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Fallacy

Consider the ...

Question

Consider the following statements. The number $12375$ is
(1) divisible by $3$
(2) divisible by $11$
(3) divisible by $9$
Of these statements:

1, 2 and 3 are correct

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1 and 2 are correct

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2 and 3 are correct

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1 and 3 are correct

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Solution

The correct option is B 1, 2 and 3 are correct
$12375$
$1 + 2 + 3 + 7 + 5 = 18$ which is divisible by 3.
Therefore, the number 12375 is divisible by 3.
$12375$
$1 + 3 + 5 = 9$
$2 + 7 = 9$
$9 - 9 = 0$ if it is 0 or 11, then it is divisible by 11.
Therefore, the number 12375 is divisible by 11.
$12375$
$1 + 2 + 3 + 7 + 5 = 18$ which is divisible by 9.
$∴$ The number $12375$ is divisible by $9$ .

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