Out of the four given alternatives, choose the most appropriate description…
2019
Out of the four given alternatives, choose the most appropriate description about the given three numbers: 3, 13, 31
- A.
These are cubes of 3
- B.
These are multiple of 3
- C.
These are cubes of odd numbers
- D.
These are prime numbers
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Show answer & explanation
Correct answer: D
Answer: 3, 13 and 31 are prime numbers.
3 is prime because its only positive divisors are 1 and 3.
13 is prime: check divisibility by integers up to √13 ≈ 3.6 (not divisible by 2 or 3).
31 is prime: check divisibility by integers up to √31 ≈ 5.6 (not divisible by 2, 3, or 5).
Why the other descriptions are incorrect:
They are not cubes: the cube of 3 is 27 (3^3 = 27), and cubes of nearby odd integers are 1, 27, 125, none of which match 3, 13, or 31.
They are not all multiples of 3: 13 and 31 are not divisible by 3.