Concept:A number is divisible by 3 if the sum of its digits is a multiple of 3.
A number is divisible by 11 if the difference between the sum of digits at odd places and the sum of digits at even places is 0 or a multiple of 11.
We need the number that fails both conditions.
Explanation:Check each option:
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3234: Sum =
3+2+3+4=12 (divisible by 3). For 11:
(3+3)−(2+4)=6−6=0 (divisible by 11). So it is divisible by both.
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2871: Sum =
2+8+7+1=18 (divisible by 3). For 11:
(2+7)−(8+1)=9−9=0 (divisible by 11). Thus divisible by both.
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4567: Sum =
4+5+6+7=22 (not divisible by 3). For 11:
(4+6)−(5+7)=10−12=−2 (not a multiple of 11). So it is neither divisible by 3 nor by 11.
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3003: Sum =
3+0+0+3=6 (divisible by 3). For 11:
(3+0)−(0+3)=3−3=0 (divisible by 11). Thus divisible by both.
Only 4567 fails both tests.
Answer:4567 (Option C)