Official Quant thread for CAT 2013

@rnishant231 said:
isn't it fine if we consider a cross section of 3D figure and solve it...like in ths case , sabse middle wala cross section with max area ?
Yes, but which cross section? juining the midpoints of the sides of the square? Or the vertices? If you take the midpoints, the vertices will protrude outside the cone.

regards
scrabbler

@scrabbler said:
Yes, but which cross section? juining the midpoints of the sides of the square? Or the vertices? If you take the midpoints, the vertices will protrude outside the cone.regardsscrabbler
as we have a 3D fig with cone , cube and sphere(all 3d objects) , if we assume cutting the objects along the vertices of the cone in vertical direction , we get a 2d fig with corresponding triangle , square and circle..

hope m able to make sense
@bodhi_vriksha said:
use similar triangles ..10-x/x=10/8 .. from this we get upper triangle's height Team BV--Pratik Gauri
sir, please explain, how can side of cube be diameter of upper cone?
i think diagonal of the sides of cube will be the diameter of the upper cone...correct me if i m wrong...
@mailtoankit said:
sir, please explain, how can side of cube be diameter of upper cone? i think diagonal of the sides of cube will be the diameter of the upper cone...correct me if i m wrong...
@scrabbler yes sir , the cross section thing doesn't seem proper.
on taking cross section , there will ne problem as mentioned by @mailtoankit
@bodhi_vriksha said:
The idea of my this post is to walk you through an observation and pattern.Suppose x is the sum of digits of a 3 digit number and N(x) denotes the number of ways of getting x as the sum. Then, N(x) =N(28-x), where x -> [1,27] For this reason maximum possible sum corresponds to N(14)= 45 +9 + 7 +5 +3 +1If the three digit number is abc, then for x = 9 to 19 we have 9 values of a. However, for remaining values of x, there are x or 28 窶度 (which ever is single digit) values of a.So the total sum possibilities of any 3 digit number can be generated as follows:For x= 1 to 9 and 19 to 27 -> Sum = Summation (Summation(n))X=10 ->Summation(9) + 9 = 45 +9X=11 -> 45 +9 + 7X=12 -> 45 +9 + 7 +5 =66 = N(16) {This is the same value that we got in our previous problem on N(16). Remember?}X=13 -> 45 +9 + 7 +5 +3X=14 -> 45 +9 + 7 +5 +3 +1-> Maximum SumX=15 -> 45 +9 + 7 +5 +3 +1 -1 = 45+9+7+5+3 = N(13)X=16 -> 45 +9 + 7 +5 +3 +1 -1 -3=45+9+7+5 = N(12)X=17 -> 45 +9 + 7 +5 +3 +1 -1 -3-5= 45+9+7= N(11)X=18-> 45 +9 + 7 +5 +3 +1 -1 -3-5-7= 45+9 = N(10)X=19-> 45 +9 + 7 +5 +3 +1 -1 -3-5-7-9= 45= N(9)For the purposes of the problem at hand, Summation(Summation(16)) = Summation (Summation (9)) + 45*7 + 9*7 +7*6+5*5+3*4+1*3-1*2-3*1=>Summation(Summation(16))= 165 +420 +40-5=620Team BV - Vineet
Sir yeh kaise aaya?
@rnishant231 said:
as we have a 3D fig with cone , cube and sphere(all 3d objects) , if we assume cutting the objects along the vertices of the cone in vertical direction , we get a 2d fig with corresponding triangle , square and circle..hope m able to make sense
Bhai cone ka ek hi vertex hota hai :blush: Draw the figure and see, I am not in a position to do so right now...sorry...

regards
scrabbler

@scrabbler said:
Bhai cone ka ek hi vertex hota hai Draw the figure and see, I am not in a position to do so right now...sorry...regardsscrabbler

yes..u are right.. i already took my words back in my prev post..

PS : it was looking too obvious , but actually not correct..

Q 8

@vbhvgupta said:
Q 8
in IV it is 2000, in III it is 1600, for II it has to be 1280

A motorist used 10% of his fuel to cover 20% of his journey. he covered another 40% of his total journey under similar condition . for the rest of journey the conditions were different. Find the maximum % by which his fuel efficiency (distance covered per unit of fuel) can drop, so that he can still cover the remaining journey without a refill.

@vbhvgupta said:
Q 8
1280 ?

(5/4)^4*x - (5/4)^3*x = 500
x = 1024
pages in II vol = 1.25*x = 1.25*1024 = 1280
@pratskool said:
in IV it is 2000, in III it is 1600, for II it has to be 1280
did u solved it using options.
@vbhvgupta said:
did u solved it using options.
u can do dat 2... if 2000 comes, we know it has to be more than half, coz x raised by 25% and again 25% would be, 1.25x*1.25 = 1.5625x ... which is less than 2x and hence more than 1000, which is 1280
@vbhvgupta said:
did u solved it using options.
bhai 25% is 500 so 100% of IV will be 2000. iske baad do baar 1.25 se divide karna hai bas.. so 1280
@vbhvgupta said:
A motorist used 10% of his fuel to cover 20% of his journey. he covered another 40% of his total journey under similar condition . for the rest of journey the conditions were different. Find the maximum % by which his fuel efficiency (distance covered per unit of fuel) can drop, so that he can still cover the remaining journey without a refill.
he covers 20%+40% of the journey utilizing 10%+20% of his fuel.. here the efficiency is 20/10=2x (distance per unit of fuel) for the remaining 40% of the distance he can use a max of 70% of fuel. the efficiency here is 40/70=.1428*4~.57x

from 2x it is dropping to .57x hence the %drop will be |.57x-2x|/2x=1.43/2=71.5%?

at the begining of 2002 sunil had 4 dozen goat with him. he increased his stock by X%. at the end of year he sold by Y%. at the begining of 2003 he again increased his stock by X%. at the end of year he sold by Y%. At the end of 2003 he had 5 dozen goats with him after his sales.

which of the following hols true
1. X> 100y/100-y 2. 100y/100-y >x>y
3. x 100y/100-y

Q28 Q29

@iLoveTorres yar solution delete kar dia
@vbhvgupta said:
Q28 Q29
28)D?
29)A?
@iLoveTorres said:
28)D?29)A?
explain?
29 B