Simple Equations 4 | CAT Preparation 2024 | Algebra | Quantitative Aptitude
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- Опубліковано 11 кві 2019
- Advance Algebra by Ravi Prakash | Quantitative Aptitude for CAT 2024
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18:40 there should be 24*2-1 solution
Bhai u r right
Sir se dhoke se ho gya h
Why *2?
Why not *4
@@NormalPerson053 yahi tareeka *2 karke 😹 I got to know later
@@NormalPerson053 because no;of factors which means it covers (a,b) &(b,a) so now all we need is all these in negative numbers so x2 .in normal we gets only (a,b) so X4
For anyone who is facing problem in calculating factors, look for "factor-1number system" video of sir at 7:00
Very helpful ❤
Thanks a lot .
If a number is in the form a^p * b^q where a and be are prime numbers then the no.of factors of that number can be calculated as (p+1)(q+1)
Thank you:)
Thank you soo much
Thank you
Thank you
IF A CASE IS AS SUCH THAT WE GET PAIR OF SOLUTIONS TO BE (a, a) then while we multiply the total number of factor*2(fo r considering ordered solutions shouldn't we subtract the case of repetition of cases when they are eqaul(in case of perfect square)
RAVI SIR = SAVIOUR FOR STUDENTS
Sir How are you getting no. of sol. by factoring the RHS. Can't get that part please help
For the first question, we can also get the eqn: (y-1)(1-x) = 98. Then we'll get 2^1 and 7^2 . 12 total factors then
in your eqn it should be -100 and not 98
If you simplify your equation then it won't match the original question
Thankyou sir
Ravi sir has a shortcut for everything 😋
ravi sir your video helped me a lot if i cracked cat then. it will be because of you.
Did you crack cat?
Congrats 👏👏👏
@@anjali5482 no lol 😂😂
@@janmejaypanda5414 😅
No issues. Keep on practicing. You can do it 👍
in first question (x-1)(y-1)=100
if -1×-100 is counted to as integral solution
if x-1=-1 then eqn will be zero
Thank you master jiii
Thankyou 💜 so much sir 🙏🏻
I have a query, that at 22:25, why did he multiply it with 2, are we looking for only +ve solutions?
Thank you Sir 🙏
sir at 19.05 min you did no of factors multiplied by 4 . But earlier you explained that for Intergral solution no of factors * 2 . Can you share the feedback about this ?
Same doubt
it will by *2 only i have checked multiple sources. He might have written it by mistake
@@jishu1998 yes there will be 47 solution .
Each Pair of the integral solutions should be multiplied by 4.
Same doubt,I think mistKe
thankus sir!😍
At 18:45 , shouldn't it be 24 * 2 -1 , instead of 24*4 - 1 ? Can you please clear my confusion?
yes it is 24*2-1.
Ya.. I corrected it later
@@raviprakash6021 sir can u explain w 24×2-1 .here i could not understand why u multiplied by 2.
Yes I agree
@@sidswamiuc6770 we have to multiply the no.of factors by 2 in order to get no.of integral solutions and have subtract it by 1 in reciprocal solutions Soo,24*2=48 ,48-1=47 solutions
|x| +|y| +|z| =15 . Sir how to find positive integral solution of this eqn ?
I know there is a confusion.
Remember the shortcut sir explained earlier?? i.e., No of factors *2 gives the total solution. So when you are solving by the number of factors method, then you need to multiply the number of factors by 2. If you are approaching the solution the usual way, then we multiply it by 4 (x, y), (y, x), (-x, -y), and (-y, -x)
As far as, if there is any mistake by Sir then Yes, and he solved the same question again and corrected it. Don't fret over it and waste your time.
Hope it helps!
Sir, In 2nd question why can't we do with the same method as Q1 by substracting 3 on both the sides we'll form an equation
please reply
bhai kitna syllabus ho gya ? cat 1st time de rhe ya 2nd??
For last question it must be be 28 integral solution.. because it is perfect square.. 14*2+1=29 then remove 29-1=28
no in case of perfect square, no of solutions are 2*no of factors. We then remove one case only.
