Quant Boosters - Gaurav Sharma - Set 6


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    N = 2^a × 3^b
    Factors of 2N = ( a + 2) ( b + 1)=28
    Factors of 3N = ( a + 1 )( b + 2 )=30
    So a = 5 and b = 3
    So N = 2^5 × 3^3
    Now Factors of 6N ( 2^6 × 3^4 )
    will be 7 × 5 = 35


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q17) If a three digit number ‘abc’ has 3 factors, how many factors does the 6-digit number ‘abcabc’ have?


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q18) Let N = 2^15 * 3^12. How many factors of N^2 are less than N but do not divide N?


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q19) If 2n has 28 factors, 3n has 30 factors, how many factors does 5n have ?


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q20) The sum of the factors of a number is 124. What is the number?
    a) Number lies between 40 and 50
    b) Number lies between 50 and 60
    c) Number lies between 60 and 80
    d) More than one such number exists


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q21) If coordinates of the vertices of a triangle are (2, 0), (6, 0) and (1, 5) then distance between its orthocentre and circumcentre is
    (a) 4
    (b) 6
    (c) 5
    (d) none of these


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q22) Let (a1, a2, a3, ….) be a sequence such that a1 = 2 and an – an-1 = 2n for all n ≥ 2. Then a1 + a2 + …. + a20 is
    (a) 420
    (b) 1750
    (c) 3080
    (d) 3500


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q23) In a class comprising 60 boys and some girls, the average age of boys is 14.8 years and that of girls is 14.1 years. If the average age of the class is 14.7 years, then how many girls are there in the class?
    a) 10
    b) 15
    c) 20
    d) 25


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q24) N is a natural number which has 4 factors. If 10 ≤ N ≤ 70, then how many values are possible for N?
    (a) 19
    (b) 20
    (c) 21
    (d) 22


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q25) The two sequences of numbers {1, 4, 16, 64, ….} and {3, 12, 48, 192, ….} are mixed as follows : {1, 3, 4, 12, 16, 48, 64, 192, ….}. One of the numbers in the mixed series is 1048576. Then the number immediately preceding it is
    (a) 786432
    (b) 262144
    (c) 814572
    (d) 786516


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q26) A, B and C individually can finish a work in 6, 8 and 15 hours respectively. They started the work together and after completing the work got Rs.94.60 in all. When they divide the money among themselves, A, B and C will respectively get (in Rs.)
    (a) 44, 33, 17.60
    (b) 43, 27.20, 24.40
    (c) 45, 30, 19.60
    (d) 42, 28, 24.60


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q27) Two trains are traveling in opposite direction at uniform speed 60 and 50 km per hour respectively. They take 5 seconds to cross each other. If the two trains had traveled in the same direction, then a passenger sitting in the faster moving train would have overtaken the other train in 18 seconds. What are the lengths of trains (in metres)?
    (a) 112, 78
    (b) 97.78, 55
    (c) 102.78, 50
    (d) 102.78, 55


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q28) Remainder when 1^4 + 2^4 + ... + 100^4 is divided by 7.


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q29) Find the largest prime number p such that p^3 divided 2009! + 2010! + 2011!


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q30) How many integers less than 500 can be written as the sum of 2 positive integer cubes?



  • @gaurav_sharma

    a + b + c =10

    => 12c2 => 66



  • @gaurav_sharma

    8c4.....................



  • @gaurav_sharma

    31..................................



  • This post is deleted!


  • @gaurav_sharma

    16 and 24 .................


 

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