CAT Quantitative Ability Questions | CAT Number System questions
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CAT/2020.3
Question . 20
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?
Explanatory Answer
Method of solving this CAT Quantitative Ability Question from Number System question
Correct Answer : 6
To find the distinct values possible for N, we need to consider the ranges of x and y and determine the valid combinations.
Given that 2 < x < 10 and 14 < y < 23, we can analyze the possible values of N based on the given conditions.
First, let's consider the minimum values of x and y: x = 3 and y = 15.
In this case, N = 3 + 15 = 18, which is less than 25.
Next, let's consider the maximum values of x and y: x = 9 and y = 22.
In this case, N = 9 + 22 = 31, which is greater than 25.
Since N needs to be greater than 25, we need to find the range of x and y values that satisfy this condition.
For x = 4 to 9 (inclusive), the minimum value of y is 14 + 2 = 16 (since y > 14), and the maximum value of y is 14 + 9 = 23 (since y < 23).
Therefore, for each value of x from 4 to 9, there is a distinct value of y that satisfies the given conditions, resulting in a distinct value of N.
Hence, there are 6 distinct values possible for N (corresponding to the 6 values of x from 4 to 9).
Therefore, the answer is 6.
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