# Quant Topic Wise Discussion CAT 2011 - Answers/Solutions/General Discussion

Hi Folks, To keep the thread ‘Quant Topic Wise Discussion CAT 2011’ spam free and as notes for all of us… Here is the another thread for posting answers, general discussions, solutions, queries, feelings and everything rela…

Hi Folks,
To keep the thread 'Quant Topic Wise Discussion CAT 2011' spam free and as notes for all of us.. Here is the another thread for posting answers, general discussions, solutions, queries, feelings 😛 and everything related...
Here is the link for the thread...
http://www.pagalguy.com/discussions/quant-topic-wise-discussion-cat-2011-25069595

Hope you understand the concern for making this new thread..

Thanks,
Fungus,
Mentally CATarted..

Another question which will, I am sure, will brush up many concepts.. on functions...
Here it goes..

How many real r are there such that the roots of x^2 + rx + 6r = 0 are both integers?

(a) 5 (b) 9 (c) 10 (d) 18 (e) none of these

Don't treat it as a question, it is a concept builder... I want Puys to participate and post... So that I can keep myself motivated that people are using this endeavor and I should continue with this,
Also, I request all to post concepts/material they find... will help everyone of us....

Needs Motivation to keep the Spark..ON
-Cheers,

Puys,
I have a plan... to tackle the QA specially with t
We have a thread
http://www.pagalguy.com/discussions/conceptstotal-fundas-25023536
where so many funda and techniques are available. If we can divide the 112 pages among 10 ppl taking 11 pages each and posting all relevant material, topic wise. It can help all of us alot..

Like we have 10 volunteers with us
so A will take care of pages (starting from the earliest post) 1-11,
B --> 12-22,
c--> 13-33 and so-on...
Please think again! It's a big application of divide and conquer and boon to save the time.. because alone nobody can but together we can and we will..
Please respond and take the charges...

--Thanks,
Fungus

Puys,
I have a plan... to tackle the QA specially with t
We have a thread
http://www.pagalguy.com/discussions/conceptstotal-fundas-25023536
where so many funda and techniques are available. If we can divide the 112 pages among 10 ppl taking 11 pages each and posting all relevant material, topic wise. It can help all of us alot..

Like we have 10 volunteers with us
so A will take care of pages (starting from the earliest post) 1-11,
B --> 12-22,
c--> 13-33 and so-on...
Please think again! It's a big application of divide and conquer and boon to save the time.. because alone nobody can but together we can and we will..
Please respond and take the charges...

--Thanks,
Fungus

Bro,

I will take charge of 12-22

Kindly solve this question. I have attached the image. AR and RB are angle bisectors. And angle R is 90 degrees. Find x?

Crina Says
Kindly solve this question. I have attached the image. AR and RB are angle bisectors. And angle R is 90 degrees. Find x?

It's functions going on in this thread. Will take this query when geometry part will arrive or you are in the wrong thread. There is a seperate thread for asking doubts in quantz. Hope you understand.
Puys,
I have a plan... to tackle the QA specially with t
We have a thread
http://www.pagalguy.com/discussions/conceptstotal-fundas-25023536
where so many funda and techniques are available. If we can divide the 112 pages among 10 ppl taking 11 pages each and posting all relevant material, topic wise. It can help all of us alot..

Like we have 10 volunteers with us
so A will take care of pages (starting from the earliest post) 1-11,
B --> 12-22,
c--> 13-33 and so-on...
Please think again! It's a big application of divide and conquer and boon to save the time.. because alone nobody can but together we can and we will..
Please respond and take the charges...

--Thanks,
Fungus

Bro i ll take in charge of the pages from 23 to 33...:p:p:p

Pages 1-11 (My responsibility)
Pages 12-22 (N Rama..'s)
Pages 23-33 (Ganu's)
Pages 34-45 (PGM)

Cheers 😁

fungus Says
It's functions going on in this thread. Will take this query when geometry part will arrive or you are in the wrong thread. There is a seperate thread for asking doubts in quantz. Hope you understand.

ya I know..sorry posted by mistake on this thread. Anyways, thanks

x^2 + rx + 6r = 0

a+b =-r
ab =6r

1/a +1/b =-1/6

a= -6 +36/(6+b)

36 has 9 factors so , we will get 18 values in total if we consider the negative factors too.

answer is 18 in IMO.

