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CAT 2015 Quantitative Ability
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© examsnet.com
Question : 14
Total: 34
Let P be the set of all odd positive integers such that every element in P satisfies the following conditions.
I. 100 ≤ n< 1000
II. The digit at the hundred's place is never greater than the digit at tens place and also never less than the digit at units place.
How many elements are there in P?
93
94
95
96
Validate
Solution:
Let n be xyz and since n is odd z can take only odd values i.e. 1, 3, 5 and 9 Now, x ≤ y and x ≥ z
Possible values
x
y
z
n
1
1,2,3,4,...9
1
9
2
2,3,..9
1
8
3
3,4..9
1,3
14
4
4,5,...9
1,3
12
5
5,6..9
1,3,5
15
6
6,7...9
1,3,5
12
7
7,8..9
1,3,5,7
12
8
8,9
1,3,5,7
8
9
9
1,3,5,7,9
5
∴ Total number of elements in P = 95.
© examsnet.com
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