Inequalities 2 | CAT Preparation 2024 | Algebra | Quantitative Aptitude

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Advance Algebra by Ravi Prakash | Quantitative Aptitude for CAT 2024
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Комментарии : 167

@AshwiniSingh-yu6pv 9 месяцев назад

For those of you who are confused about the last question: The values of the FACTORS cannot go beyond 5 because if it did then, 6-a=7--> a=6-7= -1, similarly every value beyond 5 will lead to a being a negative number. Factors of 45 :1,3,5,9,15 and 45 Due to the condition above, we stick to the factors being 1,3 and 5. But since we need 4 factors all together---- (6-a) (6-b) (6-c) (6-d), we end up considering negative factors as well which makes the factors as well as the natural numbers a,b,c and d distinct from each other. 45 is a positive number. It only makes sense to consider 2 positive and 2 negative factors. Hence -1,-3,3,5. 6-a=-1 makes a=7 6-b=-3 makes b=9 6-c=3 makes c=3 6-d=5 makes d=1 The question says A,B,C,D are NATURAL NUMBERS. Therefore, the condition is satisfied. minimum sum= a+b+c+d=7+9+3+1= 20 Hope this helps some of you and saves your time. Have a great day.

@dchakraborty79 8 месяцев назад

But in this question if you multiply 7×9×3×1 the answer is not coming 45

@dchakraborty79 8 месяцев назад

Then how is this solution possible?

@pranjalgupta_stxaviersuniv616 7 месяцев назад

We need to multiply 6-a 6-b and all together to get 45 not abcd

@sportivetech279 5 месяцев назад

But why can't you take all four negative factors

@doyelpal1846 3 месяца назад

Can you explain that in case of minimum the values should be far apart or in case of maximum, I got confused because in previous videos sir said that to find out the minimum value the values should be far apart.

@bhagirathsharma7505 3 года назад

The quality of this content is unmatched on any platform

@priyankakumar7387 3 года назад

Wow sir..last sum..your level of thinking 😳😳👏👏

@ashishsingh7165 5 лет назад

Is this inequality or max nd min value?

@VishvajeetSuryawanshi 9 месяцев назад

Good work bro

@vk9401 11 месяцев назад

In the last que the answer is correct, but que mentioned that no.s are natural ie ; No negative integers and also thank you sir for providing this amazing content!! You are the best. Edit: i was wrong ABCD are natural no.s ie; 7,9,3,1 6-a = -1 & 6-b = -3, (got confused by both sets) The que and ans is correct

@naveenkamath907 11 месяцев назад

yeah i had the same doubt... solved by your comment(edit) thanks dude...

@yashasharma9963 3 года назад

Thanks for such quality questions! 🤯🤯

@itssaurabh18 2 года назад

Super quality questions. Thanks!

@nehaagarwalla617 2 месяца назад

Sir in last question we can't take number beyond 5 but if you have taken -15 so we can also take -1,1,1,-45 so the max would be 68

@yashsrivastava7459 Месяц назад

Numbers must be unique. This doesn't satisfy that

@muhammedfasil9036 3 года назад

Great 👍

@tejaswinidaware7395 4 года назад

thank you sir

@_cat_aspirant_99.9percentile 3 месяца назад

Thank you guruji ❤

@kush8806 Год назад

I just used a simple method of deriving values of a,b,c and d in the second question and I got 178 as my answer (10×1×2×3),(9×4),(8×5),(7×6).

@SurajKumar-vu7ef Год назад

I got 175, by using this method, the trick is you have to make 8 numbers in descending order for corresponding multiplication, so my number were 10, 9, 8, 7, 6 (2*3), 6, 5, 4. Now, multiply 10×4, 9×5, 8×6, 7×6. This will give you the correct answer.👍

@Calculatorshubhamsir 2 года назад

U r grt ❤

@Shivam_General_Fitness 11 месяцев назад

Thanku sir

@chanchalbhargav5227 3 года назад

sir you should say "distinct integers' and not "distinct natural numbers" in the last question.

@saksheemalik6773 2 года назад

Right

@anuragsahu7794 Год назад

it says nat nos, but we picked -ve nos?

