Oxford University MAT 2015 Solved Papers

Question : 1 of 10

Marks: +1, -0

Pick a whole number.
Add one.
Square the answer.
Multiply the answer by four.
Subtract three.
Which of the following statements are true regardless of which starting number is chosen?
I The final answer is odd.
II The final answer is one more than a multiple of three.
III The final answer is one more than a multiple of eight.
IV The final answer is not prime.
V The final answer is not one less than a multiple of three.

I III, and V,
I and IV,
II and V,
I, III, and V,
I and V.

Validate

Solution:

Let

n

be our starting whole number. Then we get

x=4(n+1)^2-3 . x

will always be odd, since

4(n+1)^2

will always be even. Consider

n=1

, which gives

x=13

so neither III nor IV is true.

n=2

gives

x=33

, which is precisely a multiple of 3 so II is not true. The answer is (e).

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