Sir, in the second example explained, isn't it entirely upto us as to how we factorise the equation. And in doing so, one will always get different number of factors (as the factorization changes). For instance, I factorised as:
(x+1)(y-5/2) = 25
This way my number of integral solutions came down to only 6 (as 25 has only 3 factors).
Kindly explain.
Thank you
Your equation is : (x+1)(y-5/2) = 25. If you simplify, the equation will be (2xy - 5x + 2y) = 55. But, Sir's equation is (2xy - 5x + y) = 55. I think there is some error in your factorization.
55-5/2=105/2 as you have taken 1/2 common...just write it down you will understand
For the second last question, positive integral solutions will be 12?
24 will be the answer
Thanku sir
Can someone explain to me why we didn’t multiply 2 with the whole equation just the second part . Isn’t it a rule that if we multiple something on rhs the same has to be multiplied on entire lhs
4*2*3 didnt get this part @18:20
Sir what is ordered form and what do you mean by variables are given in the first lecture of simple equation in1st question there you also say variables are given so it has ordered solutions .sir I'm not getting this thing please explain
Watch Number System videos by Ravi Sir
At 10:20 , I didn't get how to get factors . how is that 2x2x2 is coming , can someone explain ?
watch numbers playlist.
At 14.00 no of sol are 3 only but sir write 5 how that possible? The sol are 1,9. 9,1 and 3,3
For the last question how 2^4 ×3^2 and why not 2×2×3 is the answer
why 2*2*2* = 8f how u calculate it???? couldn't get it......
for anybody who doesnt understand the factorization concept i.e how 2 to power 2 x 5 to the power 2 became 9, check comment by anubhav chaturvedi and reply to that. Probably 10th or 11th comment.
Hlo bro actually me also not understa... It how it is 9 . Pls tell me how it is 9
@@coc5334 I dont remember which problem but most probably its this. See, the factors were 2 squares x 5 squares right. So, we have to add 2 to the power and multiply. (2+1)(2+1) 3x3 =9. Also check the comment by ANUBHAV CHATURVEDI SOMEWHERE DOWN.
in q 1 sir is saying no. of integral solos = 2x no. of factors but @18:48 we are multiplying by 4. it should be 2 right? or am I missing something ?
it should be 2
yeah integral solutions is 4 , but while using prime factorization we multiply by 2
......got it
integral solution is 4 when calculating through conventional method
@correct sir @Rodha
How to find factor of a number using shortcut? Please help 🙏
SAME
How to determine the no. Of factors?
@ 9:46 can anyone explain why 2 is not multiplied in (2Y-5) and only done in (X+1/2). couldn't understand that part
2 * a * b = 2a * b = a * 2b
not 2a * 2b.
hope its clear
@@nisheshojha3539 but its 2ab
how to find the factors 2cube *3*5 square
how 2 cube sir
In question 2 of this video, out of the 16 solutions, 2 solutions i.e. 1 and -5 make the LHS of the equation as 0. So, do we count them as solutions?
Can you re-check your calculation once? I don't think any of the ordered pairs of the solution make the LHS 0. (1,-5) leads the original equation LHS to 0, but is not a solution.
(2*-5 -5)*(2*1+1) = -15 * 3 = -45 != 105.
You made a little conceptual mistake with the nature of solutions. 1 and -5 are not two solutions out of 16. Each solution is going to be an ordered pair of the form (x,y) which contains the respective values of x and y which together satisfy the equation.
The solution pairs are: (for (2y-5, 2x+1))
(1,105) --- (105,1)
(3,45) --- (45,3)
(5,21) --- (21,5)
(7,15) --- (15, 7)
The remaining 8 solutions are going to be negatives of the above given solution such that their product remains positive and of the same magnitude.
is vdo ke ques 2 me factor 8 kese aaya, factor kese nikalte h bata skte ho
@@anonymous-ek5iq Ye samajhne ke liye number system mein factors ki video dekh lo ek baar.
105 = 3 x 5 x 7
All factors will divide 105 completely. Each factor can either have 3^0 or 3^1 as constituents. The same is true for 5 and 7 as well.
So, total choices to create factors/Total number of factors = 2 * 2 * 2 = 8
(3^0 or 3^1) 5^0 or 5^1 7^0 or 7^1
@@VinayKumar-vk3tq Thanks for helping mate. I figured out where I got it wrong. It's the value of x and y which become 0 and not the equation.
