Question

If the unit digit of a number is 7, then find the unit digit of its cube.
A) 1
B) 3
C) 5
D) 7

Answer 1

Hint: Get the unit digit of any number, and cube it. The ones place value of the number we get after finding the cube, will be the same with the units place of the cube of the original number.

Compete Step by Step Solution:
As we know that we have to take the unit digit of the number and cube it to find the unit digit of the original number after finding the cube. In this question we are given with the unit digit of original number i.e., 7
\[\begin{array}{l}
\therefore {7^3} = 7 \times 7 \times 7\\
 = 343
\end{array}\]
Clearly the unit digit of the cube of 7 is 3
Therefore the unit digit of the cube of original number will be 3 too
For example let us try to see if our result holds for 17 and 27.
For 17,
\[\begin{array}{l}
\therefore {17^3} = 17 \times 17 \times 17\\
 = 4913
\end{array}\]
For 27,
\[\begin{array}{l}
\therefore {27^3} = 27 \times 27 \times 27\\
 = 19683
\end{array}\]
Since, the result holds for 17 and 27 also.
Therefore option B is the correct option here.

Note: Multiply the numbers carefully (finding cubes) as that's the only place to make mistakes in this type of questions. Also do check your results by taking some examples for verification. Students should remember cyclicity of numbers from 0 to 9 that will be a simple method for this type of problem.