Official Quant thread for CAT 2013

MBA CAT 2024
23727
@gnehagarg said:
Compute the sum of all n for which the equation 2x + 3y = n has exactly 2011 nonnegative (x; y >= 0)integer solutions.
Possible smallest value of x, and maximum of y are: (0, 4020), (0, 4021), (1, 4020),(1, 4021), (2, 4020), (2, 4021)

So sum of all possible 'n' is 2(0 + 1 + 2)2 + 3(4020 + 4021)3 = 12 + 72369 = 72381 :)


Team BV
23728
@scrabbler said:
Ho sakta hai...level has been varying widely in the last few years...last year most sections had a few sitters and a few nightmares...Why btw? Did you find it too easy or too painful? For me the latter since algebra is my weakest link...regardsscrabbler
bhai agar aap ko hi painful tha toh humare liye toh ROD tha :P
23729
@scrabbler said:
Ho sakta hai...level has been varying widely in the last few years...last year most sections had a few sitters and a few nightmares...Why btw? Did you find it too easy or too painful? For me the latter since algebra is my weakest link...regardsscrabbler
i also tried doing it the way you did, finding a pattern.....but then gave up on it half way...fayda nahi dikh raha tha....so i, very conveniently, told my self - "bhai aese question nahi aate" 😛
23730
@bodhi_vriksha said:
Possible smallest value of x, and maximum of y are: (0, 4020), (0, 4021), (1, 4020),(1, 4021), (2, 4020), (2, 4021)So sum of all possible 'n' is 2(0 + 1 + 2)2 + 3(4020 + 4021)3 = 12 + 72369 = 72381 Team BV
bhai aapne kya kiya hai thoda vistaar mein bataiye pls
23731
@The_Loser said:
A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is
4.14
start A____8m_____B______________.___8sec_____end

speed of a=25/18 m/sec
100m he'll cover in 4*18=72sec
92 m in 80sec.
so speed = 92/80=1.15m/sec or 4.14km/hr.


23732
@iLoveTorres said:
bhai aapne kya kiya hai thoda vistaar mein bataiye pls
It's simple..:)

Can you tell me the number of non-negative integral solutions of 2x + 3y = 15 and how do you calculate that?
23733
@bodhi_vriksha said:
It's simple..Can you tell me the number of non-negative integral solutions of 2x + 3y = 15
55?
23734
@Logrhythm said:
i also tried doing it the way you did, finding a pattern.....but then gave up on it half way...fayda nahi dikh raha tha....so i, very conveniently, told my self - "bhai aese question nahi aate"
haha.. adopted similar philosophy... said in mind , "ignore maar, ignore maar!" :D
23735
@iLoveTorres said:
bhai agar aap ko hi painful tha toh humare liye toh ROD tha
Not painful so much as boring 😞 I can never focus so well in algebra...enjoy Geom or PnC more (even though chances of error are higher there).

regards
scrabbler
23736
@iLoveTorres said:
55?
and how do you calculate that?
23737
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds
23738
@bodhi_vriksha said:
and how do you calculate that?
pata nahi.. totally blank at this point.. dono what i have done.. distributed 1 each to x and y so that it changes to no of integer solutions.. so from 15 2+3=5 gets subtracted.. hence 2x+3y=10
No of integer solutions is 11c2
23739
@The_Loser said:
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds
L1/v1=27
L2/v2=17

L1+L2/v1+v2 =23
27v2+17v2=23v1+23v2
2v1=3v2
3:2
23740
@The_Loser said:
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds
(27x+17y)/(x+y) = 23
=> x/y = 3/2
23741
@The_Loser said:
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds

l1/t1=27
l2/t2=17

l1+l2/ t1+t2 = 23
27t1 +17t2=23t1 +23t2
4t1=6t2
t1:t2 = 3:2

edited ... apparently 23-17 was 5 for me. :D
23742
@The_Loser said:
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds
3:2
23743
@iLoveTorres said:
55?
btw 55 is wrong :)

Let me explain it...

2x + 3y = 15

One solution can be very easily pointed out as (x, y) = (0, 5)
I hope that's obvious. Isn't it? :)

Next learn the trade secret :)
General values of x are of the form x = 0 + 3n (where 3 is the coefficient of other variable y)
And that of y are of the form y = 5 - 2n (where 2 is the coefficient of other variable x)

So, clearly, there are 3 non-negative integral solutions possible for this equation.

Tell me whether this point is taken or not. :)

Team BV
23744

A 6-6 GRID is cut from a 8-8 chessboard.In how many ways can we put 2 identical coins one on d white square and d other on d black in d grid such dat they are not placed in d same row or column?

23745
@Subhashdec2 said:
L/v1=27L/v2=1717:27??
@Logrhythm said:
(27x+17y)/(x+y) = 23=> x/y = 3/2
@ChirpiBird said:
t1:t2 = 5:4?l1/t1=27l2/t2=17l1+l2/ t1+t2 = 2327t1 +17t2=23t1 +23t24t1=5t2
all three diff.
23746
@bodhi_vriksha said:
It's simple..Can you tell me the number of non-negative integral solutions of 2x + 3y = 15 and how do you calculate that?
r u asking solutions like this?.. (x,y) ... (6,1) , (3,3) and (0,5) ...
rest will be -ve i think.
correct me if i am wrong.