Data Sufficiency

Source: Kaplan
OA is c
If m and n are both 2 digit numbers and m-n=11x, is x an integer?
1)The tens digit and units digit of m are the same
2) m+n is a multiple of 11.

If m and n are both 2 digit numbers and m-n=11x, is x an integer?
1)The tens digit and units digit of m are the same
2) m+n is a multiple of 11.

Rephrase: is the difference between m and n a multiple of 11.

1) Test numbers. If the tens and units digits of m are the same, and m is a two-digit number, m must be a multiple of 11.

m = 33; n = 22. m - n = 11. Answer is YES, difference is a multiple of 11.
m = 33; n = 20; m - n = 13; Answer is NO, difference is not a multiple of 11

2) Again, test numbers.

Let's reuse m = 33 and n = 22, as 33 + 22 = 55, which is a multiple of 11. We already know that m-n = 11, so YES.
Or m = 34 and n = 21. m - n = 34 - 21 = 13. NO, m - n is not a multiple of 11

Together: Again, if the tens and units digits of m are the same, and m is a two-digit number, m must be a multiple of 11. If m + n is a multiple of 11, and m is a multiple of 11, then n must also be a multiple of 11. When we take the difference of two multiples of 11, the difference will itself be a multiple of 11. (You can quickly see this by testing numbers as well. 55 -22 = 33; 66 - 44 = 22; etc.)

So Together they are sufficient. Answer is C