21:08 , why are we subtracting only 1 from 48 , there is also case of (x,y) = (-20,30) (20,-30) where x and y can be zero , so we should subtract 3 cases
those anserws will be -600, not +600,
@@fadhilu5171 thanks
@@fadhilu5171 answer ultimately become zer
for positive, it will still be the no of factors no?@@fadhilu5171
At 10:28 ,2*2*2 means ?,how
Sir at 6:30 & 9:20 we are not counting the solutions with x or y=0 by using the original equation. I mean shouldn’t we use that too?
even if you go your way, the answers will be same
i thought about it but when i solved i found no condition like this, solve it you will automatically understand
Could please someone tell me how sir did factor what is the logic behind 2*3*4 at 18:32 pls pls how to do factors
here 2^3 * 3^1 * 5^2 so we are taking the powers and adding each power by 1 so we got 3+1 * 1+1 * 2+1 = 4*2*3
read number system's factors topic of rodha
Can anyone plzz help ,
How there are 9 factors in 1st question
At 4:00
Its the formula ..3 x 3= 9 factors...(2+1)(2+1)..where 2 ,2 are the powers of prime factors...look it up in the prime factors video of RODHA
@@tusharpanda3528 which video exactly
14:47 anyone please reply:
How this satisfies
1/1+1/9=1/3
Can anyone please explain how to find the integral solution of x^2+y^2. This topic is not covered in the video. Please anyone?
facing same problem ,
they are saying to watch "numbers system" playlist .
its quadratic level questions not simple equation level
10:25 we got 16 as number of integral solutions for (2y-5)(2x+1) but how many out of them would be integral solutions for x and y, because that is what question asked?!
16 are the number of values/solutions for x and y only
2xy-5x+y=55 in this question
i took
2y(x+1)-5x-5=55-5
(2y-1)(x+1)=50
so
50=2*5^2
so (1+1)(2+1)= 6
no of intergral come out to be 12 in my case
what should i follow and what mistake im doing ?
@rodha @ravi sir
but you answere came out to be 16
How can you take 2y common when there is no 2y term
bro u did a mistake in taking common factor thr ... Factors r (2y-5)(x+1/2)=55 -5/2
So we can write (2y-5)(2x+1) = 105 = 3×5×7
14:29... You should be ignoring (3,3) because (x-3) (y-3)=9, substituting value gives 0, which is not possible.
No bro
(3,3) are not the values of (x,y) ; they are the values of (x-3,y-3). hence the x,y values will be (6,6).
@@venkatsai258 Haven't understood what u said , bro, please elaborate
Same prob here also bro ..
@@sachinkumarsingh2518 consider x-3=a; y-3= b. Now it becomes a x b = 3^2.
Find all the possible values of a,b and then check for which values x,y are becoming zero. You will get it.
Sir how are taking the factors 4×2×3 plz explain ?
bhai pata chala ho toh batado merko bhi
At 3:35 how he said 3×3 =9 factors
I couldn't get it please somebody explain
100 can be written as 4 *25 , (which can be written as 2 square * 5 square ) for 4 digit three factors ( 1, 2, 4 ) and for 25 3 factors (1, 5, 25 ) so 3*3 = 9 factors, you can apply the same method for next problem and you will get 2*2*2
3:10 how did you get 9 factors? I am not getting that part.
same here
(Power+1) factors ke liye
Yes i am also not getting how to get those factors
do you mean positive integral solutions for the same question?
both positive and negative soln
How to find no of factors???? Please explain
i think we take the powers of numbers with 1 added and find their product
14:29. Since if you substitute (-3,-3) in the denomination. You will get -2/3 in the L.H.S which is not equal to 1/3 in the RHS
(-3,-3) are solution for (x-3) and (y-3), not for x and y
@@vishwashachadad5646 thanks bro i have the same doubt...
@@vishwashachadad5646❤
Why do we multiply factors with 4 in some questions but with 2 in some . Can someone explain
the solution at 19:00 where we're multiplying the number of factors by * 4 is incorrect right? Please confirm.
sir has solved the same question again by *2, so not sure if these were 2 different cases or a mistake.
