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


    (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


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


    a^b = a * b
    let b=1
    then a=a
    we can put any integral value of a here so More than 4
    OA= 5


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


    Q15) What is the minimum value of 2x^2 + 3y^2 - 4x - 12y + 18 = 0 for real 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


    Method1-
    partial differentiation
    with respect to x
    4x-4=0 so x=1
    now with respect to y
    6y-12=0 so y=2
    now put x=1 and y=2
    2+12-4-24+18=4
    so OA=4

    Method2-
    try to make perfect square form
    2*(x-1)^2+3*(y-2)^2+4
    so x=1 and y=2 will give us min value


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


    Q16) F(x) and G(x) are two quadratic Functions such that
    F(1) - G(1) = 1
    G(2) - G(2) = 2
    F(3) - G(3) = 5
    Find value of F(4) - G(4)
    a) 8
    b) 9
    c) 10
    d) 12


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


    Method1- f(x)=ax^2+bx+c
    g(x)=dx^2+ex+m
    now f(x)-g(x)=x^2(a-d)+x(b-e)+c-m
    let a-d=M
    b-e=N
    c-m=T
    so f(x)-g(x)= Mx^2+Nx+T
    so M+N+T=1
    4M+2N+T=2
    9M+3N+T=5
    now find M,N,T= M=1 N=-2 and T=2
    so F(x)-g(x)=x^2-2x+2
    so f(4)-g(4)=10

    Quick approach = this is double difference AP if u are aware of this... it will take less than 20 seconds to solve. 1, 2, 5 so next will be 10


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


    Q17) Centroid of triangle is at (1,-1) while its orthocenter is at (5,3) then circumcentre of triangle could be
    a) (-1, -3)
    b) (8/3, 0)
    c) (0, 8/3)
    d) (7/3, 1/3)


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


    Many Methods to tackle this, centroid bisect ortho and circum in 2:1 ratio
    distance between (1,-1) and (5,3) is sqrt(16+16)=sqrt32
    so distance between centroid and circum should be sqrt32/2
    check
    sqrt(4+4)=sqrt8
    so OA= A


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


    Q18) There is a clock that has a special way of telling the time. It does not have any hands or numbers on it, but it has a chimer. If the time is 1 o'clock, it chimes once. If the time is 2 o'clock, it chimes twice, and so forth. The time gap between any two chimes is 4 seconds. How many seconds would it take you to know the time, after the first chime is heard, if it is 11 o'clock?
    a) 40 seconds
    b) 44 seconds
    c) 42 seconds
    d) none of these


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


    40 + extra 4 seconds u have to wait to confirm chimer rung no more
    44 seconds


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


    Q19) In triangle ABC, AB = 3000, BC = 875 and CA = 3125. If I is the in center of the triangle, what is the ratio of AI:ID where AD is angle bisector


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


    Method1- AD is angle bisector
    so AB/AC=BD/CD
    so 3000/3125=BD/CD
    let BD=x then CD=875-x
    so we can find x from here
    now in triangle ABD AI is angle bisector
    so BA/BD=AI/ID
    3000/x=AI/ID

    Alternate -
    AI/ID = (AB+AC)/BC, valid for every triangle
    so ((6125/875)


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


    Q20) The average of three consecutive multiples of 3 is a.
    The average of four consecutive multiples of 4 is a + 27.
    The average of the smallest and largest of these seven integers is 42.
    Determine the value of a.


 

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