# CAT Quantitative Aptitude Questions | CAT Number Theory - Digits questions

###### CAT Questions | Number Theory | Three digit number combinations CAT Questions

The question is about Three digit number combinations. Given some conditions about each digit of a three digit number and we need to find out how many the three digit number satisfy those condition. Dealing with digits and base system of a number is a vital component in CAT Number Systems. A range of CAT questions can be asked based on this simple concept in the CAT Exam.

Question 11: How many 3-digit positive integers, with digits a, b and c exist such that a < b and c < b? Assume that a is in hundred's place, b is in ten's place, c is in unit's place and a is a non-zero digit.

1. 450
2. 240
3. 364
4. 648

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##### Method of solving this CAT Question from Number Theory - Digits: Which combinations would satisfy the conditions?

Given conditions are a < b and c < b
If b = 9, a can take any numbers between 1 and 8 and c can take any numbers between 0 and 8
Total combination of such numbers = 8 x 9 = 72
If b = 8, a can take any numbers between 1 and 7 and c can take any numbers between 0 and 7
Total combination of such numbers = 7 x 8 = 56
Similarly add all combinations till b = 1
= 8x9 + 7x8 + 6x7 + 5x6 + 4x5 + 3x4 + 2x3 + 1x2
= 240
Answer = 240 numbers are there

The question is "How many 3-digit positive integers, with digits a, b and c exist such that a < b and c < b?"

##### Hence the answer is 240

Choice B is the correct answer.

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