@rishimukherjee2118 3 года назад

In the last question, why did we take the values 6-a , 6-b , 6-c, 6-d (MIN)to be more than 5 when you yourself specifically mentioned that the no values greater than 5 can be accepted ? Please explain

@bharathanem4631 3 года назад

its that 6-a,6-b,6-c,6-d values indvidulally as an expression cant be more than 5 ....but a,bc,d values can be more than 5

@arnabde5654 4 года назад

But sir these questions are based out of number systems, they don't belong to inequalities section

@sammy.3152 10 месяцев назад

Even If we know the concept. these questions will take up a long amount of time during exams and there are so many chances of making errors in them. I dont think its worth the risk and time. But they are good concepts to develop thinking habit.

@anshul4385 10 месяцев назад

bro these questions dont seem of inequalities ? are they ?

@arshiya56 10 месяцев назад

The inequality part is not started yet here in this video i guess...its in next videos

@deepikagurjar135 2 года назад

@8:39Min.. Sir.. I like this term coined by you.. "THINKING RANGE" 😂😂😂😂😂😂😂😂😂😂😂😂 (Ankur Shrivastav)

@bewithpallabi3120 2 года назад

😁 thank u for the videos. And Wish me luck as exams are near.

@Rodha 2 года назад

All the best

@bewithpallabi3120 2 года назад

@@Rodha thank you! ✨

@madhumitharajinikanthan1007 2 года назад

@@bewithpallabi3120 how did the exam go?

@AyushKumar-wl8cx 2 года назад

@Be with pallabi how was ur exam what u scored?

@krishnamouryapathapati1712 4 года назад

Super sir thank you

@VishalKumar-hx7qo 4 года назад

You said a, b, c, d can't be negative, but u have taken negative no like -1,-15 as a & d, I mean didn't able to understand whole is not taken as -negative like (6-a) or only a, b, c, d?

@krishnagarg226 4 года назад

6-a

@satishchodisetti7896 2 года назад

@@krishnagarg226 nó a,b,c,d can't be negative

@divyanshgarg8352 27 дней назад

26:32 why we have not taken a,b,c,d as 5,1,9,3 respectively as it will come when we will take (6-a), (6-b), (6-c), (6-d) as 1,-5,-3,3 respectively as by that the sum will be *18* which is less than *20* PLEASE TELL @Rodha

@adarshraj638 2 года назад

in last ques shouldnt the sum be -1 + -3 + 3 + 5= 4 becos sum of abcd is asked?

@safalmittal4226 10 месяцев назад

Yeh toh Maxima and Minima ka topic h Yeh Inequalities m kya kr rha h ?

@GokulJS-vb2rd 11 месяцев назад

So, how does the value of a from (6-a) in the last question equate to A in ABCD. We took ABCD = 45 and and it should give the value of (A+B+C+D)min but, the question asks (a+b+c+d)min.. like we found the value of A first and equated it to (6-a) and then took value of a from it to find (a+b+c+d)min when we don't know the value of abcd.

@sidhantsachdeva_0209 2 года назад

sir , mai apko apni shadi pr bulaunga pakka ..hahah, maza aajata padke

@kvivek3474 2 года назад

In ques 6-a × 6-b × 6-c × 6-d =45 , if we take value as 1,3,3,5 then value of a, b,c,d will be 7,3,3,1 and sum will be 14 which is minimum . Correct me if I am wrong?

@mansiaggarwal4718 2 года назад

We need to take distinct values as mentioned in the question, that's why we can't take two "3"

@pranavgaganan5595 Год назад

Sir in 6-A qtn -how can natural numbers be negative??

@Ankurp148 4 года назад

Sir, in second question if u take (6-a) as 1 in place of -1 then result will be positive only. = 5 instead of 7 and hence min. Value decreases by 2 = 18.

@rajatgupta4675 4 года назад

Brother but we have to take two negative and two positive to make whole product positive..... If we take 1 in place of -1 then from rest 3 values we have to choose 2 value for negative and then min value will not be there

@priyankagudivada8190 Год назад

In the last question it can be taken as (1,3,3,5) then (6-1, 6-3,6-3,6-5) is equal to (5,3,3,1) and the sum of terms is 12 which is way less than 20 then why are the values considered as (-1,-3,3,5) which in fact gives the sum of the a,b,c,d greater

@shubhamchaudhary2481 Год назад

Because it is given that a, b, c, d are distinct natural numbers, so values can not be same for 2 variables.

