tmua.fyi Paper 2 Challenge 2 · Question 20

Consider the statement: for every integer $n$ such that $n^2+n$ is odd, $n$ is a multiple of $7$ . Which of the following is correct?

AIt is false, as

n=3

shows.

BIt is true, vacuously:

n^2+n=n(n+1)

is always even, so there is no such

n

CIt is false, as

n=1

shows.

DIt is true, and every such

n

happens to be a multiple of

7

EIt is neither true nor false, because no such

n

exists.

FIt is false, as

n=7

shows.

GIt is true, but only because

7

is prime.

HIt cannot be decided without knowing which integers

n

are allowed.

examday