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CAT 2007: Quantitative Questions a Day 1 to 50 - The discussions -
16-04-2007, 03:58 AM
Dear All,
I open the 1st thread of QQAD for the season. Disucuss your approaches and solutions to the problems here.
We have always been a non-rule kinda thread as it was never felt the need to moderate on QQAD. Whoever gets the chance first in the morning, please post the question here after reading from your mailbox. A right answer along with the approach will be considered a solution. The 1st user to solve QQAD on any given day will find his/her name mentioned in the next days newsletter.
Nothing more to say, frankly. Happy solving :-) May all of you crack all of the problems all of the times.
Regards,
Last edited by Aarav; 16-04-2007 at 04:04 AM.
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Re: CAT 2007: Quantitative Questions a Day 1 to 50 - The discussions -
16-04-2007, 04:10 AM
Hola! Good morning everybody, especially you aarav! 
One word of concern to the solution providers:- except for the initial few questions, do give some time to get the answer, but not more than five minutes. The idea is to learn new approaches, but not to gain it at the cost of speed!
And try to provide a slightly detailed answer, even if you think the answer might be wrong; atleast others might be able to learn from that approach(es) as well as help improve them!
Cheerios!
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Re: CAT 2007: Quantitative Questions a Day 1 to 50 - The discussions -
16-04-2007, 06:12 AM
OK ..Here we go .First question of the season ...
Keep the discussions concentrated to the problem at hand only and no irrelevant posts please .
All the very best puys
------------------------------------------------------------
Quantitative Question # 1
------------------------------------------------------------
Question:
The equation |x-1| - |x-2| + |x-4| = m has exactly n real solutions for some real m. Then which among the following relations about m and n can not be true?
(a) m/n = 3/5 (b) m = n (c) m/n = 3/2 (d) m/n = 5/3 (e) m = n-1
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Re: CAT 2007: Quantitative Questions a Day 1 to 50 - The discussions -
16-04-2007, 06:44 AM
The equation |x-1| - |x-2| + |x-4| = m has exactly n real solutions for some real m. Then which among the following relations between m and n can not be true?
(a) m/n = 3/5 (b) m = n (c) m/n = 3/2 (d) m/n = 5/3 (e) m = n-1
Dunno!
Tried putting integral values for x in the above equation:-
For x = 3, you get m = 2:- (e)
For x = 2.5, you get m = 2.5 :- (b)
For values of x = 4,5,6,7...., you get values of m = 1,2,3,4,5....
i.e m/n = .25,.4,.5,.57,.62,.66 and so on.... :- (a) could be possible for rational values of x!
For values of x = 3,2,1,0,-1,-2 you get values of m = 2,3,2,3,4,5,6....
i.e m/n = .66,1.5,2,infinity,-4,-2.5.... :- (c),(d) could be possible
Did all this in a hurry, so open to mistakes 
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Re: CAT 2007: Quantitative Questions a Day 1 to 50 - The discussions -
16-04-2007, 06:47 AM
Quote:
Originally Posted by ninja_talli
The equation |x-1| - |x-2| + |x-4| = m has exactly n real solutions for some real m. Then which among the following relations between m and n can not be true?
(a) m/n = 3/5 (b) m = n (c) m/n = 3/2 (d) m/n = 5/3 (e) m = n-1
Dunno!
Tried putting integral values for x in the above equation:-
For x = 3, you get m = 2:- (e)
For x = 2.5, you get m = 2.5 :- (b)
For values of x = 4,5,6,7...., you get values of m = 1,2,3,4,5....
i.e m/n = .25,.4,.5,.57,.62,.66 and so on.... :- (a) could be possible for rational values of x!
For values of x = 3,2,1,0,-1,-2 you get values of m = 2,3,2,3,4,5,6....
i.e m/n = .66,1.5,2,infinity,-4,-2.5.... :- (c),(d) could be possible
Did all this in a hurry, so open to mistakes |
Nice to see you the 1st to attempt this. What exactly is your n above? The question reads n real solutions. Think!
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Re: CAT 2007: Quantitative Questions a Day 1 to 50 - The discussions -
16-04-2007, 07:38 AM
Quote:
Originally Posted by vineet.nitd
OK ..Here we go .First question of the season ...
Keep the discussions concentrated to the problem at hand only and no irrelevant posts please .
All the very best puys
------------------------------------------------------------
Quantitative Question # 1
------------------------------------------------------------
Question:
The equation |x-1| - |x-2| + |x-4| = m has exactly n real solutions for some real m. Then which among the following relations about m and n can not be true?
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answer is c m/n=3/2
for the four intervals (-inf,1)[1,2)[2,4)[4,inf)
values of x are 3-m,m-1,5-m,3+m
for m=6/5 n=2
m=2 n=3
m=1 n=1
m=10/3 n =2
hence c is the answer
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decided to come back to pg again...
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Re: CAT 2007: Quantitative Questions a Day 1 to 50 - The discussions -
16-04-2007, 07:42 AM
Going by my instincts over here .... But m/n =3/5 does appear odd man out ... No chance of attempting this qn in CAT though :satisfied: I go with option (a)
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Re: CAT 2007: Quantitative Questions a Day 1 to 50 - The discussions -
16-04-2007, 08:07 AM
Quote:
Originally Posted by krsh.vik
answer is c m/n=3/2
for the four intervals (-inf,1)[1,2)[2,4)[4,inf)
values of x are 3-m,m-1,5-m,3+m
for m=6/5 n=2
m=2 n=3
m=1 n=1
m=10/3 n =2
hence c is the answer
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I am not commenting on ur ans at this moment .
For which values of m , n takes max. value ?
Last edited by vineet.nitd; 16-04-2007 at 08:51 AM.
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Re: CAT 2007: Quantitative Questions a Day 1 to 50 - The discussions -
16-04-2007, 09:15 AM
I think its (C)!!!
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Re: CAT 2007: Quantitative Questions a Day 1 to 50 - The discussions -
16-04-2007, 09:18 AM
My answer is (c) 3/2 . Btw Vineet gud start ....pretty gud ques especially the part that m and n are real.
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