What are the tens and the units digits of 7^45?

Question

What are the tens and the units digits of  7^{45} ?

A. 07
B. 23
C. 43
D. 49
E. 63

Are You Up For the Challenge: 700 Level Questions

GMATinsight · Answer

Cyclicity of Unit digit of powers of 7 = 4

i.e. Unit digits repeat in higher powers of 7 after every 4 powers

Remainder (45/4) = 1

So unit digit of  7^{45}  = Unit digit of  7^1  = 7

Only Option A has unit digit 7 hence

Answer: Option A

preetamsaha · Answer

The last two digits of 71 are 07.
The last two digits of 72 are 49.
The last two digits of 73 are 43. 
The last two digits of 74 are 01.

The last two digits of powers of 7 go in a cycle - 07, 49, 43, 01.

So, the last two digits of 7^45 are 07.

The question is "What are the last two digits of the number 7^45?"

Hence the answer is "07"

Choice A is the correct answer.

Kinshook · Answer

Asked: What are the tens and the units digits of  7^{45} ?

Last 2 digits of 7^1 = 07
Last 2 digits of 7^2 = 49
Last 2 digits of 7^3 = 43
Last 2 digits of 7^4 = 01
Last 2 digits of 7^5 = 07

Last 2 digits of 7^n has cycllicity of 4

Last 2 digits of 7^{45} = Last 2 digits of 7^{4*11+1} = Last 2 digits of 7^1 = 07

IMO A

Prep Toolkit