QA – Placement Quizzes | Numbers, LCM and HCF | Question 8

A number leaves remainders 1, 4 and 7 on being divided successively by 3, 5 and 8 respectively. What is the product of the remainders when the order of divisors is reversed ?
(A) 28
(B) 48
(C) 24
(D) 36


Answer: (B)

Explanation: 8 x 1 + 7 = 15
5 x 15 + 4 = 79
3 x 79 + 1 = 238
Thus, 238 is the number.
 
Now, we divide 238 successively by 8, 5, 3 in that particular order.
238 / 8 => Q = 29, R = 6
29 / 5 => Q = 5, R = 4
5 / 3 => Q = 1, R = 2
Therefore, product of remainders = 6 x 4 x 2 = 48

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