The Official CAT 2007 Quant Thread

[mohit_353]

Originally Posted by hanuman

Very late .anyways


The above can be found by directly applying cauchy's in-equality



cauchy's inequality
for any number l,m,n,o
(l^2+m^2)(n^2+o^2)>=(l*n+m*o)^2

given xy + yz + zx = 2
( xy+yz+zx) ^2=4

(xy+yz+zx)^2<=(x^2+y^2+z^2)*(x^2+y^2+z^2)
=>(x^2+y^2+z^2)^2>=4
(x^2+y^2+z^2)>=2( Assuming x,y,z to be +ve reals)

hi;
can u explain the complete cauchy's inequality theorom...while taking a example..or u can go ahead with the same problem....

thanks in advance.....

[the.bombardier]

Originally Posted by vikram_k51

Hey I have taken (x+y+z)^2(Greater Than equal to)>=0(As it is a square)
Also xy+yz+zx=2 is given

i knw that,but when u solve the question,u find the minimum value at (x+y+z)^2=0 with xy+yz+zx=2.what i mean to say is that,u cant say that this WILL be true at (x+y+z)^2=0..
maybe xy+yz+zx=2 at some positive value of (x+y+z)^2,but u cant say it has to be 0..

[sastry751]

hi destiny child this is my solution for the trains problm

say the trains meet at some point p btw X and Y.now from this point train A reached the station Y in 6hr 48 min wiht the speed 49 kmph.find the distance from point p to Y came 333.2 since the trains crossed each other at P obviously both trains took same time to reach P isnt it.so 333.2=Vb*t
in this time A travelled D=49*t
for this D train B took 3hr 20 min that means equate D u get answer

49*t=time took by B* vel of Bexpress everything in t u have ur answer

hope everything is clear.ofcourse i am dead weak and dead slow in my quant

[vijay317]

Originally Posted by Destiny's_Child

Anybody with answer to these two questions???
Please come forth......

For the train problem, we can use the relation that

speed^2 * time being same for both the objects.

Very easy to prove using simple S=UT formula. Will post it later if needed!

[hanuman]

Originally Posted by mohit_353

hi;
can u explain the complete cauchy's inequality theorom...while taking a example..or u can go ahead with the same problem....

thanks in advance.....

for cauchy's inequality just go thru the link Cauchy's Inequality -- from Wolfram MathWorld

For example look at the post http://www.pagalguy.com/forum/quanti...tml#post522944 (Quantitative questions a day 101 to 150 - The discussions), IdiotR has beautifully solved a problem using this inequality. Go thru the discussion of the problem u will understand the inequality.

[mohit_353]

Hi;
guys can anyone explain the greatest integer function in detail.....or can i have a online link...it is making me cray these days...

Thanks in advance......

[the.bombardier]

Originally Posted by mohit_353

Hi;
guys can anyone explain the greatest integer function in detail.....or can i have a online link...it is making me cray these days...

Thanks in advance......

arre yaar wat problem r u having with the harmless greatest integer function?
let me try n explain it to u.
f(x)=[x] where []=greatest integer function
now wat is greatest integer function.its the greatest integer smaller than x.
for eg if x=2.3 ,then wat will be the greatest integer smaller than 2.3? 2 rite.
so f(x)=[x] = 2 for x = 2.3
suppose x is negative.say x=-2.3 ,then wat is the greatest integer less than -2.3? its -3. therefore in this case [x]=-3
is it clear?
if not,search wikipedia,im sure u would find something there..

[sastry751]

can someone help me wiht the topics of quadratic equation like how can we go about problms which says the rooots lie between so and so and for some questions we use rolle's theorem.me unable to comprehend anything someone helppp


me dead weak and dead slow in quant

[mohit_353]

Originally Posted by the.bombardier

arre yaar wat problem r u having with the harmless greatest integer function?
let me try n explain it to u.
f(x)=[x] where []=greatest integer function
now wat is greatest integer function.its the greatest integer smaller than x.
for eg if x=2.3 ,then wat will be the greatest integer smaller than 2.3? 2 rite.
so f(x)=[x] = 2 for x = 2.3
suppose x is negative.say x=-2.3 ,then wat is the greatest integer less than -2.3? its -3. therefore in this case [x]=-3
is it clear?
if not,search wikipedia,im sure u would find something there..

hi;
i did not find any doc. for this in wikkipedia.......all these things r clear to me ...the only concern is ...wht is the GIF of 7.99999999.....now u will say it is 7 but in acctual it is 8.....that is the problem......what is the application behind this....

pls check the following link for this problem....

Greatest Integer Function

waiting eagrly for ur reply......

[the.bombardier]

Originally Posted by mohit_353

hi;
i did not find any doc. for this in wikkipedia.......all these things r clear to me ...the only concern is ...wht is the GIF of 7.99999999.....now u will say it is 7 but in acctual it is 8.....that is the problem......what is the application behind this....

pls check the following link for this problem....

Greatest Integer Function

waiting eagrly for ur reply......

7.999999....
f(x)=[x] where [] = greatest integer function
if u look at the graph of greatest integer function,u will c that the value of f(x) is 7 for 7<=x<8
the value of f(x) is 8 for 8<=x<9
so from this definition,i think 7.9999999.. though almost equal to 8,it is lesser than 8.
so i think wats given on that link is incorrect.
by the way,here is a link to the wikipedia article on greatest integer function.
Floor and ceiling functions - Wikipedia, the free encyclopedia