Question

In the product of $459 \times 46 \times 28* \times 484$, the digit in the units’ place is $2$. The digit to come in place of $*$ is
A) $3$
B) $5$
C) $7$
D) $4$

Answer 1

Hint: In this question we need to know that the units’ place digit of the product is decided on the basis of the multiplication of the units’ place digit of the numbers.
For an example, $12 \times 6 = 72$
So, here we can see that the unit digit of product(i.e$72$) is $2$, which derived from the multiplication of unit digits of the numbers(i.e $2 \times 6$) as, $2 \times 6 = 12$. So, their units’ place no. is also $2$.

Complete step by step answer:
First of all before starting this question we need to know the concept of how we can find the units’ place in the product of some numbers.
So, the concept is that the units’ place digit of the product is decided on the basis of the multiplication of the units’ place digit of the numbers.
So, we can say that
 The units’ place digit of the product of the numbers given will be equal to the units’ place digit of the product of the units’ place digits of these numbers.
$ \Rightarrow $Units’ place digit$\left( {459 \times 46 \times 28 \times 28* \times 484} \right) = $Units’ place digit$\left( {9 \times 6 \times 8 \times * \times 4} \right)$
As, it is given in the question that$\left( {459 \times 46 \times 28 \times 28* \times 484} \right) = 2$
$ \Rightarrow $ Units’ place digit$\left( {9 \times 6 \times 8 \times * \times 4} \right) = 2$
$ \Rightarrow $ Units’ place digit$\left( {216 \times *} \right) = 2$
Now, here also we can say that the units’ place digit of the product of the numbers given will be equal to the units’ place digit of the product of the units’ place digits of these numbers.
$ \Rightarrow $ Units’ place digit$\left( {216 \times *} \right) = $ Units’ place digit$\left( {6 \times *} \right)$
$ \Rightarrow $ Units’ place digit$\left( {6 \times *} \right) = 2$
So, from here we have to find a single digit no. who’s multiplication with $6$leads to a no. having a units’ digit $2$. {it should be single digit because only single digit can be placed at a units’ place}
So, now as we know that multiplication of $6$with $2$or $7$leads to a no. having a units’ digit $2$.
Because $6 \times 2 = 12$and $6 \times 7 = 42$.
So, the answer will be $* = 2$or $* = 7$
$ \Rightarrow $Option C is correct.
Note: In this question we just needed to know how units’ place of product of some numbers is formed. Some students start multiplying all the numbers and then equate the units’ place of product with the given units’ place, which is also right but a quite lengthy procedure. So, this can be easily done by just multiplying the unit’s digits of the numbers.