Official Quant thread for CAT 2013

MBA CAT 2024
23747
@The_Loser said:
all three diff.
i edited
23748
@gautam22 said:
72375?????(12060+12061+........+12065) http://www.pagalguy.com/forums/quantitative-ability-and-di/official-quant-thread-c-t-88456/p-3611604/r-4225718?page=548mera hi reply hai 10942par ans 72381 tha pata nahi kaise


Check this
@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
23749
@bodhi_vriksha said:
btw 55 is wrong Let me explain it...2x + 3y = 15One 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
point taken
23750

@The_Loser said:
all three diff.
edited....did wrong subtraction
23751
@ChirpiBird said:
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.
That's correct ChirpiBird...now think that what should/cn be at RHS so that equation has exactly 2011 solutions. :)

Team BV
23752
@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?
x = 3(5-y)/2
(x,y) = (3,3) and (0,5)
y = (15-2x)/3
(x,y) = (6,1) and (3,3)

so 3 unique solutions??
23753
@The_Loser
3:2 ??

23754
@bodhi_vriksha said:
That's correct ChirpiBird...now think that what should/cn be at RHS so that equation has exactly 2011 solutions. Team BV
2011*3=6033?
23755
@gautam22 said:
sir mere method mein kya galti hai ( 6*2010 = 12060.......12065 tak jayega inme har case mein 2011 ban jayengi including 0) isme 6 ka farak aa raha hai
2x + 3y = 12060
(x, y) = (0, 4020)....(6030, 0) i.e. 2011 solutions

2x + 3y = 12061
(x, y) = (2, 4019)....(6030, 1) i.e. 2010 solutions

pls check :)

Team BV
23756
@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?
x = 0 , y = 5

now add 3 in the value of x and deduct 2 from the value of y

x = 3 , y = 3
x = 6 , y = 1

so , 3 non negative solutions
23757
@bodhi_vriksha said:
That's correct ChirpiBird...now think that what should/cn be at RHS so that equation has exactly 2011 solutions. Team BV

ok... y moves faster than x.. (excuse my lang.)
y=4021, x=0... ...... and initially y=1 , x=4020??
did this because.. i need 2011 cases and i see y increases at d=2.
so.. 4021 = 1 + (n-1)2
n=2011.


23758
@bodhi_vriksha bhai ab samajh mein aa gaya.. if you dont mind kindly put some questions on integer solutions and types so that the all the doubts are cleared and mistakes rectified
23759
@bodhi_vriksha said:
That's correct ChirpiBird...now think that what should/cn be at RHS so that equation has exactly 2011 solutions. Team BV
taking x... it'll be 6030...
23760
@Logrhythm said:
x = 3(5-y)/2 (x,y) = (3,3) and (0,5)y = (15-2x)/3(x,y) = (6,1) and (3,3)so 3 unique solutions??
This is okay for first solution but not the best way to get all the solutions..

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)


"Basically after finding one case/solution of the equation, just add the coefficient of y in values of x and subtract the coefficient of x in values of y to get further solutions"

Team BV
23761
@mohitjain
144 ???
23762
@bodhi_vriksha said:
This is okay for first solution but not the best way to get all the solutions..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)"Basically after finding one case/solution of the equation, just add the coefficient of y in values of x and subtract the coefficient of x in values of y to get further solutions"Team BV
to have "n" non negative integer solutions where the coefficient of x is m and of y is l where l>m is (l*(n-1))*m.
Is my generalization correct?
23763

Now I got to know that "Certified Pagals" are better (at least in experience) than "Hardcore Pagals" :D

@iLoveTorres Gaurav...this one(s) is for you:

How many integral solutions exist for 3x + 7y = 1000 such that x > 100 and y > 50?

For how many positive integers 'n', the equation 12x + ny = 31 has no integral solutions for n
Team BV

23764
@bodhi_vriksha said:
This is okay for first solution but not the best way to get all the solutions..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)"Basically after finding one case/solution of the equation, just add the coefficient of y in values of x and subtract the coefficient of x in values of y to get further solutions"Team BV
got it.. it'll be like this.. (0,4020)....(6030,0)..
and eq will be.. 2x+3y=12060.

>batti late jali! :(

Thanks! :D
23765
@ChirpiBird said:
got it.. it'll be like this.. (0,4020)....(6030,0).. and eq will be.. 2x+3y=12060.>batti late jali! Thanks!
jali to :P
23766
@bodhi_vriksha said:
Now I got to know that "Certified Pagals" are better (at least in experience) than "Hardcore Pagals" @iLoveTorres Gaurav...this one(s) is for you:How many integral solutions exist for 3x + 7y = 1000 such that x > 100 and y > 50?For how many positive integers 'n', the equation 12x + ny = 31 has no integral solutions for n Team BV
in d 1st q, if y = 1, x = 331, but y>50,... so y = 52,55,58... and so on... now for y = 130,x=30, for x = 51, y = 121... so no. of solutions = (121 - 52)/3 + 1 = 24