Let N, x and y be positive integers such that N = x + y, 2

Question

Let N, x and y be positive integers such that N = x + y, 2 < x < 10 and 14 < y < 23. If N > 25, then how many distinct values are possible for N?

Accepted Answer

6 — Easy List the integer ranges of $x$ and $y$ to get the maximum possible $N=x+y$. Since $N$ can take every integer up to that maximum, just count the integers exceeding $25$. 1 Integer ranges. From $2 $$\begin{aligned} &x\in\{3,4,\dots,9\},\qquad x_{\max}=9\ &y\in\{15,16,\dots,22\},\qquad y_{\max}=22 \end{aligned}$$ 2 Maximum of $N$. $$\begin{aligned} &N_{\max}=x_{\max}+y_{\max}=9+22=31 \end{aligned}$$ Every integer from the minimum up to $31$ is attainable, so once $N>25$ the possible values ar

CAT 2020 Slot 3 — QA Question 15

Answer & solution