How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits?

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6 — Easy Write the number as $10x+y$ and its reverse as $10y+x$. Translate &ldquo;more than thrice the reversed number&rdquo; into an inequality, then count the digit pairs $(x,y)$ with $y
e 0$ that satisfy it. 1 Set up the inequality. Let the number be $10x+y$ (tens digit $x$, units digit $y$, $x\ge 1$, $y\ge 1$). $$\begin{aligned} &10x+y > 3(10y+x)\ &\Rightarrow\ 10x+y > 30y+3x\ &\Rightarrow\ 7x > 29y \quad	ext{(collect terms)}\ &\Rightarrow\ x > 	frac{29}{7}\,y \end{aligned}$$ 2 Count for e

CAT 2018 Slot 2 — QA Question 25

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