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Remainder when the positive integer x is divided by 6haidgmat wrote:What is the remainder when the positive integer x is divided by 6?
1. When x is divided by 2, the remainder is 1; and when x is divided by 3, the remainder is 0
2. When x is divided by 12, the remainder is 3
OA: D but how come??? I answered B
shovan85 wrote:Remainder when the positive integer x is divided by 6haidgmat wrote:What is the remainder when the positive integer x is divided by 6?
1. When x is divided by 2, the remainder is 1; and when x is divided by 3, the remainder is 0
2. When x is divided by 12, the remainder is 3
OA: D but how come??? I answered B
Option 1:
When x is divided by 2, the remainder is 1
So we can write in general x = 2k + 1 (k is an integer) [1,3,5,7,.... (Odds)]
when x is divided by 3, the remainder is 0
So we can write in general x = 3k (k is integer) [0,3,6,9,12,15....]
Combine both,
from second set we need to find the odds as those will be div by 3 not by 2.
So those are 3,9,15,...
When these are divided by 6 we get a Remainder 3 (always)
Thus Sufficient.
Option 2: When x is divided by 12, the remainder is 3
In general x = 12k + 3
When this is divided by 6 remainder is always 3.
Thus Sufficient.
IMO D
Yes 3 is not divisible by 6. But, when 3 is divided by 6 the remainder is 3 and quotient is 0 (zero). And thats what has been proved in Option number 1.haidgmat wrote:But 3 isnt divisible by 6! Isn't remainder the number which is left behind after a number is divided by another number?
shovan85 wrote:Yes 3 is not divisible by 6. But, when 3 is divided by 6 the remainder is 3 and quotient is 0 (zero). And thats what has been proved in Option number 1.haidgmat wrote:But 3 isnt divisible by 6! Isn't remainder the number which is left behind after a number is divided by another number?
When you consider x as any of the set (3, 9, 15, 21....) and divide the x by 6 you will ALWAYS get the remainder 3.
AS you are always getting remainder as 3 this option is sufficient.
If still not clear ask yourself is 15 divisible by 6? (No. So as 3 but remainder is 3 for both the case )
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