@charumittal4813 10 месяцев назад

dosen't natural numbers mean +ve @@shubhamchaudhary2481

@Cipher0503 Год назад

in last question my min value is 12 and max value is 40. can u please check once more?

@niyatichauhan 3 месяца назад

I think this is not the content under inequalities.

@mansisingh3042 2 года назад

In 5:30 sir said if abc are distinct natural no then for maximum value a,b,c should be as close as possible and for minm value it should be as far as possible but in 27:25 sir said for max value will keep no. as far as possible. I'm little bit confused. Can anyone help me clear to my doubt?

@sarthakagarwal8532 Год назад

For addition ,its (keep far as possible ) and for product ,its( closest ).2 different things

@natwarkalwani4184 Год назад

@Rodha sir please explain! In second question it is given that abcd=45, so how 7*9*3*1 & 7*5*3*21 is satisfying that condition? please kindly reply and thankyou for your precious time and content 😇😇😇😇

@raghavojhabwr 10 месяцев назад

These are corresponding values of a, b, c, and d which satisfy the expressions (6-a), (6-b), (6-c) and (6-d) respectively. Multiplication of these 4 should be equal to 45 and not of a, b, c, and d.

@rishitripathy11 Год назад

as it is a natural number so -1 and -3 how can it possible help me to understand

@sanidhyasetu6480 4 года назад

natural number cannot be negative

@WorldwideFacts99 12 дней назад

In these two videos I had not seen any concept of inequality😢

@harshgupta-kt7kp 4 года назад

sir around 4 min in first qustion where their was no constraint on a,b,c max. will be infinity and in 2nd you calculated it as 1000 why?

@thegreat672 4 года назад

Bro because in second case it is given that they r positive real nos.. but in 1st one there is no such constraint given

@rajatgupta4675 4 года назад

Bro.... a+b+c=30 and given a, b, c are positive real no. So sir has done is like a+a+a=30.. That brings a=10 and then abc can be written as aaa i.e. 10*10*10=1000

@shubhamkhandelwal1111 Год назад

For 10! Power of 3 should be 5 na instead of 4??

@garimasahu193 Год назад

In last question aren't we considering values for a,b,c,d already?? i.e -1,-3,3,5

@manzaralam903 Год назад

It should be as far as possible ..the case you mentioned are still close ..but which sir did is farthest -1 to -15..

@novikasharma7883 3 года назад

I think there is mistake in last question..(6-a)(6-b)(6-c)(6-d)=45 ..... In last question , the values taken that is...-1,-3,3,5 are the values of a,b,c,d respectively .and giving values after deducting 6 from above (7,9,3,1) are solved values ...hence not the values of a,b,c,d...

@bharathanem4631 3 года назад

clarifying a month later, but still it may help ......the values are not taken as a,b,c,d but taken as (6-a),(6-b),(6-c),(6-d) which should be the factors of 45 ....when all these together multiplied should give 45, the factors are -1,-3,3,5 ...to get -1 from (6-a) a should be 7, and to get -3 from (6-b) b should be 9 and so on...thus a,b,c,d are 7,9,3,1 respectively

@MadhuSharma-oi7xt 2 года назад

Bro look closer, we have to solve for a,b,c,d minimum. All are positive, distinct values and satisfy our conditions mentioned above. Thus, answer is correct. It's just Higher order thinking, it may seem confusing. Replay the video some times. You will crush it. Best of luck

@suryaprasanth5719 Год назад

@@MadhuSharma-oi7xt Actually he mentioned a,b,c,d are natural numbers so cannot be -1 and -3

@mansidabhi6016 Год назад

@@suryaprasanth5719 sir never said ‘a’ is -1 but here, we need 6-a= -1, for that ‘a’ would be 7 (i.e., 6-7=-1)

@prashikgajbhiye3386 3 года назад

please sir video ki starting mein jo music hai change kro....bhot irritating hi

@komalisaigaddam1093 Год назад

Can any one provide a link to attend free mock tests

@janmejaypanda5414 2 года назад

sir i m confused you told that a,b,c.d can't be negative and cant be more than 5.. but you are solving with negative value -3, -1, 5, 9 . how is this possible please explain me sir

@TarunAsthana 2 месяца назад

abcd are not negative , it doesn’t say anything for the value of 6-a 6-b 6-c 6-d -it can be any number. Similarly abcd can be greater or lesser than 5 but 6-a 6-b……..so on cant be as it will increse the value beyond 45. Just take 6-a=A , 6-b =B ….and further solve.

