What is the remainder when 10^49 + 2 is divided by 11?  Choose the correct choice from the following:	A) 1	B) 2	C) 3	D) 5	E) 7
With exponent-based problems and huge numbers, it's often helpful to try to establish a pattern using small numbers. On this problem, while 1049+2 is a massive number that you'd never want to try to perform calculations with, you can start by using smaller numbers to get a feel for what it would look like:   10^2+2=102, which when divided by 11 produces a remainder of 3 (as 9 * 11= 
<gadget id="calculator">9 * 11</gadget>
<output>99</output>
99, leaving 3 left over)   10^3+2=1002, which when divided by 11 produces a remainder of 1 (as 9 * 110= 
<gadget id="calculator">9 * 110</gadget>
<output>990</output>
990, and when you add one more 11 to that you get to 1001, leaving one left)   10^4+2=10002, which when divided by 11 produces a remainder of 3 (as you can get to 9999 as a multiple of 11, which would leave 3 left over)   10^5+2=100002, which when divided by 11 produces a remainder of 1 (as you can get to 99990 and then add 11 more, bringing you to 100001 leaving one left over).   By this point, you should see that the pattern will repeat, meaning that when 10 has an even exponent the remainder is 3 and when it has an odd exponent the remainder is 1. Therefore, since 10 has an odd exponent in the problem, the remainder will be 1.   answer is 1
<result>A</result>
What is the remainder when 10^49 + 2 is divided by 11?