Question

The cube of a two-digit number may have seven or more digits.
A) True
B) False
C) Insufficient data
D) None of these

Answer 1

Hint: Here, in this given question, we can first of all find the cube of the largest two-digit number that is 99 and count the number of digits in it. We can make our answer on the basis of this because 99 is the largest two-digit number and if it's cube doesn’t have seven digits or more, no smaller number’s cube can have seven or more digits.
Complete step-by-step answer:
In this given question, we are asked to find whether the statement ‘The cube of a two-digit number may have seven or more digits.’ Is true or false or the data is insufficient to decide whether it is true or false.
The cube of a number is the value obtained by multiplying it with itself three times.
As larger numbers have larger cubes, no two-digit number can have a larger cube than the largest two-digit number that is 99.
So, we can get our answer from the number of digits in the cube of 99.
${{99}^{3}}=970299...............(1.1)$
As, from equation 1.1, we are able to know that the cube of 99 contains 6 digits. As no other two-digit number can have a greater cube, we conclude that no two-digit number has a cube with seven or more digits.
Hence, the given statement ‘The cube of a two-digit number may have seven or more digits.’ Is false.
Therefore, the correct option to the question is option (B) False.

Note: In this sort of question, we can use the largest number of the given digits and find their cubes or squares as required and follow the same method as above to get our needed conclusions and answers. We must also be careful before deciding whether the information is sufficient or not before giving an answer.