CAT Practice : Number System

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Three digit number combinations

    Q.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


  • Correct Answer
    Choice B. 240 numbers

Detailed Solution

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

Correct Answer: Choice B

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More questions from Number System

  1. Product of digits
  2. Sum of first n natural numbers
  3. Perfect Square
  4. Last two digits
  5. Multiples
  6. Greatest integer function
  7. Medians, Number
  8. 44th digit of a number
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