Data Sufficiency

If m and n are both two-digit numbers, and m-n = 11X, is X an integer?

(1) The tens digit and the units digit of m are the same
(2) m+n is a multiple of X

If m and n are both two-digit numbers, and m-n = 11X, is X an integer?

(1) The tens digit and the units digit of m are the same
(2) m+n is a multiple of X

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I'll take a try at this..

Statement 1 alone tells you that m can be 11, 22, 33, 44, 55,.. and so on, but it doesn't tell you anything about the other variables.
This narrows your options to BCE

Statement 2 alone is not sufficient because we don't know what m and n are. (remember to ignore statement 1)

If we combine both statements, we know m is an integer. If n as an integer than yes, X would be an integer. If n was a non-integer then X would not an integer. Since there is no explicit "Yes" or "No" response to the question then the statements are not sufficient to answer the problem. I think E is the right answer, Am I right?

Very poorly stated question. I might be wrong, but theoretically -1.5 is a 2-digit number.

Either way it's D or E.

66 - 33 = 3*11
66 + 33 = 3 * 3 * 11

66 - 64 = 2 = 11 * 2/11
66 + 64 = 130 = 11 * 130/11 = 11 * 65 * 2/11

It has to be E

It's B, strictly in my opinion.

Also, that doesn't take away from the fact that the question could have been worded better. I request you to state the source.

Statement 1: let 2 numbers be 18 and 51, there difference is 33, and X is an integer. Now take 37 and 23, their difference is 14, and X is not an integer. Insufficient.

Statement 2: take any 2 numbers whose difference is a multiple of 11, say 51 and 18, or, 17 and 39. In the case of 17 and 39, their difference is 22, i.e 2x11. and the sum of 17 and 39 is divisible by 2. Now reverse this logic in your head and feel the bulb light up.

I agree with E.

The question says m and n are two digit NUMBERS not INTEGERS

m = 22.43, 33.45, 88.98, etc

why are you guys assuming m and n to be an integer.

Hence, answer should be E.