Question : When a number is successively divided by 3, 4 and 7, the remainder obtained are 2, 3 and 5, respectively. What will be the remainder when 84 divides the same number?
Option 1: 71
Option 2: 30
Option 3: 48
Option 4: 53
Correct Answer: 71
Solution :
Remainders corresponding to the divisor
(Divisor × Quotient) + Remainder = Dividend
Start from the last digits
The number gives a remainder of 5 when it is divided by 7
= (7$x$ + 5)
The number gives the remainder 3 when it is divided into 4
= 4 × (7$x$ + 5) + 3
Also, the number when divided by 3 gives the remainder 2
= 3 × {4 × (7$x$ + 5) + 3} + 2
= 3 × (28$x$ + 20 + 3) + 2
= 84$x$ + 71
The number is 71 more than a multiple of 84.
So, if the number is divided by 84, the remainder will be 71.
Hence, the correct answer is 71.
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