Number Theory Previous Year Questions (CAT) - Set 0023


  • Content & PR team - MBAtious


    Previous years`s CAT questions: Number Theory

    Post your solutions as reply to respective questions below.


  • Content & PR team - MBAtious


    Question 1

    For real numbers x, y, let

    f(x, y) = Positive square-root of (x + y), if (x + y)0.5 is real

                = (x + y)2, otherwise

    g(x, y) = (x + y)2, if (x + y)0.5 is real

                 = –(x + y), otherwise

    Under which of the following conditions is f(x, y) necessarily greater than g(x, y)?

    (1) Both x and y are less than –1

    (2) Both x and y are positive

    (3) Both x and y are negative

    (4) y > x                 (CAT 2000)


  • Content & PR team - MBAtious


    Answer: Option 1


  • Content & PR team - MBAtious


    Question 2

    For a real number x,

    let f(x) = 1/(1 + x), if x is non-negative

                 = 1+ x, if x is negative

    f n(x) = f(f n – 1(x)), n = 2, 3, ....

    r is an integer > 2. Then, what is the value of f r – 1(–r) + f r(–r) + f r + 1 (–r) ?

    (1) -1

    (2) 0

    (3) 1

    (4) None of these   (CAT 2000)


  • Content & PR team - MBAtious


    Answer: Option 2


  • Content & PR team - MBAtious


    Question 3

    For two positive integers a and b define the function h(a,b) as the greatest common factor (G.C.F) of a, b. Let A be a set of n positive integers. G(A), the G.C.F of the elements of set A is computed by repeatedly using the function h. The minimum number of times h is required to be used to compute G is

    a. n/2

    b. (n – 1)

    c. n

    d. None of these         (CAT 1999)


  • Content & PR team - MBAtious


    Question 4


  • Content & PR team - MBAtious


    Question 5


  • Content & PR team - MBAtious


    Question 6


  • Content & PR team - MBAtious


    Question 7

    I have one-rupee coins, 50-paisa coins and 25-paisa coins.

    The number of coins are in the ratio 2.5 : 3 : 4

    If the total amount with me is Rs. 210, find the number of one-rupee coins.

    a. 90

    b. 85

    c. 100

    d. 105    (CAT 1998 )


  • Content & PR team - MBAtious


    Question 8

    In a locality, there are five small cities: A, B, C, D and E. The distances of these cities from each other are as follows.

    AB = 2 km AC = 2km AD > 2 km AE > 3 km BC = 2 km

    BD = 4 km BE = 3 km CD = 2 km CE = 3 km DE > 3 km 

    If a ration shop is to be set up within 2 km of each city, how many ration shops will be required?

    a. 2  

    b. 3  

    c. 4  

    d. 5  (CAT 1996)


  • Content & PR team - MBAtious


    Question 9

    In a locality, there are five small cities: A, B, C, D and E. The distances of these cities from each other are as follows.

    AB = 2 km AC = 2km AD > 2 km AE > 3 km BC = 2 km

    BD = 4 km BE = 3 km CD = 2 km CE = 3 km DE > 3 km 

    If a ration shop is to be set up within 3 km of each city, how many ration shops will be required?

    a. 1  

    b. 2  

    c. 3  

    d. 4  (CAT 1996)


  • Content & PR team - MBAtious


    Question 10

    A student gets an aggregate of 60% marks in five subjects in the ratio 10 : 9 : 8 : 7 : 6. If the passing marks are 50% of the maximum marks and each subject has the same maximum marks, in how many subjects did he pass the examinaiton?

    a. 2

    b. 3

    c. 4

    d. 5   (CAT 1997)


Log in to reply
 

Looks like your connection to MBAtious was lost, please wait while we try to reconnect.