Quant Boosters  Hemant Malhotra  Set 6

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q11) Find numerically the largest term in the expansion of (2+3x)^9 when x=3/2

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
(nr+1)/(r) * (a/x) >= 1
(10r)/r * (3x/2) >= 1
(10r)/r * (9/4)>= 1
909r > = 4r
so 13r < = 90
r < = 6.9
so r = 6
so 7th term

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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)

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q13) Find remainder when 1^99 + 2^99 + 3^99 + .... + 99^99 is divided by 100

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Method1
partial differentiation
with respect to x
4x4=0 so x=1
now with respect to y
6y12=0 so y=2
now put x=1 and y=2
2+12424+18=4
so OA=4Method2
try to make perfect square form
2*(x1)^2+3*(y2)^2+4
so x=1 and y=2 will give us min value

hemant_malhotra last edited by hemant_malhotra
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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(ad)+x(be)+cm
let ad=M
be=N
cm=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^22x+2
so f(4)g(4)=10Quick 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

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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)

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
40 + extra 4 seconds u have to wait to confirm chimer rung no more
44 seconds

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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=875x
so we can find x from here
now in triangle ABD AI is angle bisector
so BA/BD=AI/ID
3000/x=AI/IDAlternate 
AI/ID = (AB+AC)/BC, valid for every triangle
so ((6125/875)

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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.