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Number Theory PrevQ - Set 0001

  • 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)

  • 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)

  • 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)     

  • 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)          

  • 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)    

  • 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)         

  • (CAT 2005)

  • 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)          

  • (CAT 2003 Retest)

  • 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)