# CAT 2020 Question Paper | Quants Slot 3

###### CAT Previous Year Paper | CAT Quants Questions | Question 2

This question is from Number Theory. It discusses about a positive integer N that is a sum of the other two positive integers. We need to find the distinct possible values for N. But there are some restrictions to that. Will you be able to find that out, or will you miss it by a whisker? Let's find that out. Give this question a shot and then check out the video solution of it. A range of questions can be formed from Number Theory. Make sure a get a good hold on this topic by practicing tons of questions CAT Question Paper during your CAT preparation.

Question 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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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.

The question is "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?"

##### Hence, the answer is, "6"

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