Question

Which number is equal to the sum of cubes of their digits?
A.143
B.149
C.151
D.153

Answer 1

Hint: In this question for each option find the cube of each digit of numbers mentioned in the options and use the addition operation using this information we can get a better approach towards the solution of the question.

Complete step-by-step answer:
The cube of any number is represented as suppose we have a number 2 then the cube of the number is given by ${2^3} = 2 \times 2 \times 2 = 8$
Now let’s find the cubes of the digit present in 1st option i.e. 143 and 1, 4 and 3 are the digits present in this number 143
Cube of 1 is equal to ${1^3} = 1 \times 1 \times 1 = 1$
Cube of number 4 is equals to ${4^3} = 4 \times 4 \times 4 = 64$
And ${3^3} = 3 \times 3 \times 3 = 27$is the cube of number 3
Now adding the results of cubes of digits 1, 4 and 3
1 + 64 + 27 = 92
Since 92 is not equal to 143 therefore option A is not the correct option
For 2nd option the given number is 149 which consist of digits 1, 4 and 9
So cube of number 1 is equal to ${1^3} = 1 \times 1 \times 1 = 1$
Cube of number 4 is equals to ${4^3} = 4 \times 4 \times 4 = 64$
Now cube of number 9 is \[{9^3} = 9 \times 9 \times 9 = 729\]
Using the addition operation in the cubes of numbers 1, 4 and 9
1 + 64 + 729 = 794
Since 794 is not equal to 149 therefore option B is also not a correct option
Now let’s find out the cubes of digits of number given in 3rd option i.e. 151 which have digits 1, 5 and 1
So ${1^3} = 1 \times 1 \times 1 = 1$ is the cube of 1
Cube of number 5 is ${5^3} = 5 \times 5 \times 5 = 125$
And cube of 1 is ${1^3} = 1 \times 1 \times 1 = 1$
Adding the cubes of numbers 1, 5 and 1
1 + 125 + 1= 127
Now checking for 4th option i.e. 153 the digits are 1, 5 and 3
So cube of 1 is ${1^3} = 1 \times 1 \times 1 = 1$
Cube of 5 is ${5^3} = 5 \times 5 \times 5 = 125$
And cube of 3 is ${3^3} = 3 \times 3 \times 3 = 27$
Adding the cubes of digits 1, 5 and 3
1 + 125 + 27 = 153
Since the result of sum of cubes of digits is equal to the number
Therefore option D is the correct option.

Note: In the above solution we used a term named operation which can be defined as the function that bring out some defined outputs using none or some inputs the example of operation is addition, subtraction, multiplication and etc., In operations like addition, subtraction, multiplication you need minimum 2 operand to operate the operation for example 1 + 2 = 3 here 1 and 2 are the operands of addition which are needed to operate an addition operation whereas in some operations like cube root, square root and etc. you don’t need 2 operands these operation operate using minimum 1 operands for example $\sqrt 4 = 2$ here 4 is the operand of the operation square root these types of operation which need minimum 1 operand to operate the operation is called unary operation.