CAT Questions | CAT Number Systems Questions | Digits

A CAT Number theory question from Number Systems: Digits that appears in the Quantitative Aptitude section of the CAT Exam will consist of concepts from Digits, Test of Divisibility, Perfect squares and so on. In CAT Exam, one can expect to get 1~2 questions from CAT Number Systems: Digits. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.

1. CAT Number Theory: Product of Digits

   How many numbers with distinct digits are possible product of whose digits is 28?
   
   A. 6
   
   B. 4
   
   C. 8
   
   D. 12
   
   

   Correct Answer

   Choice C
   8

   Explanation
   

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2. CAT Number Theory: Sum of first n natural numbers

   A page is torn from a novel. The sum of the remaining page numbers is 10000. What is the sum of the two page-numbers on the torn page of this novel?
   
   A. 77 and 78
   
   B. 33 and 34
   
   C. 8 and 9
   
   D. None of these
   
   

   Correct Answer

   Choice D
   None of these

   Explanation
   

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3. CAT Number Theory: Perfect Square

   A 4-digit number of the form aabb is a perfect square. What is the value of a - b?
   
   A. 3
   
   B. 2
   
   C. 4
   
   D. 1
   
   

   Correct Answer

   Choice A
   3

   Explanation
   

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4. CAT Number Theory: Last two digits

   What are the last two digits of the number 7⁴⁵?
   
   A. 7
   
   B. 23
   
   C. 49
   
   D. 43
   
   

   Correct Answer

   Choice A
   7

   Explanation
   

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5. CAT Number Theory: Multiples

   n² + 5n + 6 is a multiple of 6. n is natural number less than 100. How many values can n take?
   
   A. 33
   
   B. 65
   
   C. 66
   
   D. 67
   
   

   Correct Answer

   Choice C
   66

   Explanation

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6. CAT Number Theory: Greatest integer function

   [x] is the greatest integer less than or equal to x. Find the number of positive integers n such that [] = []
   
   A. 31
   
   B. 25
   
   C. 35
   
   D. 40
   
   

   Correct Answer

   Choice C
   35

   Explanation

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7. CAT Number Theory: Medians, Number

   Positive numbers 1 to 55, inclusive are placed in 5 groups of 11 numbers each. What is the maximum possible average of the medians of the 5 groups?
   
   A. 34
   
   B. 28
   
   C. 35
   
   D. 38
   
   

   Correct Answer

   Choice D
   38

   Explanation

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8. CAT Number Theory: 44^th digit of a number

   N is an 80-digit positive integer (in the decimal scale). All digits except the 44^th digit (from the left) are 2. If N is divisible by 13, find the 44^th digit?
   
   A. 5
   
   B. 6
   
   C. 1
   
   D. 2
   
   

   Correct Answer

   Choice B
   6

   Explanation

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9. CAT Number Theory: Divisibility of powers

   A number 4¹⁶ + 1 is divisible by x. Which among the following is also divisible by x?
   
   A. 4⁹⁶ + 1
   
   B. 4³² + 1
   
   C. 4⁸ + 1
   
   D. 4⁴⁸ + 1
   
   

   Correct Answer

   Choice D
   4⁴⁸ + 1

   Explanation
   

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10. CAT Number Theory: Test of Divisibility

    Which among the following is the smallest 7 digit number that is exactly divisible by 43?
    
    A. 1000043
    
    B. 1000008
    
    C. 1000006
    
    D. 1000002
    
    

    Correct Answer

    Choice B
    1000008

    Explanation
    

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11. CAT Number Theory: Three digit number combinations

    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.
    
    A. 450
    
    B. 240
    
    C. 364
    
    D. 648
    
    

    Correct Answer

    Choice B
    240

    Explanation
    

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