Let N, x and y be positive integers such that N - Quantitative Aptitude - CAT Equation
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The question below is from previous year CAT question from CAT 2020 exam comes from CAT Equation : Q.2. 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 ?
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CAT 2020 - Slot 3 - Quantitative Aptitude - Equation - Question 2 - Let N, x and y be positive integers such that N
Q. 2: 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 ?
Correct Answer: 6
2 < x < 10
x can take any of the values from the set {3, 4, 5, 6, 7, 8, 9}
14 < y < 23
y can take any of the values from the set {15, 16, 17, 18, 19, 20, 21, 22}
The highest value N (i.e x+y) can take = 9+22 = 31. (at x = 9; y = 22)
30 can be obtained at x = 9; y = 21
29 can be obtained at x = 9; y = 20
28 can be obtained at x = 9; y = 19
27 can be obtained at x = 9; y = 18
26 can be obtained at x = 9; y = 17
25 can be obtained at x = 9; y = 16
But, x+y=25 is not the desired sum, hence the different values of x+y are {31,30,29,28,27,26}.
Hence, x+y, and thereby N can take 6 distinct values.
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