Number Theory Previous Year Questions (CAT) - Set 0021


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    Question 4


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    Answer: Option 1


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    Question 5


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    Answer: Option 3


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    Question 6

    Ashish is given Rs. 158 in one rupee denominations. He has been asked to allocate them into a number of bags such that any amount required between Re. 1 and Rs. 158 can be given by handing out a certain number of bags without opening them. What is the minimum number of bags required?

    (1) 11

    (2) 12

    (3) 13

    (4) None of these  (CAT 2001) 


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    Answer: Option 4


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    Question 7

    In some code, letters, a, b, c, d and e represent numbers 2, 4, 5, 6 and 10. However, we don’t know which letter represent which number.

    Consider the following relationships:

    i. a + c = e

    ii. b – d = d

    iii. e + a = b

    (1) b = 4, d = 2

    (2) a = 4, e = 6

    (3) b = 6, e = 2

    (4) a = 4, c = 6   (CAT 2001)


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    Answer: Option 2


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    Question 8

    A change making machine contains 1 rupee, 2 rupee and 5 rupee coins. The total number of coins is 300. The amount is Rs. 960. If the number of 1 rupee coins and the number of 2 rupee coins are interchanged, the value comes down by Rs. 40. The total number of 5 rupee coins is

    (1) 100

    (2) 140

    (3) 60

    (4) 150  (CAT 2001) 


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    Answer: Option 2


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    Question 9

    Let n be the number of different 5 digit numbers, divisible by 4 with the digits 1, 2, 3, 4, 5 and 6, no digit being repeated in the numbers. What is the value of n?

    (1) 144

    (2) 168

    (3)192

    (4) None of these   (CAT 2001) 


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    Answer: Option 3


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    Question 10

    New Age Consultants have three consultants Gyani, Medha and Buddhi. The sum of the number of projects handled by Gyani and Buddhi individually is equal to the number of projects in which Medha is involved. All three consultants are involved together in 6 projects. Gyani works with Medha in 14 projects. Buddhi has 2 projects with Medha but without Gyani and 3 projects with Gyani but without Medha. The total number of projects for New Age Consultants is one less than twice the number of projects in which more than one consultant is involved. 

    What is the number of projects in which Gyani alone is involved?

    (1) Uniquely equal to zero

    (2) Uniquely equal to 1

    (3) Uniquely equal to 4

    (4) Cannot be determined uniquely

    What is the number of projects in which Medha alone is involved?

    (1) Uniquely equal to zero

    (2) Uniquely equal to 1

    (3) Uniquely equal to 4

    (4) Cannot be determined uniquely  (CAT 2003 Leaked) 


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    Answer: Option 4 Option 2


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