The number when divided by 2, leaves remainder 1; when divided by 3, leaves remainder 2 and when divided by 4, leaves remainder 3, is || ADRE 1.0 SLRC 2022 PAPER-III SOLVED QUESTIONS

The number when divided by 2, leaves remainder 1; when divided by 3, leaves remainder 2 and when divided by 4, leaves remainder 3, is:

(A) 25 

(B) 41 

(C) 13 

(D) 11



Solution:

Let's find the number htat satisfies the conditions:

  • x ≡ 1 (mod 2)
  • x ≡ 2 (mod 3)
  • x ≡ 3 (mod 4)

We start by finding a number x that satisfies x ≡ 1 (mod 2). This means x is odd. 

Next, since ≡  2 (mod 3), x when divided by 3 lives a reainder of 2. 

Similarly, x ≡  3 (mod 4) means when x is divided by 4, the memainder is 3. 


To find such a number, we check the options:

  • Option A: 25 (odd, check divisibility)
    • 25÷2 = 12 remainder 1 (satisfies condition 1)
    • 25÷3= 8 remainder 1 (does not satisfy condition 2)
    • 25÷4= 6 remainder 1 (does not satisfy condition 3)
            So, 25 does not satisfy all the given conditions. 

  •  (odd, check divisibility):

    •  remainder 
      (satisfies condition 1)

    •  remainder 2 (satisfies condition 2)
    •  remainder 1 (does not satisfies condition 3)

            So, 41 does not satisfy all the given conditions. 
  • Option C:  (odd, check divisibility):
    •  remainder 1 (satisfies condition 1)
    •  remainder 1 (does not satisfy condition 2)

    •  remainder 1 (does not satisfy condition 3)
            So, 13 does not satisfy all the given conditions. 
  • Option D:  (odd, check divisibility):
    •  remainder 1 (satisfies condition 1)
    •  remainder 2 (satisfies conditon 2)
    •  remainder 3 (Satisfies condition 3)
Thus, the number x that satisfies all the conditions is 11.


Why this problem is important?

  • Mathematical Foundations: Essential for mastering number theory in competitive exams.
  • Problem-solving Practice: Develops effective methods for similar questions.
  • Exam Readiness: Efficiently prepares for ADRE SLRC Paper III.

Comments

  1. Please give me the answer

    ReplyDelete
    Replies
    1. Option D

      Delete
    2. The number x that satisfies all the conditions is 11.

      Delete

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