SOLUTION: All 4-digit integers with the same digits as the number 2011 (two 1’s, 0, and 2) are written in increasing order. What is the difference between the two neighbours of the number 20

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Question 943224: All 4-digit integers with the same digits as the number 2011 (two 1’s, 0, and 2) are written in increasing order. What is the difference between the two neighbours of the number 2011 on this list?
(A)890
(B)891
(C)900
(D)909
(E)990
please be noted that answer is B , explain how?
Found 2 solutions by richard1234, Edwin McCravy:
Answer by richard1234(7193)   (Show Source): You can put this solution on YOUR website!
2011 is between 1210 and 2101, and 2101-1210 = 891.
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
We need 

1. the LARGEST 4-digit number we can make with two 1’s, 0, and 2
that is LESS than 2011.  That's 1210.

and

2. the SMALLEST 4-digit number we can make with two 1’s, 0, and 2
that is GREATER than 2011.  That's 2101.

Subtract them to find the difference:

2101-1210 = 891

Answer: 891 

Edwin
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