Quant Boosters - Maneesh - Set 1


  • Converted IIM Indore call | Mentor for Banking/RBI/SSC exams


    Number of Questions - 30
    Topic - Quant Mixed Bag
    Solved ? - Yes
    Source -


  • Converted IIM Indore call | Mentor for Banking/RBI/SSC exams


    Q1) N = 2^3 * 3^4 * 5^9
    Find the product of all factors of N which are not divisible by 12


  • Converted IIM Indore call | Mentor for Banking/RBI/SSC exams


    Number of factors = 4 * 5 * 10 = 200
    Product of factors = 2^300 * 3^400 * 5^900
    Number of factors which are divisible by 12 = 2 * 4 * 10 = 80
    Product of factors which are divisible by 12 = 2^40 * 3^120 * 5^360 * 12^80
    Required product = 2^300 * 3^400 *5^900 / 2^40 * 3^120 * 5^360 * 2^160 *3^80
    = 2^100 * 3^200 * 5^540


  • Converted IIM Indore call | Mentor for Banking/RBI/SSC exams


    Q2) N = 2^15 * 3^12 How many factors of N^2 are less than N but do not divide N completely?


  • Converted IIM Indore call | Mentor for Banking/RBI/SSC exams


    Factors of N = 16 * 13 = 208
    Factors of N less than N = 208 - 1 = 207
    Factors of N^2 = 31 * 25 = 775
    Factors of N^2 less than N = (775 - 1)/2 = 387
    So ans = 387 – 207 = 180


  • Converted IIM Indore call | Mentor for Banking/RBI/SSC exams


    Q3) The numbers 2604,1020 and 4812 when divided by a number N give the same remainder of 12. Find the highest such number N


  • Converted IIM Indore call | Mentor for Banking/RBI/SSC exams


    Since all the numbers are giving remainder 12, (2604-12),(1020-12),(4812-12) are multiples of N
    2592, 1008, 4800
    So N will be HCF of 2592,1008 and 4800
    2592 = 2^5 * 3^4
    1008 = 2^4 * 7 * 3^2
    4800 = 2^6 * 5^2 * 3
    HCF = 2^4 * 3 = 48


  • Converted IIM Indore call | Mentor for Banking/RBI/SSC exams


    Q4) The numbers 400,536 and 645 when divided by a number N gave remainders of 22,23 and 24 respectively.Find the greatest such number N


  • Converted IIM Indore call | Mentor for Banking/RBI/SSC exams


    N will be the HCF of (400-22),(536-23) and (645-24)
    HCF(378,513,621) = 27


  • Converted IIM Indore call | Mentor for Banking/RBI/SSC exams


    Q5) The HCF of two numbers is 12 and their sum is 288. How many pairs of such numbers are possible?


  • Converted IIM Indore call | Mentor for Banking/RBI/SSC exams


    Let numbers be 12a, 12b
    12(a+b) = 288
    a+b = 24 and a and b are co prime
    Hence(1,23)(5,19)(7,17)(11,13)
    Hence 4 pairs available.


  • Converted IIM Indore call | Mentor for Banking/RBI/SSC exams


    Q6) HCF of 2 numbers are 12 and their product is 31104. How many such numbers are possible?


  • Converted IIM Indore call | Mentor for Banking/RBI/SSC exams


    Let numbers are 12a n 12b
    144ab = 31104
    ab = 216
    a and b are coprime
    (1,216)(8,2)
    Only two pairs possible.


  • Converted IIM Indore call | Mentor for Banking/RBI/SSC exams


    Q7) Find the Highest five digit number that is divisible by each of the numbers 24, 36, 45 and 60?


  • Converted IIM Indore call | Mentor for Banking/RBI/SSC exams


    LCM (24,36,45,60) => 24 = 2^3 * 3
    36 = 3^2 * 2^2
    45 = 3^2 * 5
    60 = 2^2 * 3 * 5
    LCM = 2^3 * 3^2 * 5 = 360
    So we have to find highest five digit multiple of 360
    99999 mod 360 = 279
    so answer 99999-279 = 99720


  • Converted IIM Indore call | Mentor for Banking/RBI/SSC exams


    Q8) Find the lowest number which gives a remainder of 5 when divided by any of the numbers 6, 7, 8 ?


  • Converted IIM Indore call | Mentor for Banking/RBI/SSC exams


    LCM(6, 7, 8) = 168
    number = 168 + 5 = 173


  • Converted IIM Indore call | Mentor for Banking/RBI/SSC exams


    Q9) What is the smallest number which when divided by 9,18 and 24 which leaves a remainder of 5, 14 and 20 respectively


  • Converted IIM Indore call | Mentor for Banking/RBI/SSC exams


    Q10) In a book store “OM INNOVATIVE BOOK STORE“ is flashed using neon lights. The words are individually flashed at intervals of 8/3, 16/3 , 14/3 and 15/2 seconds respectively and each word is put off after a second. The least time after which the full name of the book store can be read for a second?


  • Converted IIM Indore call | Mentor for Banking/RBI/SSC exams


    Q11) A number when divided by 3, 4, 5 and 6 always leave a remainder 2, but leaves no remainder when divided by 7. What is the lowest such number possible?


Log in to reply
 

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