Official Quant thread for CAT 2013

@mani0303 said:
an = 2^n + 1 then (a1 + a2 + - - - - + a20) €“ a21 is?
2^1 + ... + 2^20 -2^21 +19
= -1 + 19 = 18
@hexagon said:
Vicky and Nicky run back and forth between the town hall and the county station at respective speeds of 12 kmph and 18 kmph. They start simultaneously - Vicky from the town hall and Nicky from the county station. If they cross each other for the first time 14 minutes from the start, at what distance from the county station do they cross each other for the fifth time?ans 4.2 km
It should be easy i think

If they meet after 14 mins,the total distance b/w them should be 30*(14/60) = 7km

Except the first meeting,they both would travel 2*D(it's rule if the ratio is 2b>a>b) ie 14km

For 5th meet,they both would have covered 7 + 4*14 = 63km

Considering Nicky alone,he would have traveled 63*(3/5) = 37.8km

So running back and forth of 37.8km,he would meet Vicky 4.2km from County station
@meenu05 said:
please solve it
join A to E
BE is median
=> A(BCE) = 40 ....(1)

area of shaded region be a, A(DEF) = b
B is mid point and BG is parallel to AD => G is mid point of CD

CD = DE = 2b (say) => CG = GD = b

FE/FB = 2 /1 (similar triangles)

A(EDF) / A(EBG) = b/ (a + b) = 4/9

=> 5b = 4a

a + b + 10 = 40 (from 1)

=> a = 50/3


@pratskool said:
2^1 + ... + 2^20 -2^21 +19= -1 + 19 = 18
bhai yeh -1 kaise aaya...i m getting -2..
@mailtoankit said:
bhai yeh -1 kaise aaya...i m getting -2..
sorry, -2 hi hoga.... 2 + 2^2 + .. 2^20 = 2^21 - 2

@pratskool said:
sorry, -2 hi hoga.... 2 + 2^2 + .. 2^20 = 2^21 - 2
then the answer should be 17 right ?
@arpit554 said:
Can anyone please provide the link to " key of Wren and Martin". Sorry guys, I know I am posting it in wrong thread but I am in urgent need of it.Thanks in advance.
You have already booked seat for FMS 2014-2016 :wow: ?
@mani0303 said:
an = 2^n + 1 then (a1 + a2 + - - - - + a20) €“ a21 is?
a1+a2+...a20 = 2(2^20-1) = 2^21 - 2 + 20 = 2^21+18
a1+a2+...a20 - a21 = 2^21+18-2^21-1 = 17..

A closed box measures EXTERNALLY 9dm long, 6dm broad, 4.5dm high, and is made of wood 2.5 dm thick. Find the cost of lining it on the inside with metal at 6Paisa per sq metre. (1m=10dm)

Guys...i am nt getting hw to find internal dimensions in this Q. Plz guide.

@amandeep2020 said:
A closed box measures EXTERNALLY 9dm long, 6dm broad, 4.5dm high, and is made of wood 2.5 dm thick. Find the cost of lining it on the inside with metal at 6Paisa per sq metre. (1m=10dm)Guys...i am nt getting hw to find internal dimensions in this Q. Plz guide.
Dude - Are data the correct? Because if I'm not wrong,we can subtract thickness from either ends of length,height and breadth to find the inner dimensions of the cuboid,but here one of the sides ie height is less than 2*thickness...
@amandeep2020 said:
A closed box measures EXTERNALLY 9dm long, 6dm broad, 4.5dm high, and is made of wood 2.5 dm thick. Find the cost of lining it on the inside with metal at 6Paisa per sq metre. (1m=10dm)Guys...i am nt getting hw to find internal dimensions in this Q. Plz guide.
not possible as height is 4.5 and thickness is 2.5 ... 2.5*2 = 5... so not possible as said by mani bhai...
@mani0303 said:
Dude - Are data the correct? Because if I'm not wrong,we can subtract thickness from either ends of length,height and breadth to find the inner dimensions of the cuboid,but here one of the sides ie height is less than 2*thickness...
you are right bhai.. there seems some to be discrepancy..
@amandeep2020 said:
A closed box measures EXTERNALLY 9dm long, 6dm broad, 4.5dm high, and is made of wood 2.5 dm thick. Find the cost of lining it on the inside with metal at 6Paisa per sq metre. (1m=10dm)Guys...i am nt getting hw to find internal dimensions in this Q. Plz guide.
Data incorrect

From QE: http://www.quantexpert.co.in/questionoftheday.html
Q1 and Q2

Three equal circles are drawn inside a unit semicircle such that no circles intersect each other. Find the largest possible radius of the three equal circles approximately. ?
A. 1/3
B. 3/8
C. 2/5
D. 1/2

is it by any chance 1/3?
@Asfakul said:
Three equal circles are drawn inside a unit semicircle such that no circles intersect each other. Find the largest possible radius of the three equal circles approximately. ?A. 1/3B. 3/8C. 2/5D. 1/2is it by any chance 1/3?
it's 3/8.
How many ordered pairs (a, b) exist such that L.C.M. of a and b is (2^3)(5^7)(11^13) (a, b
ˆˆN)?
a) 2460
b) 2835
c) 2645
d) 2840
@catahead said:
Q1>> 3000
Q2>>(9)4^3
@Asfakul said:
How many ordered pairs (a, b) exist such that L.C.M. of a and b is (2^3)(5^7)(11^13) (a, b ˆˆN)?a) 2460b) 2835c) 2645d) 2840
It's 2835 ie (4^2 - 3^2)*(8^2 - 7^2)*(14^2 - 13^2) = 7*15*27 = 2835


@jaspunit said:
3 circles touching each other, find possible radius of circle circumscribing all these, if radius of each 3 circle is 'r'?
(2/3)*(_/3/2)*2r + r = (1/_/3)*2r + r = r((2/_/3) + 1)