CAT 2003 Slot 1 — QA Question 34
Each question is followed by two statements, A and B. Answer each question using the following instructions
Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.
How many three digit positive integers, with digits x, y and z in the hundred's, ten's and unit's place respectively, exist such that x < y, z < y and x ≠ 0?
Answer & solution
- A
245
- B
285
240
- D
320
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).