This is a question from a Chinese GMAT practice sample:
"n" is a natural number. When "n" is divided by 3 the remainder is 2 and when divided by 4 the remainder is 1. What is the remainder when n is divided by 12?
a 1
b 2
c 3
d 4
e 5
What'd be the fastest way of doing this? please be clear with the steps (I always get confused with remainders)
The explanation given was really confusing to me:
[spoiler]n = 3a+2 (a is some natural number)
n = 4b+1 (b is some natural number)
so 3a+2 = 4b+1
so 3a+2 = 4*(b'+1) +1 (where b' is some natural number)
3a+2 = 4b'+5
3a-3 = 4b'
3(a-1) = 4b'
so 4b' is a multiple of 4 and a multiple of 3, so 4b' is a multiple of 12
so (4b'+5)/12 => 4b'/12 + 5/12
so 4b'/12 remainder is 0, 5/12 remainder is 5
so e: remainder is 5
What I don't get is the line: 3a+2 = 4*(b'+1) +1
and why 4*(b'+1) +1, why not 4*(b'+2) +1, or +3 +4 +5...[/spoiler]
"n" is a natural number. When "n" is divided by 3 the remainder is 2 and when divided by 4 the remainder is 1. What is the remainder when n is divided by 12?
a 1
b 2
c 3
d 4
e 5
What'd be the fastest way of doing this? please be clear with the steps (I always get confused with remainders)
The explanation given was really confusing to me:
[spoiler]n = 3a+2 (a is some natural number)
n = 4b+1 (b is some natural number)
so 3a+2 = 4b+1
so 3a+2 = 4*(b'+1) +1 (where b' is some natural number)
3a+2 = 4b'+5
3a-3 = 4b'
3(a-1) = 4b'
so 4b' is a multiple of 4 and a multiple of 3, so 4b' is a multiple of 12
so (4b'+5)/12 => 4b'/12 + 5/12
so 4b'/12 remainder is 0, 5/12 remainder is 5
so e: remainder is 5
What I don't get is the line: 3a+2 = 4*(b'+1) +1
and why 4*(b'+1) +1, why not 4*(b'+2) +1, or +3 +4 +5...[/spoiler]