Second one is correct...*2
@@manthansahu5582 cool, thanks
Typo it is
@@manthansahu5582 it means previous all questions which is multiply by *4 which Is wrong?
At 22:10 I don't understand how 15 factors will come??
can anyone explain me how
at 3:40 it is 9 factors?
No of power of prime factor +1 => 3*3=9
first prime factorized the number and then (power of the number +1)...... 100 : 2^2*5^2 : 2+1=2+1 (powers of factors +1
last question answer I am getting 31 integrals solution. Do anyone getting same?
@16:33 is it (abc)^2 or a b c^2??
a b c^2
It should be 24*4-1....right??.....As we to find the negative solutions as well
2*no of factors includes the negative solutions
left me confused with the last two questions
Very easy explanation! 🙏
did u get into any IIM?
@@Tuuuuusssjjjjjjnrnfnnfnfn no she did not
@@swapnilrajput8086 how do u know?
@@Tuuuuusssjjjjjjnrnfnnfnfn she is in MDI gurgaon . i checked on linkedin
RESPECTED SIR
KINDLY CLEAR ONE DOUBT.
IN QUESTION 1/X+1/Y=1/3
INTEGRAL SOLUTIONS SHOULD BE (24*4 )-1 OR (24*2)-1
KINDLY CLARIFY
WITH REGARDS
ROHIT SHARMA
47. It was a mistake
@@Rodha THANKS SIR FOR CLEARING THE DOUBT
Why (24*2)-1
@@snehamohapatra7039 because no of solutions will be (no of factors *2)
And 1 is subtracted becuz 0 cant be in the denominator
@@vishwarajgaur3953 no there will be only one solution which needs to be excluded i.e. when x,y =(0,0) .......(0,-10) and (-10,0) wont satisfy the equation kindly check again
Can anybody please explain how 100 became 2 square x 5 square or how at 10:05 105= 3x5x7?
factorization
first prime factorized the number and then (power of the number +1)...... 100 : 2^2*5^2 : 2+1=2+1 (powers of factors +1)
sir why it is 24 x 4 -1 instead we have to multiply 2 .
how at 6:40, we got 9 factors???
Same doubt
that's because of a formula, when we add the powers to +1 and multiply, we get total no. of factors.
for ex: 2²+5²= (2+1)(2+1)=9
we simply added the powers
@@aanyarawat9120 thank you ❤️
Sir can you please tell how to get no. of factors.
Numbers chapter - Factors topic
in last sum how 2^4 *3^2 = 15f is come???
because 5*3 =15. in number system you must have learnt that power +1 of one prime factor * power + 1 of other prime factor
sir, how 3*7*5 becomes the factor of 2*2*2 ? plz clear it.
Watch the "Numbers" playlist.
3 has factors as-1, 3
7 has factors as -1, 7
5 has factors as-1, 5
So 2 factors each hence 2*2*2
@@vikrantverma1000 then y didnt we do the same in previous question..y it is 18??
Why did u multiple with 2 only on 1 side
At 18:05 why sir multiplied 24 with 4???
Bcoz one integral value has 4 soln which is +-, -+,++,-- that's why
Why did he multiply 24 * 4 while solving the shortcut it should be 24*2-1
Its total integers solution including negative integrs aswell
In 10:29, can anyone explain why sir did 2×2×2?
Find the factors for the number in prime numbers.
Then add 1 to power of each number and multiply them.
105=3*35. Further break it down. 35= 7*5
So 105=3*5*7. The powers are. 1*1*1
Each have 1 power. Now add +1 and multiply them. It becomes 2*2*2
In 2nd ques how the factors part took place -2*2*2 how did we took 8 factors pls explain..
ua-cam.com/video/co30DI-DAlU/v-deo.html 7:20
Find the factors for the number in prime numbers.
Then add 1 to power of each number and multiply them.
