Quant Boosters - Hemant Malhotra - Set 6


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Method1- c.p.100
    m.p.125
    sp..125 * 7/8==109.375
    so profit==9.37%

    Method2- let CP=1
    MP=1+1/4=5/4
    and 12.5%=1/8 discount
    so 5/4 * 7/8=35/32
    so profit=35/32-1=3/32 * 100=9.37%


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q5) A car leaves P at 8 AM and travels to Q at a constant speed. A bus leaves Q at 8:45 AM and travels to P at a speed three times that of the car. If they meet at 10:00 AM, find the ratio of the distance traveled by the bus to the distance traveled by the car when they meet.


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    S = speed of car
    D1 = distance of car
    D2 = distance bus
    D1=2s
    D2=(2-3/4)(3s)
    D2=15/4s
    D1:D2
    2s:15/4s
    Ratio is 8:15


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q6) A, B and C start simultaneously from X to Y. A reaches Y, turns back and meet B at a distance of 11 km from Y. B reached Y, turns back and meet C at a distance of 9 km from Y. If the ratio of the speeds of A and C is 3:2, what is the distance between X and Y


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Let a, b, c are the speeds of A, B, C respectively;
    let x be the distance between X and Y. Note that speed is proportional to distance.
    We have
    a/b = (x+11)/(x-11) and b/c = (x+9)/(x-9) and a/c = 3/2,
    (x+11)/(x-11) * (x+9)/(x-9) = (a/b)(b/c) = a/c = 3/2,
    2(x^2+20x+99) = 3(x^2-20x+99),
    x^2-100x+99 = 0,
    (x-1)(x-99) = 0.
    bcz x > 11, so x = 99 km.


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q7) A beaker contained V litres of a mixture of milk and water, with milk and water in the ratio of 3 : 2. The total volume of the mixture was increased by 60% by adding water. Next, 38.4 litres of the solution in the beaker was replaced by water. If the final ratio of milk and water in the beaker is 3:7, then find the value of V (in litres)
    a) 80
    b) 96
    c) 120
    d) 192


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Milk=3v/5
    and water=2v/5 +(v * 60/100)=2v/5+3v/5=v
    now 38.4 liter removed
    so MF=(8v/5 -38.4)/(8v/5)
    so milk=3v/5 * (8v/5 -38.4)/(8v/5)'
    now equate to ratio and answer = 192 x 5/8 = 120


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q8) In how many ways can 6 letters A, B, C, D, E and F be arranged in a row such that D is always somewhere between A and B?
    a) 324
    b) 240
    c) 60
    d) 48


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    ways to arrange D,A,B =3! but we need A,D,B or B,A ,D so out of 3! , 2 favorable cases , so out of 6! we have 2/3! * 6! = 6 * 5 * 4 * 2 = 240


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q9) Raju has forgotten his six-digit id number, he remembers the following: the first two digits are either 1,5 or 2,6,the number is even and 6 appears twice. If Raju uses a trial and error process to find his ID number at the most, how many trial does he need to succeed?


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    when 1,5 at first two place
    then last four places a b c d
    when d=6 then out of 3 places one place will be filled by 6 so 3c1 and rest two have 9 choices so
    3c1 * 9 * 9 = 243
    now when d=0/2/4/8 so 4 choices so out of 3 places 2 places will be filled by 6 and one place have 9 choices so 3c2 * 9 * 4 = 108
    now when 2,6 at first two places then d=6 then other 3 places have 9 * 9 * 9 = 729 choices
    and when d=0/2/4/8 then one place should have 6 and rest 2 places have 9 choices so 4 * 3c1 * 9 * 9 = 972
    so sum=2052


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q10) If average of 20 double digit numbers is 18 , but becomes 21.8 when we interchange digits of a no , then how many original no's are possible ?


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    (10a1+b1+10a2+b2+....10a20+b20)=360
    10(a1+a2+a3+...a20)+(b1+b2+...b20)=360
    now
    10*(b1+b2+b3+...b20)+(a1+a2+a3...a20)= 436.0
    so 9(b1+b2+...b20)-9(a1+a2+....a20)=76
    so this is factor of 9 so not possible case


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q11) Find numerically the largest term in the expansion of (2+3x)^9 when x=3/2


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    (n-r+1)/(r) * (a/x) >= 1
    (10-r)/r * (3x/2) >= 1
    (10-r)/r * (9/4)>= 1
    90-9r > = 4r
    so 13r < = 90
    r < = 6.9
    so r = 6
    so 7th term


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q12) If a quadrilateral with sides 2, 3, 4 and 5 is inscribed in a circle and circumscribed to another circle then
    find area of Quadrilateral


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Direct formula : If any quadrilateral with sides a, b, c and d inscribed in a circle and circumscribed to another circle then area of quadrilateral is sqrt(abcd). So here answer is sqrt(120)


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q13) Find remainder when 1^99 + 2^99 + 3^99 + .... + 99^99 is divided by 100


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    1 to 99 there are 99 terms
    1^99+99^99 will be div by 100
    2^99+98^99 will be div by 100
    now 49^99+51^99 mod 100=0
    but there will be one more term
    50^99 mod 100
    which is also divisible by 100
    so OA=0


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q14) How many integral solutions (a,b) does the equation a^b=a * b have
    a) 1
    b) 2
    c) 3
    d) 4
    e) More than four


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