IMAS 2015 — Upper Primary Grades 5–6 — Round 2 Question 2

Question 2

The positive integers a, b, c and d are such that $\frac1{a-2013}=\frac1{b+2014}=\frac1{c-2015}=\frac1{d+2016}$ . Which of the following orderings of these four numbers is correct?

$b\lt d\lt a\lt c$
$d\lt b\lt a\lt c$
$d\lt a\lt b\lt c$
$d\lt b\lt c\lt a$
$b\lt d\lt c\lt a$