atarafder wrote:1. if m and n are positive integers, what is the remainder when 3 ^ (4n +2) + m is divided by 10?
A. n= 2
B. m =1

Please note it is only 3 to the power of (4n+2)

1 - insufficient. Without knowing m, we cannot find the remainder

2 - sufficient.

3^(4n+2) + m
= 9^(2n+1) + m

We know that 9^(2n+1) will yield a number with units digit 9

So, knowing m, we can find the last digit of 3^(4n+2) + m
and hence the remainder when the above is divided by 10.


Hence B.

atarafder wrote: 2. for which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers a and b?
A. f(x) = x^2
B. f(x) = f(x+1)
C. f(x) = sqrt x
D. f(x) = x/2
E. f(x) = -3x
Ans: E

Is the question copied correctly ?

Is B f(x) = f(x+1) or just x+1 ?

A - f(a) + f(b) = a^2 + b^2 which is not equal to (a+b)^2
B - please check
C - sqrt-a + sqrt-b not equal to sqrt (a+b)
D - seems to satisfy as well
E - seems to satisfy

you are right, D is 2/x and NOT x/2
and B is f(x) = x+1