TMUA 2020 Paper 2 Q3 — Worked Solution

P2·Algebra & Surds, Logic & Quantifiers·6.0Official · 2020 · Q3

proof-errorsign-errorexpanding-brackets

A student makes the following claim:For all integers $n$ , the expression $4 (\frac{9 n + 1}{2} - \frac{3 n - 1}{2})$ is divisible by 3.Here is the student's argument:

(I)

4 (\frac{9 n + 1}{2} - \frac{3 n - 1}{2}) = 2 (2 (\frac{9 n + 1}{2} - \frac{3 n - 1}{2}))

(II)

= 2 (9 n + 1 - 3 n - 1)

(III)

= 2 (6 n)

(IV)

= 12 n

(V)

= 3 (4 n)

(VI)

which is always a multiple of

3

, so the expression is always divisible by

3

Which one of the following is true?

All questions

Discussion

Discuss this question

No discussions yet. Stuck, or want to share an approach? Start the first one.

TMUA 2020 Paper 2 Question 3

Discussion