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“The product of three consecutive positive integers is divisible by 6”. Is this statement true or false? Justify your answer.

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Yes, the statement “the product of three consecutive positive integers is divisible by 6” is true.

Justification:

Consider the 3 consecutive numbers 2, 3, 4

(2 × 3 × 4)/6 = 24/6 = 4

Now, consider another 3 consecutive numbers 4, 5, 6

(4 × 5 × 6)/6 = 120/6 = 20

Now, consider another 3 consecutive numbers 7, 8, 9

(7 × 8 × 9)/6 = 504/6 = 84

Hence, the statement “product of three consecutive positive integers is divisible by 6” is true.

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