4 Views

Question : Let $x$ be the least number which when divided by 8, 9, 12, 14 and 36 leaves a remainder of 4 in each case, but $x$ is divisible by 11. The sum of the digits of $x$ is

Option 1: 5

Option 2: 6

Option 3: 9

Option 4: 4


Team Careers360 13th Jan, 2024
Answer (1)
Team Careers360 21st Jan, 2024

Correct Answer: 4


Solution : Given numbers = 8, 9, 12, 14, and 36
LCM(8, 9, 12, 14, 36) = 2 × 2 × 2 × 3 × 3 × 7 = 504
Let the required number = (504k + 4) which is divisible by 11,
⇒ (504k + 4) → $\frac{ (9k + 4)}{11}$
Putting k = 1, 2, 3, 4,……..
when k = 2
⇒ $\frac{(9 × 2 + 4)}{11}$ = $\frac{22}{11}$ =  2
Now,
504k + 4 is divisible by 11 when k = 2
Required number =  504 × 2 + 4
= 1008 + 4
= 1012
Sum of digits of 1012 = 1 + 0 + 1 + 2 = 4
Hence, the correct answer is 4.

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