Every Number Serves A Purpose

Number Theory Level 2

The integer A A is even. Is it true that 3 × A 3 \times A must be divisible by 6?

Part 2 Part 3 .

No, it is not true Yes, it is true

Ronald Chén by Ronald Chén , 32, Guatemala

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2 solutions

Ronald Chén
Nov 8, 2016

Yes, since both 2 and·3 belong to the decomposition of the number 3A.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Viki Zeta
Nov 9, 2016

A is even ⟹ A ≡ 0 m o d 2 3 A ≡ x m o d 6 ⟹ 3 × A ≡ x m o d 2 × 3 ⟹ A ≡ x m o d 2 ∴ x = 0 ⟹ 3A is divisible by 6 \text{A is even} \\ \implies A \equiv 0 \ \mathbb{mod} \ 2 \\ 3A \equiv x \ \mathbb{mod} \ 6 \\ \implies 3 \times A \equiv x \mathbb{mod} \ 2 \times 3 \\ \implies A \equiv x \ \mathbb{mod} \ 2 \\ \boxed{\therefore x=0 \implies \text{3A is divisible by 6}}

1 Helpful 0 Interesting 0 Brilliant 1 Confused

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