If x and y are non-negative integers such that x + 9 = z, y + 1 = z and x + y

Question

If x and y are non-negative integers such that x + 9 = z, y + 1 = z and x + y < z + 5, then the maximum possible value of 2x + y equals

Accepted Answer

23 — Easy Express $x$ and $y$ in terms of $z$ using the two equalities, feed them into the inequality to bound $z$, then write $2x+y$ as a linear function of $z$ and use the largest allowed integer $z$. 1 Express in terms of $z$. From the two equations: $$\begin{aligned} &x = z - 9,\qquad y = z - 1 \end{aligned}$$ 2 Apply the inequality. Substitute into $x+y $$\begin{aligned} &(z-9)+(z-1) Also $x=z-9\ge 0$ requires $z\ge 9$, so $z$ is an integer with the largest value $14$. 3 Maximise $2x+y$. Write i

CAT 2020 Slot 2 — QA Question 6

Answer & solution

Related Number Theory questions