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Linear Equations
by Total Gadha - Tuesday, 23 October 2007, 08:37 AM
  cat 2007 cat 2008 linear equations xat 2008 mba 2008I am sure that this chapter is considered easy by many CAT 2007/ 2008 aspirants. But it is one of the most frequently occurring chapters in CAT. Mastery with equations helps you solve many problems in other areas also. As we progress deeper into Algebra on TG, we think it would be better to stat with this small but useful lesson. As your D- day comes nearer, revising some old concepts wouldn’t hurt you. smile



Any equation of the form p = 0, where p is a polynomial of degree one, is known as a linear equation. The polynomial p can contain a single variable, two variables, or more than two variables. Some examples of linear equations are given below:

cat mba linear equations

cat mba linear euqations

cat mba linear equations

cat mba linear euqations

cat mba

I shall have to end here and leave the rest of it for my CBT Club students. I shall cover some problems based on this in the CBT Club this week.


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Re: Linear Equations
by Kumar Varun - Tuesday, 23 October 2007, 11:45 AM
  Nice Stuff TG...
as the D day is coming nearer and nearer my apprehensions r increasing .Mor so about the English section.. now i just think ki " English ka kuch nahi ho satka.. leave it and pay attention to other sections.." kuch solution batao sir iska..
There is one query TG:
What is the approach to solve these type of problems in which eqn of line(s) is given and we have to find the no. of integral solutions.
Find the number of integral solutions of 3x +5y = 7 where x and y lie between -50 and 50 (both inclusive).
Plz tell any general approach to solve these type of questions..

Waiting for reply,
Re: Linear Equations
by yetandra Adireddy - Tuesday, 23 October 2007, 03:40 PM


Could pl write an article on how to fine tune our preparations for the coming D-day.

like what should be our prime concerns in the last week and day before exam things like that.

will be pretty much owed to you if u can do that.


thanks in advance.

Bhavani kumar


Re: Linear Equations
by fundoo bond - Tuesday, 23 October 2007, 04:20 PM
  hi TG sir,
the much awaited article appears... smile
i consider ur articles as a treassure n in d coming days i ll study them again as my revision...

Re: Linear Equations
by Srikanth deshpande - Tuesday, 23 October 2007, 05:12 PM

Hi Total Gadha,

We are waiting for the Geometry Material such as you deliovered for Number systems.any news regarding the time by which it will be probably ready ?


srikanth d

Re: Linear Equations
by Rishi Kapoor - Tuesday, 23 October 2007, 10:29 PM

Thanks fot the article sir.


Re: Linear Equations
by sourav nandi - Wednesday, 24 October 2007, 08:06 AM

hi varun

for the ques u posted

integral soln of 3x+5y=7

the approach is discussed in the article itself!

we find a pair of integer soln for the eqn is (4,-1)

now from here on we jus form an A.P for x with common difference 5

so we have, -46,-41..............-1, 4,9,...................49

in all 20 integral soln in the range (-50, 50)

do tell if it works!



Re: Linear Equations
by Sandy P - Saturday, 27 October 2007, 07:15 PM

Hi TG sir,

excellent article, its a good refresher....



Re: Linear Equations
by Kumar Varun - Wednesday, 31 October 2007, 01:23 PM

it works fine saurav..


by Varun Choudhary - Monday, 5 November 2007, 05:31 PM

Thanks a lot TG ..


please cum up with concepts of Geometry asap.....

thanks a lot

Re: Linear Equations
by Varun Choudhary - Monday, 5 November 2007, 05:45 PM

write it as  x = (7-5y)/7

and start from y=-50 to have x betwen -50 & 50..

we get first y as -28 and so move on with a common difference  of 3 in an AP . like .-28,-25, can go upto 29.

so count the num of terms in this AP answer shud be 20..please correcty me if i am

Re: Linear Equations
by brendan decruz - Tuesday, 6 November 2007, 02:27 PM

tg sir,

how do we access the previous quants discussion articles particularly the one on permutations and combinationssss........ have they been permanently removed......??????? please reply....

