Official Quant thread for CAT 2013

@arnabdutta77 said:
if p,q,r are in ap then 1/p,1/q,1/r are in H.P.If the squares of p,q,r are in hp then the terms are 1/p^2,1/q^2 & 1/r^2 which implies p^2,Q^2 & r^2 are in a.p. Am I interpreting the question wrong??
then 1/p^2,1/q^2 & 1/r^2 are in AP
@arnabdutta77 said:
if p,q,r are in ap then 1/p,1/q,1/r are in H.P.If the squares of p,q,r are in hp then the terms are 1/p^2,1/q^2 & 1/r^2 which implies p^2,Q^2 & r^2 are in a.p. Am I interpreting the question wrong??
buddy, its not sayngi that the inverse of thethe square of the nos are in hp. it says their squares are in hp so, 1/p^2 , 1/q^2 and 1/r^2 are in ap
@Estallar12 max area of a square that can fit in a isoceles triangle? how to solve?
A set of data consists of the following 5 numbers: 0,2,4,6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers? (A) -1 and 9 (B) 4 and 4 (C) 3 and 5 (D) 2 and 6 (E) 0 and 8
@vikranth504 said:
@Estallar12 max area of a square that can fit in a isoceles triangle? how to solve?
Need more info on isosceles triangle.
If the question is max area of a square that can fit in an equilateral triangle of side say a cm__?

Then draw a sqaure of side x inside and use tan60=root(3)
Get x/root(3) + x x/root(3) = a
and now we solve and get x=?
@grkkrg said:
(2) 2532 7/24 = 775/24The number of consecutive number is 24k (+ 1)25/2 ( 2a + 25 - 1) > 77525 ( 2a + 24) > 1550(2a + 24) > 622a > 38a > 19a = 2025/2 ( 40 + 24) = 800800 - 775 = 25
plz explain 25/2 (2a + 25 -1)>775 this step

x^2 + bx + c =0
is Sum of roots is greater den product of roots ?

a) b is not greater den c
b) b & c are positive integers

either/neither/1st/2nd/both
can u tell me dis one sir ?

q(x) is aquadratic eqn in x . it has a min. value of -28 when x=-3 . it has avalue of -10 when x=0 . find its value when x=4.

a) 55
b) 60
c)65
d)70
@bs0409
D
@bs0409
D
@Cat.Aspirant123
EITHER
@raopradeep said:
plz explain 25/2 (2a + 25 -1)>775 this step
I took k = 1
LHS represents sum of 25 terms of the AP
Since the average of 24 numbers is 775/24
the sum of 24 numbers is 775 (assuming k = 1)
and the sum of 25 number is greater than 775.

@raopradeep said:
q(x) is aquadratic eqn in x . it has a min. value of -28 when x=-3 . it has avalue of -10 when x=0 . find its value when x=4.a) 55b) 60c)65d)70
Let f(x)=ax^2+bx+c
Now at x=0 value is 10 so c=-10
Minimum value occurs at x= -b/2a = -3 => b=6a
And f(-3)=-28=> 9a-3b-10=-28=>b-3a=6
SOlve the 2 equations and get a=2 and b=12
Now f(4) = 70
@ishu1991 said:
@Cat.Aspirant123EITHER
OA is BOTH together
@raopradeep
D
@raopradeep said:
q(x) is aquadratic eqn in x . it has a min. value of -28 when x=-3 . it has avalue of -10 when x=0 . find its value when x=4.a) 55b) 60c)65d)70
should be 70...
let the equation be ax^2+bx+c
for min value find the d/dx of the eqn
2ax+b=0
so min occurs at x=-b/2a
-3=b/2a
b=6a
also for x=0, c=-10
q(x)=ax^2+bx-10
q(-3)=9a-3b-10
9a-3b=-18
3a-b=-6
3a-6a=6
so a=2 and b=12
q(4) = 70
@raopradeep said:
q(x) is aquadratic eqn in x . it has a min. value of -28 when x=-3 . it has avalue of -10 when x=0 . find its value when x=4.a) 55b) 60c)65d)70
q(x)=ax^2+bx+c
at x=0 ...c=-10
now min value at x=-b/2a
-3=-b/2a
b=6a
q(-3)=9a-3b-10=-28
a=2..b=6*2=12
q(4)=2(4)^2+12(4)-10=70?
@Cat.Aspirant123
If i take secnd statement where both are positive
sum of roots is -b and product of roots is c so here we can sum of roots can never be grtr than product of roots so we can answer here no
@Cat.Aspirant123 said:
x^2 + bx + c =0 is Sum of roots is greater den product of roots ?a) b is not greater den cb) b & c are positive integerseither/neither/1st/2nd/bothcan u tell me dis one sir ?
both the statements together....coz from (1) we can get prod=sum. eg- (x-2)^2
hence we require both the statements...
@Logrhythm
how product is equal to sun suppose if u take b=2 and c=2 then still sum of roots is -b and product of roots is c still -b is less than c