Successive division of a number by 2, 3, 5, and 7 gives remainders 1, 4, 0, and 5, respectively. What will be the sum of the remainders if the same number is divided by 7, 5, 3, and 2 successively?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 9.
Let the last number be divided by 7 and leaving the remainder 5 be x
According to the Remainder theorem
Dividend = Divisor × Quotient + Remainder
Hence,
⇒ 7 × 0 + 5 = x
⇒ 5 = x
Now 5 is the quotient when 5 divides a number and leaves the remainder 0
Again using the remainder theorem
Dividend = 5 × 5 + 0 = 25
Now 25 is the quotient when 3 divides a number and leaves the remainder of 4
Again using the remainder theorem
Dividend = 25 × 3 + 4 = 79
Now 79 is the quotient when 2 divides a number and leaves the remainder 1
Again using the remainder theorem
Dividend = 97 × 2 + 1 = 159
Hence the Number is 159
Now when 159 is successively divided by 7, 5, 3, and 2 we get the remaining 5, 2, 1, and 1 respectively
Hence, Sum of remainders = 9