Re: Linear Equations
by Total Gadha - Friday, 9 November 2007, 05:50 AM
  Hi Brendan,

We rarely write an article that needs to be deleted. You can find all the articles/lessons in "Total Gadha's Quant/Verbal Lessons."

Total Gadha
Re: Linear Equations
by Neha Vyas - Saturday, 10 November 2007, 04:47 PM
  Hi Tg,
Well I dont reply much or comment much on any of the articles ever. But i just want to let you know that when i am appearing for the CAT paper this year i will be thanking you. And also if i do get through its a hell lot of thanks to you. You've been great all the while meticulously posting these articles for us. Just wanted you to know that each one of them helped. And thanks to Dagny too.
Re: Linear Equations
by shiny das - Saturday, 10 November 2007, 05:59 PM


 im new to this site nd wish to appear for cat 2008.... im quite scared of complex maths problems..i simply dnt knw how to start...nd also i wd like to ask is it possible to crack the xam wdout joining an institute wd just the materials nd the reqd books...nd


Re: Linear Equations
by ash gupta - Thursday, 15 November 2007, 06:45 PM
  nice article sir..........
Re: Linear Equations
by Total Gadha - Sunday, 18 November 2007, 04:29 AM
  Hi Shiny,

If you're planning for CAT 2008, studying solely on TG would be enough. We did not get enough time this year but for CAT 2008 aspirants, we shall have the complete material for study. smile

Total Gadha
Re: Linear Equations
by the underdog - Monday, 19 November 2007, 11:17 AM
  A question extremely similar to the cheque one out here was asked in the CAT 2007 exam smile.
Re: Linear Equations
by ankush gupta - Friday, 18 April 2008, 01:14 PM

Hi Total gadha,

I am logging first time to ur site.I have never seen such a beautifull,well-articulated site for Mba aspirants in my life.I want to thank you for this.

U have solved one question above which has come in CAT 2007.The perfect square(first 2 are equal and last 2 are equal).Hav u written this article after CAT 2007

Re: Linear Equations
by Total Gadha - Saturday, 19 April 2008, 09:26 AM
  Hi Ankush,

You can see the date of the article at the top. Maybe this would help you see TG in new light smile

Total Gadha
Re: Linear Equations
by ATOM ANT - Thursday, 12 June 2008, 04:28 PM
I ve a few doubts in this

In the yoga/tennis problem

you ve equated the no of idle days as
24-x = 14-y

is it not 24-y = 14-x ?

as in a day when nothing is done in morning  they either tennis
or 2. remain idle

so you ve to subtract the no of days they play tennis from 24 to get the no of idle days..

correct me if am wrong...
Re: Linear Equations
by ATOM ANT - Thursday, 12 June 2008, 04:32 PM
anothr one..

you ve said that there is no soln if

a1/a2 = b1/b2 != c1/c2

but in the simultaneous equation given above

5x+6y-30=0 and

the soln is unique.. but the condn is not satisfied...

Kindly explain sir
Re: Linear Equations
by ganesh ram - Monday, 4 August 2008, 08:52 PM




Re: Linear Equations
by niharika mishra - Tuesday, 23 September 2008, 08:05 AM

hi ganesh i think by now u must hav got the explaination...but still..... here is my version.

make a table


                             grandfather             father               son


(after n yrs)           x+n                              x                      y+n


present age                 x                               x-n                     y


now according to conditions we g8 following equations.




solving we get







Re: Linear Equations
by ganesh ram - Sunday, 15 February 2009, 04:44 PM



Re: Linear Equations
by Rajarshi Guha - Saturday, 18 July 2009, 07:06 PM
  Dear TG,
I have an observation.Please correct me if I am wrong.

In the question where we have to find the difference in the incorrect and correct valuation of the cheque,Option E states that the sum of the digits of the correct amount can be a multiple of 9.

