Official Quant thread for CAT 2013

@kingsleyx said:
coefficient of x^18 in the expansion (x+x^2+x^3+....+x^6)^4 ?
coeff. of x^18 in (x+x^2+x^3+....+x^6)^4
= coeff. of x^14 in (1+x+x^2...+x^5)^4
= coeff. of x^14 in (x^6-1)^4*(1-x)^-4

(x^6-1)^4=4c0*x^24-4c1*x^18+4c2*x^12-4c3*x^6+1
(1-x)^-4=1+4x+4*5/2*x^2+4*5*6/6*x^3+..+4*5*6*...*11/8!*x^8+..+4*5*..*17/14!*x^14 ......

==> 4c2*10-4c3*165+680
==> 60-660+680
==> 80


@tiwarishiva said:
6. ABCD is a square. P is the midpoint of AB. The line passing through A and perpendicular to DP intersects the diagonal at Q and BC at R. If AB = 2 then PR = ______ ?
@gautam22 said:
sir denom mein x=1/x=1... hoga to vo min hoga..x+1/x=2.....AM>GM.................(x+1/x)/2>=rt x*1/x....=>x+1/x>=2....sir plz correct me if i m wrong
Sir mat bol bhai nd yeah u r right jaldi2 me dhyaan hi nahi diya 😛 Tab b ans a gaya i wonder kaise
@kingsleyx said:
coefficient of x^18 in the expansion (x+x^2+x^3+....+x^6)^4 ?
(x+x^2+x^3+....+x^6)^4
=>x^4*(1+x+x^2+x^3+....+x^5)^4
=>x^4*(1-x)^-4*(1-x^6)^4
=>x^4*(3C3+4C3x+5C3x^2+.....)*(1-4C1x^6+4C2x^12)
=>x^4*(17C3x^14+4C2*5C3x^14-4C1*11C3x^14)
=>740-660=80
PS:@gautam22 guess so... nd wht i tld u no sir

DS:
The base of a triangle is 60 cms, and one of the base angles is 60째. What is length of the shortest side of the triangle?
I. The sum of lengths of other two sides is 80 cms.
II. The other base angle is 45째.

@tiwarishiva said:
DS:The base of a triangle is 60 cms, and one of the base angles is 60째. What is length of the shortest side of the triangle?I. The sum of lengths of other two sides is 80 cms.II. The other base angle is 45째.
II is enough?
@maddy2807 said:
II is enough?
confusion is with first, solution say that can be answered using any of those......but I think I will not determine a unique triangle. What say?
@tiwarishiva said:
confusion is with first, solution say that can be answered using any of those......but I think I will not determine a unique triangle. What say?
@maddy2807 said:
II is enough?
We can find out the values by 1st also
cosine formula se ek eqn a jaegi nd the other is already given

@tiwarishiva said:
confusion is with first, solution say that can be answered using any of those......but I think I will not determine a unique triangle. What say?
i dont find a way. let c wat others say
@deedeedudu said:
We can find out the values by 1st alsocosine formula se ek eqn a jaegi nd the other is already given
didn't get......explain further plz

@tiwarishiva said:
didn't get......explain further plz
@deedeedudu is correct.
Cos A= (B^2+C^2-A^2)/(2*B*C)
use this formula.
@kingsleyx said:
Which among the following is the largest 2^1/2 , 3^1/3 , 4^1/4 , 6^1/6 and 12^1/12 ?
3^1/3??
It takes six days for 3 women and 2 men, working together, to complete a work. 3 men would do the same work 5 days sooner than 9 women. How many times does the output of a man exceeds that of a woman?

@jain4444 said:
It takes six days for 3 women and 2 men, working together, to complete a work. 3 men would do the same work 5 days sooner than 9 women. How many times does the output of a man exceeds that of a woman?
man output= 6* women output.
?
@stellarPG said:
@gautam22@maddy2807@maddy2807 said:man output= 6* women output.?@gautam22 said:m=6w? can u guyz plz explain
total wrk done= 6*(3w+2m)
days taken by 3m to complete the wrk is= Total wrk/ No of men
=> (18w+12m)/3m
similarly for 9 women
time taken= (18w+12m)/9w

Acc to the question.
(18w+12m)/9w - (18w+12m)/3m = 5
solve to obtain a quad equation.
m= 6w
Though the method is a bit length n tedious.
@jain4444 said:
It takes six days for 3 women and 2 men, working together, to complete a work. 3 men would do the same work 5 days sooner than 9 women. How many times does the output of a man exceeds that of a woman?
m = 6w..
The weight of an iron bucket increases by 33.33% when filled with water to 50% of its capacity. Which of these may be 50% of the weight of the bucket when it is filled with water( assume the weight of bucket and its capacity in kg to be integers?..
plz explain in detail with steps.
a 7 kg b 5 kg c 6 kg d 8 kg

There are 2 buses running from terminuses A nd B, each bus making 5 round trips in a day with no stops in btw.These buses ply on the same route with diff but uniform speeds. Each morning the buses start at 7am from their respective terminuses. They meet for teh 1st time at a dist of 7km from A and. Thier next meeting takes place at a dist of 4km from B, while travelling in opp directions.Assuming that the time taken by the buses at the terminuses is negligible and the cost of running a bus is Rs20/km.Find the daily cost of running the buses.
3200
4000
6400
6800
none
@YouMadFellow

@sonamaries7 said:
There are 2 buses running from terminuses A nd B, each bus making 5 round trips in a day with no stops in btw.These buses ply on the same route with diff but uniform speeds. Each morning the buses start at 7am from their respective terminuses. They meet for teh 1st time at a dist of 7km from A and. Thier next meeting takes place at a dist of 4km from B, while travelling in opp directions.Assuming that the time taken by the buses at the terminuses is negligible and the cost of running a bus is Rs20/km.Find the daily cost of running the buses.3200400064006800none@YouMadFellow
6800?
@IIM-A2013 said:
The weight of an iron bucket increases by 33.33% when filled with water to 50% of its capacity. Which of these may be 50% of the weight of the bucket when it is filled with water( assume the weight of bucket and its capacity in kg to be integers?..plz explain in detail with steps.a 7 kg b 5 kg c 6 kg d 8 kg
option b : 5 Kg ?