I'm getting more and more confused...

The example above was mis-typed, my fault -- on my scratch paper I've got down two 12 digit numbers:
121212121213 (5 twos, 6 ones, and 1 three)
212113211221 (also 5 twos, 6 ones, and 1 three)
Total =
333325332434
= (3+3+2+3+2+3) - (3+3+5+3+4+4)
= 16 - 22
= -6 --> Hence 333325332434 is not a multiple of 11.

Statement 2 is definitely insufficient with this counter-example.

Statement 1, in gmatclubmember's explanation is sufficient. I was doubting it for a second, because he did it only in absolute reverse, but each combination, regardless of how you combine them, is a multiple of 11.

This would not be on the GMAT...

Anyway:
n is the number of digits, not the number itself
Statement 1 is saying that n = p*q*r, and the point of this is to tell you that n is even
Statement 2 is basically telling you that n is 12

It so happens that whenever you take a number with an even number of digits, and you add it to the number that results when the digits are reversed, the result is a multiple of 11:

2-digit number:
AB = 10A + B
BA = 10B + A
Sum = 11A + 11B = multiple of 11

4-digit number:
ABCD = 1000A + 100B + 10C + D
DCBA = 1000D + 100C + 10B + A
Sum = 1001A + 110B + 110C + 1001D = multiple of 11 because 1001 and 110 are each multiples of 11

This will continue if you try 6-digit numbers, 8-digit, etc.
So, since each statement tells you that the NUMBER OF DIGITS IS EVEN, each statement is sufficient. D.

Note that for numbers with an odd number of digits, this may or may not be the case:
3-digit number:
ABC = 100A + 10B + C
CBA = 100C + 10B + A
Sum = 101A + 20B + 101C

If we started with a multiple of 11, like 132, this result will be a multiple of 11. Otherwise, it might not be.

Hello Greg (gmatboost),

Everything you've said makes perfect sense, but the question is stating that the numbers are interchanged; does this necessarily mean that the number is reversed? The way I'm interpreting "interchange" is like an anagram, where any combination/rearrangement of the numbers is possible.

Take the number 1,234. We can rearrange it in 4! = 24 ways. Some of the sums when added to 1,234 might be a multiple of 11, such as 4,321 or 2,341; some of the sums when added to 1,234 might not be a multiple of 11, such as 3,412 or 1,432.

So, with the definition of "interchanged" meaning "reversed," D is an acceptable solution. But, as a test taker, I expect "interchanged" to mean "changed around, possibly randomly, not necessarily reversed," which would then cause insufficiency in statement 2, changing the answer to A. The only way I would expect "reversed" to be the meaning of interchanged is if the question was worded "the two elements are interchanged."

Does anyone have any input on the usage of interchanged in this question?
Has anyone ever seen a similar official GMAT question with this ambiguous a statement?

--Rishi

Does anyone have any input on the usage of interchanged in this question?
Has anyone ever seen a similar official GMAT question with this ambiguous a statement?

This would never, ever happen on the GMAT. This is just another in the long line of overly complex, unrealistic, poorly phrased questions that for some reason make their way into students' hands.

Questions on the GMAT never suffer from poorly defined math vocabulary. They also never would have a question that involved adding 12-digit numbers together and determining if the result is divisible by 11. They also would never be so ambiguous in Statement 1 (Is pqr a three-digit number? Is it a product?). And so on...