CAT Questions | CAT Number Systems Questions

A CAT Number systems question that appears in the Quantitative Aptitude section of the CAT Exam broadly tests an aspirant on the concepts - factors, HCF and LCM, base system & remainders of the above mentioned concepts. In CAT Exam, one can generally expect to get 1~2 questions from CAT Number Systems: HCF-LCM. In multiple places, extension of HCF and LCM concepts are tested by CAT Exam and one needs to understand HCF-LCM to be able to answer the same. CAT Number theory is an important topic with lots of weightage in the CAT Exam. 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: - HCF LCM

   How many pairs of integers (x, y) exist such that the product of x, y and HCF (x, y) = 1080?

   1. 8
   2. 7
   3. 9
   4. 12

   Correct AnswerChoice C
   9

   Explanation

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2. CAT Number Theory - Remainders LCM

   Find the smallest number that leaves a remainder of 4 on division by 5, 5 on division by 6, 6 on division by 7, 7 on division by 8 and 8 on division by 9?

   1. 2519
   2. 5039
   3. 1079
   4. 979

   Correct AnswerChoice A
   2519

   Explanation

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3. CAT HCF LCM - Theory

   There are three numbers a,b, c such that HCF (a, b) = l, HCF (b, c) = m and HCF (c, a) = n. HCF (l, m) = HCF (l, n) = HCF (n, m) = 1. Find LCM of a, b, c. (The answer can be "This cannot be determined").

   Correct AnswerCannot be determined

   Explanation

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4. CAT HCF basics

   How many pairs of positive integers x, y exist such that HCF of x, y = 35 and sum of x and y = 1085?
   

   1. 12
   2. 8
   3. 15
   4. 30

   Correct AnswerChoice C
   15

   Explanation

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5. CAT HCF-LCM

   How many pairs of positive integers x, y exist such that HCF (x, y) + LCM (x, y) = 91?

   1. 10
   2. 8
   3. 6
   4. 7

   Correct AnswerChoice B
   8

   Explanation

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6. CAT HCF: Basics

   Sum of two numbers x, y = 1050. What is the maximum value of the HCF between x and y?

   1. 350
   2. 700
   3. 1050
   4. 525

   Correct AnswerChoice D
   525

   Explanation

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7. CAT Number System: HCF basics

   The sum of two non co–prime numbers added to their HCF gives us 91. How many such pairs are possible?

   1. 2
   2. 4
   3. 3
   4. 6

   Correct AnswerChoice C
   3

   Explanation Video Solution

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8. CAT Number System: HCF LCM basics

   There are 2 numbers such that a > b, HCF (a, b) = h and LCM (a, b) = l. What is the LCM of a – b and b?

   1. l
   2. (a - b) b
   3. (a - b) b / h
   4. h (a - b)

   Correct AnswerChoice C
   (a - b) b / h

   Explanation

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9. CAT Number Systems: No of sweet boxes

   6 different sweet varieties of count 32, 216, 136, 88, 184, 120 were ordered for a particular occasion. They need to be packed in such a way that each box has the same variety of sweet and the number of sweets in each box is also the same. What is the minimum number of boxes required to pack?

   1. 129
   2. 64
   3. 48
   4. 97

   Correct AnswerChoice D
   97

   Explanation

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10. CAT Number Systems: Minimum number of students

    In a large school auditorium, the students are made to sit to watch the programmes. If the teachers make a row of students of 16 each, there will be 12 students left. If they make rows of 24 each, then there will be 20 students left, if they make rows of 25 each, there will be 21 students left and if they make rows of 30 each, there will be 26 students left. What is the minimum number of students present in the school?

    1. 1216
    2. 1784
    3. 1196
    4. 2396

    Correct AnswerChoice C
    1196

    Explanation

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11. CAT Number Systems: Sum of the digits

    LCM of 2 natural numbers p and q where p > q is 935. What is the maximum possible sum of the digits of q?

    1. 1
    2. 16
    3. 8
    4. 2

    Correct AnswerChoice B
    16

    Explanation

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12. CAT Number Systems: Number of Carpenters

    4 logs of woods of lengths 5 1/4 m, 1 13/15 m, 3 1/2 m and 4 9/10 m are cut into small pieces, all of which have equal length. Each piece of wood is as lengthy as possible. Each cut piece is given to a set of 2 carpenters to work on something. How many carpenters are there in all to work?

    1. 148
    2. 210
    3. 332
    4. 266

    Correct AnswerChoice D
    266

    Explanation

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The Questions that follow, are from actual IPMAT papers. If you wish to take them separately or plan to solve actual IPMAT papers at a later point in time, It would be a good idea to stop here.

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1. IPMAT 2020 Sample Paper - IPM Rohtak Quants

   Find the HCF of \\frac{2}{3}, \frac{4}{6}, \frac{8}{27}\\)

   1. \\frac{2}{27}\\)
   2. \\frac{8}{3}\\)
   3. \\frac{2}{3}\\)
   4. \\frac{8}{27}\\)

   Correct AnswerChoice A
   \\frac{2}{27}\\)

   Explanation

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