Hi, I searched this question through the Beat the GMAT archives and found 2 posts on it. However (before anyone deletes this), I want to note that each of the posts gave a different response/explanation for the right answer (one arrived at A, while the other arrived at B). Can someone take a look at this and explain it again? By the way, OA is B. Thanks so much!
If n and m are positive integers, what is the remainder, when 3^(4n+2) + m is divided by 10?
1. n=2
2. m=1
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ReenaMo wrote:Hi, I searched this question through the Beat the GMAT archives and found 2 posts on it. However (before anyone deletes this), I want to note that each of the posts gave a different response/explanation for the right answer (one arrived at A, while the other arrived at B). Can someone take a look at this and explain it again? By the way, OA is B. Thanks so much!
If n and m are positive integers, what is the remainder, when 3^(4n+2) + m is divided by 10?
1. n=2
2. m=1
3^(4n+2) = 3^2(2n+1)= 9^(2n+1)
2n+1 is an ODD number
and 9^(2n+1) will always have 9 at its unit digit
Remember that N is Positive and an integer!
9^3 = XX9
9^5 = xxxx9
......
So we really don't need to know what N is to tell what the unit digit is, but we have to know what "m" is so we can find out the unit digit of :
3^(4n+2) + m
You also need to remember that when you divide any number by 10, the remainder is the unit number!
So,
1) Insuf
2) Suf
Hence, B
LGTCH
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If n and m are positive integers, what is the remainder, when 3^(4n+2) + m is divided by 10?
1. n=2
2. m=1[/b][/quote]
3/10...remainder = 3
3^2/10..........9
3^3/10 .........7
3^4/10...............1
3^5/10...........3
3^6/10...........9
so we have a sequence repeating every 4 exp multiple of 3, now lets look at the question
from one if n = 1
thus 3^(6)+m if m = 1 , then 3^7.remainder is 7, if m=2 remainder is 1
insuff
from 2
3^(4n+2)+1..........if n = 1 thus 3^7 has emainder of 7
if n = 2 then 3^(11) has remainder of 7
if n = 3 then 3^15 has remainder of 7...........suff
B
1. n=2
2. m=1[/b][/quote]
3/10...remainder = 3
3^2/10..........9
3^3/10 .........7
3^4/10...............1
3^5/10...........3
3^6/10...........9
so we have a sequence repeating every 4 exp multiple of 3, now lets look at the question
from one if n = 1
thus 3^(6)+m if m = 1 , then 3^7.remainder is 7, if m=2 remainder is 1
insuff
from 2
3^(4n+2)+1..........if n = 1 thus 3^7 has emainder of 7
if n = 2 then 3^(11) has remainder of 7
if n = 3 then 3^15 has remainder of 7...........suff
B
