tmua.fyi Paper 2 Challenge 2 · Question 16

Let $S$ be a set of ten distinct positive integers, each less than $100$ . Which of the following must be true?

S

contains two elements whose sum is

100

S

contains three elements in arithmetic progression.

S

contains two elements whose difference is

10

DThe elements of

S

have sum at least

100

S

has two disjoint non-empty subsets with the same sum.

S

contains two elements, one of which divides the other.

S

contains a multiple of

10

HThe largest element of

S

is at least

55

examday