If 1N3N is a four digit number and it is divisible by 11, then what is the…
2021
If 1N3N is a four digit number and it is divisible by 11, then what is the value of N?
- A.
0
- B.
2
- C.
9
- D.
5
Attempted by 88 students.
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Correct answer: B
Key idea: use the divisibility rule for 11.
For the number 1N3N, the sum of digits in odd positions (1st and 3rd) is 1 + 3 = 4.
The sum of digits in even positions (2nd and 4th) is N + N = 2N.
A number is divisible by 11 when the difference between these sums is a multiple of 11: 4 − 2N = 0 or ±11, ...
Solve 4 − 2N = 0 → 2N = 4 → N = 2. Other possibilities 4 − 2N = ±11 give non-integer or non-digit values for N, so they are not valid.
Check: with N = 2 the number is 1232 and 1232 ÷ 11 = 112, so it is divisible by 11.
Answer: N = 2