Question

Ajay multiplied 484 by a certain number to get the result 3823a. Find the value of ‘a’.

Answer 1

Hint: In general if some number say ‘A’ is multiplied by some number say ‘B’ gives ‘AB’. Then ‘A’ is a factor of ‘AB’ also ‘B’ is a factor of ‘AB’. We use this concept to answer the given problem. In 3823a, we need the value of unit place ‘a’. We find the factor of 484 that is \[484 = 11 \times 4 \times 11\] . The factors are 11 and 4. Using this we solve this.

Complete step-by-step answer:
Since 484 is multiplied by a certain number and we get 3823a.
It is obvious that 3823a is divisible by 484. Hence 484 Is a factor of 3823a.
We know that factors of 484 are 11 and 4 only.
Hence, 3823a is divisible by both 4 and 11.
We know that if the last two digits of a whole number are divisible by 4, then the entire number is divisible by 4.
The last two digits are ‘3a’, we can choose values 2, 4, 6, 8 for ‘a’.
But we know that ‘a’ can take 6 because \[4 \times 9 = 36\] . and 2 as \[4 \times 8 = 32\] .
but 38232 is not divisible by 11 whereas 38236 is divisible..
Hence the required answer is \[a = 6\] .
So, the correct answer is “a=6”.

Note: For clarification, 484 is multiplied by 79, we get 38236. All the simple things explained above go through every step. Follow the same procedure for this kind of problem. Factors is a number that divides another number or expression evenly, that is with no remainders.