas for ur comprehensive answer.. I did not revise my Q stem... if I initially put all in Bracket, becuz I did not want the Q to create ambiguity and it shows that all expression is divided by 3 not for example just n
actually i am not sure about OA... i had written this in my note... let's see what is other people's opinion and maybe we receive an expert opinion on this..

all the best

Let me change my answer from A to E finally with the full proof for myself using my own solution in the prior post, i had to test the numbers too, the approach seems sustainable

st(1) m>n, if we divide both sides by 3 and add 1/3 (consider given m,n=positive integers) the sign won't change, hence m/3 +1/3 > n/3 +1/3. We can answer No to the original question, Sufficient.

we input m=4,5,6 (i don't start from 1 as it says m>n and n cannot be 0 for the all numbers are positive integers) as the remainder cycles for the divisor of 3 to test the distance between numbers here and correspondingly assess the remainder:
m=4, n=3 -> 4/3 + 1/3 > 3/3 +1/3 true, the remainder on LHS is 2 and on the RHS is 1
m=5, n=4 -> 5/3 +1/3 >! (should be < ) 4/3 +1/3 true, the remainder on LHS is 0 and on the RHS is 2
m=6,n=5 -> 6/3+1/3 > 5/3 + 1/3 true, the remainder on LHS is 1 and on the RHS is 0

we have Yes/No situation and this will make statement (1) alone Not Sufficient

statement(2) suggests n=6 alone is Not Sufficient

combined statements(1&2) we have n=6 and m>n
(n+1)/3 will always return the remainder of 1 -> (6+1)/3= 2 + 1/3
while m>6 may also return the remainder of 0,1 and 2 Not Sufficient

Now, I'm sure it's E