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What is the tens digit of 11^(13)?

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What is the tens digit of 11^(13)?

by Vincen » Wed Feb 21, 2018 1:56 am
$$\text{What}\ \text{is}\ \text{the}\ \text{tens}\ \text{digit}\ \text{of}\ 11^{13}\ ?$$

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

The OA is the option C.

Experts, may you give me a good and fast way to solve this PS question? How can I determine it? I'd appreciate your help.
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by Jay@ManhattanReview » Fri Mar 09, 2018 12:48 am
Vincen wrote:$$\text{What}\ \text{is}\ \text{the}\ \text{tens}\ \text{digit}\ \text{of}\ 11^{13}\ ?$$

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

The OA is the option C.

Experts, may you give me a good and fast way to solve this PS question? How can I determine it? I'd appreciate your help.
Tha pattern of the exponents of 11 is simple to get.

11^1 = 11; tens digit = exponent = 1;
11^2 = 121; tens digit = exponent = 2;
11^3 = 1331; tens digit = exponent = 3;
11^4 = 14441; tens digit = exponent = 4;
.
.
.
11^9 = 1999999991; tens digit = exponent = 9;
11^10 = (11^9)*11 = 1999999991*11 = ..............01; tens digit = units digit of the exponent = 0;

Thus,

Tens digit of 11^13 = units digit of the exponent = 3.

The correct answer: C

Hope this helps!

-Jay
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