RonPurewal
If n is an integer greater than 5, what is the remainder when n is divided by 5 ?
(1) The remainder when \(n^{2}\) is divided by 5 is less than the remainder when n is divided by 5.
(2) The remainder when 2n is divided by 5 is less than the remainder when n is divided by 5.
Hi..
(1) The remainder when \(n^{2}\) is divided by 5 is less than the remainder when
n is divided by 5.
You are basically squaring the remainder here..Remove all those number that have same units digit in their SQUARE - 0,1,5,6 as all of them will give SAME remainder when squared
Now, as shown above by
RonPurewal that the number can be written as 5k+m - what can we infer here..
two set of numbers will behave same way when it comes to remainder..
0 and 0+5=5
1 and 1+5=6
remaining
2 and 2+5=7
3 and 3+5=8
4 and 4+5=9..
just check for only 1 in the set..
units digit 2 will give remainder 2 and 2^2 means 4, so remainder =4...4>2 so discard
units digit 3 will give remainder3 and 3^2 means 9, so remainder = 9-5=4...4>2 so discard
units digit 4 will give remainder 4 and 4^2 will give 16, so remainder = 16-15=1 here 4<1.. same will be the case in 9
in both cases remainder = 4
As all other cases discarded
Suff
(2) The remainder when 2
n is divided by 5 is less than the remainder when
n is divided by 5.
you are basically doubling the remainder hereremainder can be 1,2,3,4.. the remainder when the dividend is 2n will be 2,4,6-5,8-5 ......2,4,1,3 respectively
so in two cases the statement works 3 and 4
insuff
A