Official Quant thread for CAT 2013

@amresh_maverick said:
Given that f(x) = ax^2 + bx + c and f(4) = 100. If a, b, c are distinct positive integers, then the maximum possible value of a + b + c is a 79 b 87 c 122 d 82 e Data Insufficient
ans: 79

f(4)=16a+4b+c=100


for maximum sum of a, b, c,, the variables(here a,b,c are considered to be variables) with higher coefficient should have minimum value.
so, we have to assume a=1(lowest possible), b=2(a and b should be distinct,next lowest value)
16*1 +4*2 +c=100;

c=76;
a+b+c=1+2+76=79;

@amresh_maverick said:
Given that f(x) = ax^2 + bx + c and f(4) = 100. If a, b, c are distinct positive integers, then the maximum possible value of a + b + c is a 79 b 87 c 122 d 82 e Data Insufficient
@pavimai said:
79??
OA : 79


Given f(x) is a function satisfying f(x + y) = f(x) — f(y) for all real values of x and y. If f(1) = 3 and f(1) + f(2) + f(3) ....+ f(n) = 1092, then find the value of n.
@Subhashdec2 said:
yes ofcourse
not all, the line joining the centre, and two opposite vertices would form a straight line... but yeah, any three points of a square would always form a right triangle...
@amresh_maverick said:
OA : 79Given f(x) is a function satisfying f(x + y) = f(x) — f(y) for all real values of x and y. If f(1) = 3 and f(1) + f(2) + f(3) ....+ f(n) = 1092, then find the value of n.
6 ?

3 + 9 + 27 + 81 + 243 + 729 = 1092
@amresh_maverick said:
OA : 79Given f(x) is a function satisfying f(x + y) = f(x) — f(y) for all real values of x and y. If f(1) = 3 and f(1) + f(2) + f(3) ....+ f(n) = 1092, then find the value of n.

f(x) = a^kx
f(1) = 3 => a^k = 3
f(2) = a^2k = 3^2 = 9
..
.
f(1) + f(2) + f(3) ....+ f(n) = 3 + 9 + 27 + 81 + 243 + 729 = 1092

so n = 6


@amresh_maverick said:
OA : 79Given f(x) is a function satisfying f(x + y) = f(x) — f(y) for all real values of x and y. If f(1) = 3 and f(1) + f(2) + f(3) ....+ f(n) = 1092, then find the value of n.
OA: 6
@amresh_maverick said:
Given that f(x) = ax^2 + bx + c and f(4) = 100. If a, b, c are distinct positive integers, then the maximum possible value of a + b + c is a 79 b 87 c 122 d 82 e Data Insufficient
ax^2+bx+c=f(x)

f(4)=16a+4b+c=100

FOR max. a+b+c , c will be max., a min
as a,b are positive distinct

a=1,b=2

c=100-16-8=76

1+2+76=79
@amresh_maverick said:
OA : 79Given f(x) is a function satisfying f(x + y) = f(x) — f(y) for all real values of x and y. If f(1) = 3 and f(1) + f(2) + f(3) ....+ f(n) = 1092, then find the value of n.
3+6+9+27+81+243+729=1092,so n=6
@varathawins Sorry but ITs wrong
@scrabbler Thanks man..finally got ur approach for my prob.Really nice one.
Q. 4 dice are thrown.In how many ways can a sum of 20 be obtained? for this question

the number of solutions of log5+log(a^2+1)/log(a-2)=2 is

a 1/2 b 2 c 1 d none

@ravi6389 said:
Q. 4 dice are thrown.In how many ways can a sum of 20 be obtained? for this question
this can also be thought in a different way.
max.sum=24
so taking complementary values for each dice i mean 6-a for a dice if a is the value on the dice

(6-a)+(6-b)+(6-c)+(6-d)=4

take 6-a=A and so on..


A+B+C+D=4


each of A B C D can take all values from 0-5

so total solutions are 7c3=35
@IIM-A2013 said:
the number of solutions of log5+log(a^2+1)/log(a-2)=2 isa 1/2 b 2 c 1 d none
d
@IIM-A2013 said:
the number of solutions of log5+log(a^2+1)/log(a-2)=2 isa 1/2 b 2 c 1 d none
How can the no of solutions be 1/2 ?? ( option A )
A hemispherical roof is on a circular room, inner diameter of the roof is equal to the height of the room. If 48,510 cm3 air is inside the room, find the height of the room.
Two line segments AB and CD bisect each other. If their ends are joined to form a quadrilateral ADBC, then which of the following is(are) true?
I. ∠ADB = 90°
II. AD = AC
III. AD = BC
@amresh_maverick said:
Two line segments AB and CD bisect each other. If their ends are joined to form a quadrilateral ADBC, then which of the following is(are) true? I. ˆ ADB = 90 ° II. AD = AC III. AD = BC
AD = BC ?
@amresh_maverick said:
Two line segments AB and CD bisect each other. If their ends are joined to form a quadrilateral ADBC, then which of the following is(are) true? I. ˆ ADB = 90 ° II. AD = AC III. AD = BC
at least 2&3
didnt check for 1 (time constraint need to hop out)
@amresh_maverick said:
Two line segments AB and CD bisect each other. If their ends are joined to form a quadrilateral ADBC, then which of the following is(are) true? I. ˆ ADB = 90 ° II. AD = AC III. AD = BC