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CAT 2020 Quant Question [Slot 3] with Solution 17

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?

Option: 6
Solution:

Given, \(2 < x < 10\) and \(14 < y < 23\) \( \Rightarrow 17 < (x + y) < 32\) i.e. \(17 < N < 32\)

But \(N > 25\) hence \(25 < N < 32\)

N can take 6 distinct values.

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