CAT 2025 Question Paper | Quant Slot 1

CAT Questions

CAT 2025 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 17 : The number of distinct pairs of integers \((x, y)\) satisfying the inequalities \(x>y \geq 3\) and \(x+y<14\) is

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Video Explanation

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Explanatory Answer

For \(y=3\):
\(4\le x\le10\Rightarrow x\in\{4,5,6,7,8,9,10\}\)   7 pairs

For \(y=4\):
\(5\le x\le9\Rightarrow x\in\{5,6,7,8,9\}\)   5 pairs

For \(y=5\):
\(6\le x\le8\Rightarrow x\in\{6,7,8\}\)   3 pairs

For \(y=6\):
\(7\le x\le7\Rightarrow x\in\{7\}\)   1 pair

Total \(=7+5+3+1=16\)

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The question is " The number of distinct pairs of integers \((x, y)\) satisfying the inequalities \(x>y \geq 3\) and \(x+y<14\) is "

Hence, the answer is '16'

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