official quant thread for cat08

[pallaviagrawal]

Originally Posted by implex

New Problem!!
Given that a,b and c are roots of the equation x^3-ax+bx-c=0. find the number of ordered triplets (a,b,c)

a)0 b) 1 c) 2 d) 3 e) none of these

since its a cubic equation with roots a,b and c
abc=c....(1)
ab+bc+ac=b-a....(2)
and a+b+c=0...(3)


either ab=1 or c=0

when ab=1 from 1,2 and 3, we get a^4-a^3+a^2+a+1=0
this i dont think has any real solution.
if c=0,a+b=0 and ab+0=b-a
solving we get a=-b=0 or 2
hence 2 solutions.
this equation also has a solution when a=b=c=0.
hence answer is 3.is that right??

[selebratinglife]

Originally Posted by implex

New Problem!!
Given that a,b and c are roots of the equation x^3-ax+bx-c=0. find the number of ordered triplets (a,b,c)

a)0 b) 1 c) 2 d) 3 e) none of these

Substituting a,b,c in the equations would give,
a^3-a^2+ab-c=0--1
b^3+b^2-ab-c=0--2
c^3-ac+bc-c=0--3
1-2=>a^3-b^3=a^2+b^2-2ab=>(a-b)(...)=0
1-3=>(a-c)(.......)=0
2-3=>(b-c)(...)=0
a=b=c
Substituting we get x^3=c..Gives only 0 as the solution

[selebratinglife]

Originally Posted by pallaviagrawal

since its a cubic equation with roots a,b and c
abc=c....(1)
ab+bc+ac=b-a....(2)
and a+b+c=0...(3)


either ab=1 or c=0

when ab=1 from 1,2 and 3, we get a^4-a^3+a^2+a+1=0
this i dont think has any real solution.
if c=0,a+b=0 and ab+0=b-a
solving we get a=-b=0 or 2
hence 2 solutions.
this equation also has a solution when a=b=c=0.
hence answer is 3.is that right??

Nice..Guess that should be it!

[nikunj14_83]

Hi,
Please help me out with this ques on TSD...

A dog travelled 50 Km & met a swami who advised him to reduce his speed to 3/4 of his original speed which ultimately resulted in dog reaching his destination 35 minutes late.Had he travelled for 24 Km more on his usual speed he would have been late by 25 min in reaching his destination.What is the original speed of the dog???
a)48 Kmph
b)54 Kmph
c) 58 Kmph
d) None of these

Ans-- 48 Kmph

My approach---

Since distance is constant I assumed it to be 96 Km
Going by the options...
Time taken(original)= 96/48=2hrs
As given in ques=50/48+46/36----this is not equal to 155 min as given in the ques(35 min late)
I tried with all the options still no luck
Is my approach wrong???

P.S. Its 50 ques from LOD(2) Arun Sharma

[dashing]

Originally Posted by nikunj14_83

Hi,
Please help me out with this ques on TSD...

A dog travelled 50 Km & met a swami who advised him to reduce his speed to 3/4 of his original speed which ultimately resulted in dog reaching his destination 35 minutes late.Had he travelled for 24 Km more on his usual speed he would have been late by 25 min in reaching his destination.What is the original speed of the dog???
a)48 Kmph
b)54 Kmph
c) 58 Kmph
d) None of these

Ans-- 48 Kmph

My approach---

Since distance is constant I assumed it to be 96 Km
Going by the options...
Time taken(original)= 96/48=2hrs
As given in ques=50/48+46/36----this is not equal to 155 min as given in the ques(35 min late)
I tried with all the options still no luck
Is my approach wrong???

P.S. Its 50 ques from LOD(2) Arun Sharma

24/(3/4 * x) - 24/x = 10/60
=> 24/3 *x = 1/6
=> x = 48

[dashing]

Originally Posted by nikunj14_83

Hi,
Please help me out with this ques on TSD...

A dog travelled 50 Km & met a swami who advised him to reduce his speed to 3/4 of his original speed which ultimately resulted in dog reaching his destination 35 minutes late.Had he travelled for 24 Km more on his usual speed he would have been late by 25 min in reaching his destination.What is the original speed of the dog???
a)48 Kmph
b)54 Kmph
c) 58 Kmph
d) None of these

Ans-- 48 Kmph

My approach---

Since distance is constant I assumed it to be 96 Km
Going by the options...
Time taken(original)= 96/48=2hrs
As given in ques=50/48+46/36----this is not equal to 155 min as given in the ques(35 min late)
I tried with all the options still no luck
Is my approach wrong???

P.S. Its 50 ques from LOD(2) Arun Sharma

"Since distance is constant I assumed it to be 96 Km"

Where did you get the 96 KM from

[nikunj14_83]

Originally Posted by dashing

"Since distance is constant I assumed it to be 96 Km"

Where did you get the 96 KM from

I assumed it to be 96....as it will remain constant throughout...

[deep@k]

Originally Posted by dashing

24/(3/4 * x) - 24/x = 10/60
=> 24/3 *x = 1/6
=> x = 48

very good approach .......

keep it up.....

[implex]

Originally Posted by pallaviagrawal

since its a cubic equation with roots a,b and c
abc=c....(1)
ab+bc+ac=b-a....(2)
and a+b+c=0...(3)


either ab=1 or c=0

when ab=1 from 1,2 and 3, we get a^4-a^3+a^2+a+1=0
this i dont think has any real solution.
if c=0,a+b=0 and ab+0=b-a
solving we get a=-b=0 or 2
hence 2 solutions.
this equation also has a solution when a=b=c=0.
hence answer is 3.is that right??

yeah right nicely done

[Fuzon]

24/(3/4 * x) - 24/x = 10/60
=> 24/3 *x = 1/6
=> x = 48

this din strike to me ... was involved in a hell long calc ... ...

keep posting such short cuts dashin ... wd help us realise a lot of things