f2001290 wrote:77. What is the remainder when n is divided by 10?
1). The tens digit of 11^n is 4
2). The hundreds digit of 5^n is 6
OA after few explanations
Whats the source for this one?
You'll need properties for multiplication by 11 to solve this one -- if a number say ab1 is multiplied by 11, the units digit will be 1, tens digit will be b+1.
Now, just calculating the tens digit, we have
11^1 = 11
11^2 = 121
11^3 = x31
11^4 = x41
...
11^9 = x91
11^10 = x01
...
11^14 = x41
...
The sequence repeats and so whenever n = 4, 14, 24 ... we get the
tens digit of 11^n to be 4.
So, n/10 will always yield a remainder of 4.
2 - insufficient. After n = 4, we get alternating x125 and x625. So, we
cannot say what n is for sure.
Hence A.
Again, I'm not too sure if such questions are tested on the GMAT.
