Question : When a number is successively divided by 3, 4, and 7, the remainder obtained is 2, 3, and 5 respectively. What will be the remainder when 42 divides the same number?
Option 1: 41
Option 2: 30
Option 3: 29
Option 4: 31
Correct Answer: 29
Solution :
Start from the last digits
The number gives a remainder of 5 when it is divided by 7
⇒ Dividend = $(7x + 5)$ where $x$ is any positive integer. It will be equal to the quotient when the number is divided by 4.
The number gives a remainder of 3 when it is divided by 4
So, dividend when number is divided by 4 = $[4 × (7x + 5) + 3]$
Similarly, the dividend when the number is divided by 3
= $[3 × (4 × (7x + 5) + 3) + 2]$
= $[3 × (28x + 23) + 2]$
= $84x + 71$
On dividing $84x + 71$ by 42,
Remainder = 29
Hence, the correct answer is 29.
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