@shivacharan944 2 года назад

at 20 min min value should be 172.8.?

@safalmittal4226 10 месяцев назад

Sir Coaching m Inequalities m kuch aur pdhaya h can you plzz tell yeh topic Inequalities hi h na ?

@anshul4385 10 месяцев назад

Times se ho na ? xD

@rakeshkonkumalla5405 4 года назад

In last question if 6-a=1,6-b=1,6-c=-3,6-d=-15 then max(a+b+c+d)=40

@prakhargalgale5048 4 года назад

a & b would be equal to 5..they both would be equal and not distinct.

@thegreat672 4 года назад

Distinct kaha h ? 🤨

@prakhargalgale5048 4 года назад

@@thegreat672 Que m positive and distinct solutions puche h

@rupalichaudhary7128 3 года назад

@@prakhargalgale5048 but positive and distinct bola h but sir ne a-1 and b-3 kyu liya h fir??

@prakhargalgale5048 3 года назад

@@rupalichaudhary7128 a is not taken as -1 rather (6-a) is taken as -1. Therefore a would be equal to 7.

@titikshaanand8362 27 дней назад

sir why cant we take : -3, -5, 3, 1 then the min value will be : -4 ?

@shantivaranasi231 3 года назад

Where can I find these type of questions I mean which book

@user-tm8wy1hx7n 3 года назад

arun sharma for quant . These are CAT level quant questions.

@varunjain2622 11 месяцев назад

will constraint given in the question or we have to find it by its own observation??

@Kanishma658 11 месяцев назад

Same doubt

@user-ws2rj4vb5z Год назад

Why have you used negative values of a,b in the example 2 when its mentioned that a,b,c,d are natural numbers?

@Rodha Год назад

a,b,c,d I have taken natural only

@vins686 3 года назад

how to calculate factorisation 10! question, when I have 2^8 3^4 5^2 and 7?

@asmitasehgal6135 3 года назад

1= 1 2= 1*2 3= 1*3 4= 1*2*2 5 =1*5 6= 1*2*3 7= 1*7 8= 1*2*2*2 9= 1*3*3 10= 1*2*5

@vins686 3 года назад

@@asmitasehgal6135 oh there you go! Thanks

@AshishPal-sh2yo 4 года назад

In second question we can take values -15,-5,3 and 5 taking all the maximum possible values still getting 36 as an answer why didn't you take these values ?

@DevendraSingh-hs1gj 4 года назад

look at ur product value

@vineetdubey2063 Год назад

The product of your numbers is way higher than 45.

@fuzailqureshi369 Год назад

I have a confusion whether this is a part of Inequality or not? And is the video relevant for 2022?

@AyushKumar-wl8cx Год назад

obviously it is releveant

@akhilsingh1349 Год назад

Yes, totally relevant but actually this is the part of number system...

@amitchoudhary2821 2 года назад

How the selection of value being made can anyone can help this out?

@Kanishma658 11 месяцев назад

Same doubt

@jatingupta4912 3 года назад

Didn't get the concept that why can't we put abcd beyond 5. Can someone explain in detail?

@nikhiljohn369 3 года назад

bro cuz if u put (6-a)> or =6 the value of a,b,c,d will be = or

@kanantrivedi5537 Год назад

Can someone explain why we can't take 0 anywhere, as in the video it is just said that it is not possible but not explained why it is not possible?

@mrunaldeshpande8972 Год назад

Because a,b,c,d are natural numbers. Google what are natural numbers. It is not mentioned whole numbers.

@priyanshikushwaha4048 2 месяца назад

in question (6-a) (6-b) first you said we cannot take abcd value less than but still you have taken that

@Aaditya2k03 Месяц назад

Need of gejo sir varc?

@Kitcatt_tv 12 дней назад

Yez@@Aaditya2k03

@vaidikgupta111 3 года назад

in 2nd Part: max(a+b+c+d) = 40 for (a = 5,b=5,c=9,d=21) : (6-a)= 1,(6-b)= 1,(6-c)= -3, (6-d)= -15 as -3 is more farther than -1 please comment if agree or not..

