Question

N is an integer between $ 1 $ and $ 93. $ What is the value of N?
I.N is both the square of an integer and the cube of an integer.
II.The square root of N is divisible by $ 8 $
A.Statement (I) alone is sufficient, but statement (II) alone is not sufficient.
B.Statement (II) alone is sufficient, but statement (I) alone is not sufficient.
C.Both statements together are sufficient, but neither statement alone is sufficient.
D.Each statement alone is sufficient.

Answer 1

Hint: Integers can be defined as the smallest group and the smallest ring which contains the natural numbers. Here will find one number which is within the range and it can be square and the cube of the number and follows the given conditions.

Complete step-by-step answer:
Here we will take both the given conditions one by one –
N is both the square of an integer and the cube of an integer.
Here jot down the squares of the numbers with in the given range –
 $
  {1^2} = 1 \\
  {2^2} = 4 \\
  {3^2} = 9 \\
  {4^2} = 16 \\
  {5^2} = 25 \\
  {6^2} = 36 \\
  {7^2} = 49 \\
  {8^2} = 64 \\
  {9^2} = 81 \\
  {10^2} = 100 \;
 $
And similarly cubes of the numbers –
 $
  {1^3} = 1 \\
  {2^3} = 8 \\
  {3^3} = 27 \\
  {4^3} = 64 \\
  {5^3} = 125 \;
 $
From the squares and cubes of the numbers, we can identify that $ N = 64 $ is both the square and the cube of the number.
The square root of N is divisible by $ 8 $
When $ N = 64 $ , the square root of N is divisible by $ 8 $
Hence, from the given multiple choices the option D is the correct answer.
So, the correct answer is “Option D”.

Note: Be good in multiples, squares and the cubes of the number at least till twenty. Here more mental mathematics can help you to get an efficient and accurate answer. Square is the term multiplied with the same number twice and the cube is the number when multiplied with the same number thrice.