Another question which will, I am sure, will brush up many concepts.. on functions...
Here it goes..

How many real r are there such that the roots of x^2 + rx + 6r = 0 are both integers?

(a) 5 (b) 9 (c) 10 (d) 18 (e) none of these

Don't treat it as a question, it is a concept builder... I want Puys to participate and post... So that I can keep myself motivated that people are using this endeavor and I should continue with this,
Also, I request all to post concepts/material they find... will help everyone of us....

Needs Motivation to keep the Spark..ON
-Cheers,
x^2 + rx + 6r = 0

a+b =-r
ab =6r

1/a +1/b =-1/6

a= -6 +36/(6+b)

36 has 9 factors so , we will get 18 values in total if we consider the negative factors too.

answer is 18 in IMO.

Can you please explain further, the solution and those 18 values.

Prior Thanks,
Can you please explain further, the solution and those 18 values.

Prior Thanks,

6+b can take 1,2,3,4,6,9,12,18,36 (and negatives of these)

so u will have 18 values for b and corresponding 18 values for a.

6+b can take 1,2,3,4,6,9,12,18,36 (and negatives of these)

so u will have 18 values for b and corresponding 18 values for a.

Hey,
Let's try with your method.
x^2 + rx + 6r = 0

a+b =-r
ab =6r

1/a +1/b =-1/6

a= -6 +36/(6+b)

b cannot take values like 1,2 as both the roots are integers. and b with these values will not result a as integer.
(6+b) should be the factor of 36 not just b.
values that b can take are
{0,3,6,12,30, -2,-3,-4,-5,-7,-8,-9,-10,-12,-15,-18,-24,-42} These should be the values. which satisfy.

so, answer is 18.

Hey,
Let's try with your method.
x^2 + rx + 6r = 0

a+b =-r
ab =6r

1/a +1/b =-1/6

a= -6 +36/(6+b)

b cannot take values like 1,2 as both the roots are integers. and b with these values will not result a as integer.
(6+b) should be the factor of 36 not just b.
values that b can take are
{0,3,6,12,30, -2,-3,-4,-5,-7,-8,-9,-10,-12,-15,-18,-24,-42} These should be the values. which satisfy.

so, answer is 18.

isnt it wat i had exactly said above??
or did i said 6+b should be factor of b ??
isnt it wat i had exactly said above??
or did i said 6+b should be factor of b ??

U said this..

'6+b can take 1,2,3,4,6,9,12,18,36 (and negatives of these)'
not 6+b but b can take values and values are different from what you have mentioned
U said this..

'6+b can take 1,2,3,4,6,9,12,18,36 (and negatives of these)'
not 6+b but b can take values and values are different from what you have mentioned

I am not sure if u have understood what i have meant from above. To reiterate it clearly , this is what i meant :

when i say
'6+b can take 1,2,3,4,6,9,12,18,36'

that means 6+b =1,2,3,4...

or b=-5,-4,-3,-2,0,3,6,12,30 ....

and accordingly u can find the 'a' values to make it a pair.

Hope i am clear now.

Got it. Both of us were discussing the same point. Sorry, I could not understand ur point and pointing it again and again. 😞

How many five digit numbers can be formed using the digits from 1 to 9, such that the first three digits are in increasing order and the last three digits are in decreasing order?

1576
1596
84
None of these

How many five digit numbers can be formed using the digits from 1 to 9, such that the first three digits are in increasing order and the last three digits are in decreasing order?

1576
1596
84
None of these

if one selects 9 as the middle digit then,

8C2*8C2=784(1st two digits and last two digits can be (1,...,
Similarly,
If 8 is the middle digit, then
7C2*7C2...441
If, 7......
6C2*6C2..225
6......
5C2*5C2..100
5.............36
4..............9
3...............1

Total is 1596.