[Aarav]

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,

[ninja_talli]

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!

[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


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Quantitative Question # 1
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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

[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

[Aarav]

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!

[krsh.vik]

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?

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

[siddhesh_j]

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)

[vineet.nitd]

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

I am not commenting on ur ans at this moment .

For which values of m , n takes max. value ?

[Dhaval Patel]

I think its (C)!!!

[Apple]

My answer is (c) 3/2 . Btw Vineet gud start ....pretty gud ques especially the part that m and n are real.