9 Views

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


Team Careers360 4th Jan, 2024
Answer (1)
Team Careers360 6th Jan, 2024

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.

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books