The correct value is 18.36.which implies 1+8+3+6=18.This is divisible by 9.Should nt this option be regarded as true then?

Re: Linear Equations
by srujan duddukuri - Thursday, 13 August 2009, 10:28 PM
  Kudos to TG for his gr8 work.......keep rocking TG!!!!smile
Re: Linear Equations
by aashish biala - Monday, 17 August 2009, 11:01 AM

great work TG.


Re: Linear Equations
by iim freak - Friday, 21 August 2009, 02:46 AM
  hi Rajarshi

The answer is not fixed there can be many more like 75.93 where digit sum = 6

i hope it helps smile

Best Regards
iim freak
Re: Linear Equations
by ajay arunabh - Monday, 24 August 2009, 04:56 PM
  dear tg
in shayam run question i have a doubt.
suppose total no of runners taking participation in race are x+1,
now from first situation
x/2,x/2 runners will run infront and behind of shyam
now from second situation
solving equation (a)
we get total no of runners=5
Re: Linear Equations
by Netra Mehta - Saturday, 29 August 2009, 03:04 AM
  Hi Atom Ant!

Even I got confused on your doubt earlier but when you ll check u can see that..

we have got 2 equations..

24-y=14-x --- (1)
=> y-x=10

& x+y=22 ---(2)

On solving (1) & (2)

We get y=16 & x=6
therefore no. of days when they did nothing is 24-y = 24 -16 = 8
which comes out the same as wz given in the solution by tg.

So ,finally ans comes out to be 16+6+8=32.

I hope it helps you..
n plz check me if m wrong..
Re: Linear Equations
by brij g - Tuesday, 13 October 2009, 01:22 AM
  You are correct, answer will be same but I will go with Atom Ant that 24-y and 14-x will give us the no. of days on which they did nothing.....think it out..
Re: Linear Equations
by abhishek rai - Friday, 11 June 2010, 02:30 AM
  In the question when Shyam visited Ram during his vacations, How can there be 24 mornings when they did nothing and still managed to do yoga for 16 days? Think there's a Typo there, which lead to the bizarre conclusion.

Shouldn't the equation be

24-y=14-x (Days when they did nothing should be equal.)
So, y-x=10



So, Y=16, x=10. When they did nothing= 24-16=8. So the total no of days is 30.

Correct me If I am wrong
Re: Linear Equations
by priyanka j - Friday, 9 September 2011, 05:33 PM
We can solve these ques in this way also na:

1) Restaurant ques (CAT 2001)

3b+7s+f=120 -------(1)
4b+10s+f=164.5 -----(2)

equ. (2)-(1)
b+3s=44.5 -------(3)

rewrite equ.(1) as
2*44.5 +b+s+f = 120
=31 ans

2)no. a,b,c,d,e satisfy given conditions
13a+26b+2c+13d+3e=18 -------(1)
6a+12b+c+6d+e=7 -------(2)
5a+10b+c+5d+e=6 -------(3)

11a+22b+2c+11d+2e=13 -------(4)

2a+4b+2d+e=5 ---------(5)

a+2b+d=1 --------(6)

put equ(6)in equ(5)
e=3 ans


Re: Linear Equations
by nick depp - Thursday, 10 November 2011, 11:59 AM
  Linear Equations Help???

1. In 2000, the minimum wage in Washington was $6.50 per hour. In 2010, it was $8.55 per hour.

(a) If x is the number of years past 2000 (so in 2000, and in 2010, ), and y is the minimum wage per hour, write two ordered pairs representing the minimum wages given.

(b) What is the slope of the line between these two points? What does the slope specifically represent here?

(c) What is the y-intercept? What does the y-intercept specifically represent here?

(d) Find the equation of this line – write your final answer in slope-intercept form.

(e) Write your equation as a function of x.

(f) If you do not earn a college degree and you are earning minimum wage in 2020, what do you predict you will be earning per hour?