Question
Download Solution PDFThere are two natural numbers m and n (m > n). When m is divided by 12, it leaves a remainder 4. When n is divided by 12, it leaves a remainder 6. Which of the following statements is/are correct?
I. The remainder when (m + n) is divided by 12 is 10.
II. The remainder when (m - n) is divided by 12 is 10.
Select the correct answer using the code given below :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
m ≡ 4 (mod 12)
n ≡ 6 (mod 12)
Formula used:
If a ≡ r1 (mod m) and b ≡ r2 (mod m), then:
a ± b ≡ r1 ± r2 (mod m)
Calculations:
Statement I: (m + n) mod 12
⇒ m + n ≡ 4 + 6 ≡ 10 (mod 12)
The statement I is correct.
Statement II: (m − n) mod 12
⇒ m − n ≡ 4 − 6 ≡ −2 ≡ 10 (mod 12)
The statement II is correct.
∴ The correct answer is: Both I and II
Last updated on Jul 7, 2025
-> The UPSC CDS Exam Date 2025 has been released which will be conducted on 14th September 2025.
-> Candidates can now edit and submit theirt application form again from 7th to 9th July 2025.
-> The selection process includes Written Examination, SSB Interview, Document Verification, and Medical Examination.
-> Attempt UPSC CDS Free Mock Test to boost your score.
-> Refer to the CDS Previous Year Papers to enhance your preparation.