Number Theory Previous Year Questions (CAT) - Set 0001


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    Previous years`s CAT questions: Number Theory

    Post your solutions as reply to respective questions below.


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    Question 1

    Which among  21/2,  31/3,  41/4,  61/6,  121/12 is the largest?

    a.   2 1/2

    b.   3 1/3

    c.   4 1/4

    d.   6 1/6

    e.   12 1/12    

    (CAT 2006)


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    Answer: Option b


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    Question 2

    If x = − 0.5, then which of the following has the smallest value?        

    a.   2 1/x

    b.   1/x

    c.   1/x2

    d.   2 x

    e.   1/ √-x         

    (CAT 2006)


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    Answer: Option b


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    Question 3

    If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4

    then what is the value of abc/def

    (1) 3/8

    (2) 27/8

    (3) 3/4

    (4) 27/4

    (5) 1/4            

    (CAT 2006)     


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    Answer: Option 1


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    Question 4

    Consider a sequence, where the nth term is tn = n/ (n+2) , n = 1, 2….

    The value of t3 * t4 * t5 * … t53 is

    (1) 2/495

    (2) 2/477

    (3) 12/55

    (4) 1/1485

    (5) 1/2970   

    (CAT 2006)          


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    Answer: Option 1


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    Question 5

    A group of 630 children is arranged in rows for a group photograph session. Each row contains three fewer children than the row in front of it. What number of rows is not possible?

    (1) 3

    (2) 4

    (3) 5

    (4) 6

    (5) 7       

    (CAT 2006)    


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    Answer: Option 4


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    Question 6

    What are the values of x and y that satisfy both the equations?

    2 0.7x * 3 -1.25y   = 8 √6 / 27

    4 0.3x * 9 0.2y = 8 * (81)1/5

    (1) x = 2, y = 5

    (2) x = 2.5, y = 6

    (3) x = 3, y = 5

    (4) x = 3, y = 4

    (5) x = 5, y = 2        

    (CAT 2006)         


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    Answer: Option 5


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    Question 7

    (CAT 2005)


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    Answer: Option 3


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    Question 8

    The sum of four consecutive two digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?

    (1) 21

    (2) 25

    (3) 41

    (4) 67      

    (CAT 2006)          


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    Answer: Option 3


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    Question 9

    (CAT 2003 Retest)


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    Answer: Option 3


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    Question 10

    Consider the set S = {1, 2, 3, …., 1000}. How many arithmetic progressions can be formed from the elements of S that start with 1 and with 1000 and have at least 3 elements?

    (1) 3

    (2) 4

    (3) 6

    (4) 7

    (5) 8      

    (CAT 2006)


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