Question

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Explanation:

Identify the divisibility conditions

The feedback text at the bottom explains divisibility rules for \(2\), \(3\), and \(5\). It states:

• A whole number is divisible by \(2\) if its units digit is even.
• A whole number is divisible by \(3\) if the sum of its digits is divisible by \(3\).
• A whole number is divisible by \(5\) if its units digit is \(0\) or \(5\).

The cut-off text in option E mentions "divisible by 2 and [3 and 5]". We seek a number divisible by \(2\), \(3\), and \(5\).

Find the least common multiple

To be divisible by \(2\), \(3\), and \(5\), a number must be a multiple of their least common multiple (LCM).
Since \(2\), \(3\), and \(5\) are prime numbers:

$$ \text{LCM}(2, 3, 5) = 2 \times 3 \times 5 = 30 $$

Test the given options

We evaluate each option to see which is a multiple of \(30\):

• For A: \(56\) is not divisible by \(5\) or \(3\).
• For B: \(24\) is not divisible by \(5\).
• For C: \(15\) is not divisible by \(2\).
• For D: \(30\) is divisible by \(2\), \(3\), and \(5\).

Formulate the final selection

Option D (\(30\)) is the only number that satisfies all three divisibility criteria.

Answer:

• A. 56
• B. 24
• C. 15
• D. 30 (Correct answer)
• E. There is no whole number which is divisible by 2 and 3 and 5