105=3*35. Further break it down. 35= 7*5
So 105=3*5*7. The powers are. 1*1*1
Each have 1 power. Now add +1 and multiply them. It becomes 2*2*2
ua-cam.com/video/hlEjsEVLkbg/v-deo.html or 18.40 at this time, I think the number of solutions should be 24*2-1 instead of 24*4-1. sorry of me not correct!
but please clarify
47 is correct answer he clarified in a comment reply
Can anyone help to break down the equations? Like sir did in the reciprocal solution questions
7:00 for soln(1,100):
(X-1)(y-1)=100
1-1)(100-1)=100
Not satisfied....please correct me where I'm wrong
x and y are not 1 and 100 here...,.. x-1 and y-1 are 1 and 100 respectively.
thus making it x-1 = 1 and y-1=100
x= 2 and y = 101
hi sir please explain about the factorise in reciprocal case
why 15* 2 no of factor not 15*4
can anyone please tell me how it is 4*2*3 in 20:30 mins please anyone!!!
sir in last 2 questions please explain why you multiplied by 2 instead of 4 ? please
it is because:
there will be n/2 pairs for n factors.
and those n/2 pairs will have 4 patterns each.: (x,y), (y,x), (-x,-y),(-y,-x)
therefore, (n/2)*4 = 2n.
Hope this solves ur issue.
@@priyankmehra7416
at 10.18, how 3*5*7 gives 2*2*2 = 8 factors ?
How ?
Shashank Gupta if N = a^p * b^q * c^r, where a,b,c are prime numbers, then N will have (p+1)*(q+1)*(r+1) factors.
@@priyankmehra7416 Thanks got it👍
@@priyankmehra7416 so how in previous question he took *4 instead of *2
Sir I have a doubt- how i can find factors..
please also lmk if u do find a way
18:47, how does it become 4*2*3= 24 factors, i am not able to understand this concept
me too not able to get this concept
@@learnwithbina4100did u get this concept by now ?
10:05 h0w 2×2×2 came from 3×5×7 factorial
3*5*7 from this we will take number of factors as like
(Taking all the previous powers)
3 as 3° and 3^1 =total 2
5 as 5° and 5^1= total 2
7 as 7° and 7^1=total 2
Therefore the total factors came out to be 2*2*2=8
at 10:18, how 3*5*7 gives 2*2*2 = 8 factors ?
Power of all prime base in the number is 1 so power+1 and then multiply (2*2*2)
@@nehasingh5593 👍
Can anybody explain me that after 100= 2^2*5^2 then how these integral factors 3*3 came ???? What’s the logic
add one to the power,then multiply, eg here powers are both two so (2+1) x (2+1) we get 3x3=9, if say factors are 2 power 3 and 3 power 2, then factors are = (3+1) x (2 +1) = 4x 3 = 12 factors
At 3.41 there is 3*3 as number of factors...how is that?
refer number system, factor one
Sir how do u calculate no. Of factors
a^ p x b^ q x c^ r where a,b and c are prime factors and p, q and r are the powers hence, (p+1) (q+1) (r+1) = no. of factors
Lcm le le bhai easy
How is sir getting the number of factors
By taking the powers . See his first video on factors at around 7:00
At 3:35 , can somebody please simplify how could there be 3×3=9 factors from 2^2×5^2
No. Of factors
a^p*b^q no. Of factors= p+1 * q+1
Hi Sir, Is simple equations important topic for CAT 2023 ?
Same question 🥲
I think quadratic equation are the most important topic
Linear quadratic cubic and biquadratic
95 or 47????
47
how factors are calculated?
Multiply all (powers+1)
@@jahnavijayaprakash9643 means can you explain it properly
@@jahnavijayaprakash9643 thanku. 😊
how is he finding no. of factors anyone help
find on youtube "factor-1number system" watch till 10:00
Can somebody please help how (2 to the power 4 X 3 to the power 2) has 15 factors.
If a number is in the form a^p * b^q where a and be are prime numbers then the no.of factors of that number can be calculated as (p+1)(q+1)
@@nivethakrishnamurthi6410 Thanks :)
2^4 means there are 5 solutions Becoz if you take 4 as 'p'..then the formula for no.of factors is P+1 & for 3^2 there are 3factors.multiply both the factors 5*3=15.
@@nivethakrishnamurthi6410 thanx you saved my life
Thank you
Hello sir,
In few question you have multiplied the factors by 2 to get no. of integral solution.
And in few question you have multiplied it by 4 to get no. of integral solution ????🙄
same doubt
In the last question why it is into 2 ?
every factor will have 2 solution in the form (a,b) and (b,a) so no. of soln = no. of factors*2