Question : M is the largest 4-digit number which, when divided by 4, 5, 6, and 7, leaves the remainder as 2, 3, 4, and 5, respectively. What will be the remainder when M is divided by 9?
Option 1: 2
Option 2: 1
Option 3: 3
Option 4: 6
Correct Answer: 1
Solution :
The least common multiple (LCM) of 4, 5, 6, and 7 is 420.
The required largest 4-digit number will be a multiple of 420.
Remainder of $\frac{9999}{420}$ is 339.
The largest 4-digit number will be 9999 – 339 = 9660 which is divisible by 4, 5, 6, and 7.
Now, as given, when the number is divided by 4, 5, 6, and 7, it leaves 2, 3, 4, and 5 as remainders.
The difference between each divisor and the remainder is 2, as shown below.
| Divisor | Remainder | Difference |
| 4 | 2 | 2 |
| 5 | 3 | 2 |
| 6 | 4 | 2 |
| 7 | 5 | 2 |
Hence, the required number is 9660 – 2 = 9658
When 9658 is divided by 9, it will leave the remainder 1.
Hence, the correct answer is 1.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Result | Eligibility | Application | Selection Process | Preparation Tips | Admit Card | Answer Key
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
