Question

if abc represents any 3-digit number then, what will be the value of, (abcabc) $\div $ (abc) ?
(a) 11
(b) 101
(c) 1001
(d) can’t be determined

Answer 1

Hint: To solve these kinds of problems we need to first read and analyse the problem carefully so that we may be able to think about the first step that we need to perform to solve this. After the initial step we can very easily solve it. So we can observe that in the equation (abcabc) $\div $ abc we have abc as the variable so we will split the number abcabc to (abc $\times $ 1000 + abc ) and then will divide it by denominator and from that we will get the desired answer.

Complete step by step answer:
We are given that abc represents any 3-digit number and we have to find the value of,
(abcabc) $\div $ (abc)
So if we carefully observe the above equation we will find that abc is the variable here and if somehow we eliminate the variable abc from this equation we will get the value of the given expression,
We know that we can also write abcabc as,
abcabc = abc $\times $ 1000 + abc
we can write like this because we know that if abc is 3-digit number then abcabc will form a 6-digit number and hence it can be split like this,
Now we have the expression as,
\[\dfrac{abc\times 1000+abc}{abc}\]
Now dividing it by denominator, we get
\[\begin{align}
  & =\dfrac{abc\times 1000}{abc}+\dfrac{abc}{abc} \\
 & =1000+1 \\
 & =1001 \\
\end{align}\]

So, the correct answer is “Option C”.

Note: You can also solve this problem easily by taking any random 3-digit number and putting it in the given expression and you will get the same answer as shown. But if this question appears in the subjective exam then you have to do it for the general number and by the method shown in the solution.