CAT 2003 Slot 1 — QA Question 34

x, y and z are at hundred’s , ten’s and unit's position in a three digit number.

Both x and z have to be less than y.

When y = 9, then x can take values from 1 to 8 and z can take values from 0 to 8.

∴ Total number of ways in which this number can be written when y is 9 = 8 × 9 = 72

The table given below represents the number of ways of writing this number for all possible values of y from 2 to 9.

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∴ Total number of ways = 72 + 56 + 42 + 30 + 20 + 12 + 6 + 2 = 240

Hence, option (c).