Quant Boosters - Swetabh Kumar - Set 3


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    Number of Questions - 30
    Topic - Quant Mixed Bag
    Solved ? - Yes
    Source - Compilation of my solutions from various CAT prep forums.


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    Q1) If N = 2^3 * 3^4 * 5^9, then find the number of trailing zeroes at the end of product of all factors of N which are not divisible by 12.


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    number formed from 2 * 3^3 * 5^9 = 80 factors.
    so product of these = 12^80 * (2 * 3^3 * 5^9)^40 = 2^200 * 3^83 * 5^360.
    total product = (2^3 * 3^4 * 5^9)^(100) = 2^300 * 3^400 * 5^900
    so not divisible ke liye divide the above two.
    2^100 * 3^x * 5^540 so 10^100
    100 trailing zeros.


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    Q2) Let a secret three digit number be cba. If the sum of cab + bac + bca + abc + acb = 2536, what is c+b+a ?


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    221a + 212b + 122c = 2536
    122(a+b+c) + (99a + 90b) = 2536
    2536 mod 9 = 7
    99a + 90b mod 9 = 0
    122(a+b+c) mod 9 = 7
    5(a+b+c) mod 9 = 7
    so : a+b+c = 14 as 70 mod 9 = 7


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    Q3) Find the number of ordered pairs of integers for : x^2 + y^2 - xy = 727


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    x^2 + y^2 - xy = 727
    x^2 - yx + (y^2 - 727 ) = 0
    D = y^2 - 4(y^2 - 727)
    D = 2908 - 3y^2
    2907-3y^2+1 should be a perfect square
    3(969-y^2)+1 should be a perfect square
    clearly y=31 , which gives 2 possible x = 13 and x= 18
    values can be interchanged here :
    y =13 will give x=31 , x=18
    y=18 will also give x=31 , x=13
    same will be possible when all these values are of negative sign
    so total 3 * 2 * 2 = 12 values


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    Q4) Find the maximum power of 12 in C(100,60) ?


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    100! / 60! * 40!
    12 = 2^2 * 3
    max power of 3 in 100! = 100/3+100/9+100/27+100/81 = 33+11+3+1 = 48
    max power of 3 in 60! = 60/3 + 60/9 + 60/27 = 20 + 6 + 2 = 28
    max power of 3 in 40! = 40/3 + 40/9 + 40/27 = 13 + 4 + 1 = 18
    3^48 / 3^28 * 3^18 = ( 3^2 )
    max power of 4 in 100! = 100/4 + 100/16 + 10/64 = 32
    max power of 4 in 60! = 60/4 + 60/16 = 18
    max power of 4! in 40! = 40/4 + 40/16 =12
    2^32 / 2^18 * 2^12 = 2^2
    so highest power is 1


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    Q5) Two motorists set out at the same time to go from A to B, a distance of 100 miles. They both followed the same route and travelled at different, though uniform speeds of an integral number of miles per hour. The difference in their speeds was a prime number of miles per hour and after they had been driving for 2 hours, the distance of the slower car from A was 5 times that of the faster car from B. At what speed did the two motorists drive?


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    Sp and Sq and | Sp - Sq | = prime number
    Sp * 2 = b
    Sq * 2 = 500 - 5b
    10Sp + 2 Sq = 500
    (42, 40) satisfies


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    Q6) If Ap is the sum to the first p terms of the series A = 12^144 + 12^143 + 12^142 + ………, then find Bp, which is the sum to the first p terms of the series A1 + A2 + A3 ...?


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    sum of P terms :
    12^144 + 12^143 +....12^145-P
    12^144 [ 1 - (1/12)^P ] / [ 11/12 ]
    12^145 [ 1 - 1/12^P ] / 11 = Ap
    Bp = A1 + A2 + .... Ap
    12^145 [ 1 - 1/12^P ] / 11
    12^145 / 11 [ 1 - 1/12 + 1-1/12^2+....1/12^P ]
    12^145 / 11 [ 11P/11 - 1/11 + (1/12)^P/11 ]
    12^145/121 [ 11P -1 + (1/12)^P ]


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    Q7) Sara has just joined Facebook. She has 5 friends. Each of her five friends has twenty five friends. It is found that at least two of Sara’s friends are connected with each other. On her birthday, Sara decides to invite her friends and the friends of her friends. How many people did she invite for her birthday party?


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    a0 , b0 , c0 , d0 , e0
    a0 : a1 to a24 + sara
    b0 : b1 to b24+ sara
    c0 : c1 to c24 + sara
    d0 : d1 to d24 + sara
    e0 : e1 to e24+ sara
    2 friends of sara are connected to each other : say a-b
    24 * 5 + 3 = 123
    all five friends are mutual friends
    each has 20 distinct friends and give people a0,b0,c0,d0,e0 : 20 * 5 + 5 = 105


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    Q8) There are two vessels A and B, both containing vinegar solution of 40% concentration. I add some pure vinegar to A to bring the concentration to 50%. In the vessel B, I take out some quantity of the solution and replace it with an equal quantity of pure vinegar, to bring the concentration to 50%. What is the ratio of the amount of vinegar added in A and B, if the quantity of initial solutions in A and B are in the ratio of 1 : 2?


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    For A
    vinegar : 40
    water : 60
    20 ml vinegar added
    conc of vinegar = 50%

    For B
    vinegar =80 + 3x/5
    water = 120-3x/5
    80+3x/5 = 120 - 3x/5
    x = 100/3 ml was added
    20 : 100/3 = 3:5


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    Q9) If Ratio of Cost Price and Mark Price is 5:8 and that of % profit on sale to % discount is 2:3 then find % of Discount


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    profit on sale = profit on SP = Profit/SP *100%
    CP=50, MP=80.
    3 * (SP-50) * 100/SP = 2 * D (D=discount%)
    Also, SP = (1-D/100) * 80 = 80 * (100-D)/100
    so 3 * {80(100-D)/100 -50 } * 100 = 2D * {80 * (100-D)}/100
    150 { 75-2D} = D {200-2D}
    D^2 - 250D + 5625 = 0
    D= (250-200)/2 = 25%


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    Q10) A faulty clock gains 10 minutes every hour. If the time is set correctly at 12 Noon on 1st Jan 2010,then how many times will its minute-hand and hour-hand meet in the next 24 hours ?
    (a) 22
    (b) 26
    (c) 24
    (d) 25


 

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