@rakshitchauhan3866 2 года назад

1 , 1 same ho jayenga na

@Kastrom_ 2 года назад

Sir at 28:08 why can't we take -45 instead of -15? Any particular reason?

@Kastrom_ 2 года назад

nvm got it

@aarthisris5103 2 года назад

I have this doubt too!!! Did u find the reason?

@Kastrom_ 2 года назад

@@aarthisris5103 because the total has to Equal 45 so if you talk -45 you won't be getting 45

@aarthisris5103 2 года назад

@@Kastrom_ omg yeah right!! Thanks for the help:)

@RAVIKUMAR-lv2qn 2 года назад

Can any one please explain , a,b,c,d is natural no. But sir taken two variables as negative .What's the logic behind it

@Rodha 2 года назад

a,b,c,d is not negative. 6-a, 6-b ..... is negative

@satishchodisetti7896 2 года назад

@@Rodha sir u said a,b,c,d are less than 5 , but u took 7,9, which are greater than 5

@heystalkers 2 года назад

In 2nd question How did we get a=(2⁸ X 3⁴ X 5² X 7¹)¹/⁴

@AagyaJain-kh6xz Год назад

watch number system playlist facorials part

@shubhamSingh-ly2kl Год назад

@@AagyaJain-kh6xz The factorial has been further simplied into multiples of 2,3,5,7. Here 5 and 7 are prime numbers (2,3 are also prime numbers) but they can be further broken down, for say in case of 9, you can write it as 3*3 and even 6 can be written as 3*2 and 3 ofcourse can be written as 3*1. 2^8 has been further obtained the same way. Lmk if you still have not understood this.

@vinaygupta609 2 года назад

Can anyone explain how sir wrote 10! In power?

@Kastrom_ 2 года назад

Basically, you have to count the number of unique digits repeating in 10! or 10 in general 2 repeats 8 times in 2 (Once) in 4 twice, Once in 6 then thrice in 8 and once is ten which will be equal to 2^8 you can figure the rest out for 3 5 and 7

@hamzahaider4553 Год назад

6:49

@VedaMithra- 2 года назад

as close as possible means can't we take -1,-3,1,3 in last question, 5 is too far

@tonymartial1211 2 года назад

we need produvt of 45

@mrunaldeshpande8972 Год назад

Note: Correction in qs: (6-a), (6-b), (6-c),(6-d) cannot be negative and zero.

@Rodha Год назад

Not required. It's mentioned a,b c,d are natural numbers

@mrunaldeshpande8972 Год назад

@@Rodha But sir, ultimately a=-1,b=-3,c=1,d=3 is giving the answer, right? But these -1,-3 are not natural numbers. If it mentioned that a,b,c,d are distinct integers instead of natural numbers, then it will work. But natural numbers are positive, aren't they?

@shivanshu5702 11 месяцев назад

@@mrunaldeshpande8972bro -1, -3 , 3,5 are the values of those 4 multiples (6-x types) from which if you calculate the values of a,b,c,d are 7,9,3,1 which are natural only

@saptarshimozumdar1657 2 года назад

10:00 how did you convert that factorial to that form?

@satishchodisetti7896 2 года назад

Refer factorial videos,these all are in sequence,if u randomly saw the video,u can't understand,so better to follow sequence

@adhilmohammed1581 Год назад

Sir why cant we take -45 for max in last question?

@manzaralam903 Год назад

How can -45 max brother

@sockyali7551 Год назад

If we take -45..then we need to take 1,1,-1. For the other three no...but we can't take 1,1 same no.. because in question clearly mentioned number should be distinct..😊

@MDMotivatorHD 4 года назад

In the second question, abcd are all distinct natural no, so how it can be -3 and -1?

@krishnagarg226 4 года назад

a b c d are distinct natural, not (6-a) (6-b) and so on

@vinodluhana9776 3 года назад

@@krishnagarg226 so why (6-a) is taken as 'a' in(a+b+c+d)maxormin

@vinodluhana9776 3 года назад

@@krishnagarg226 something is wrong in question 2

@arunadityarajjain1129 3 года назад

@@vinodluhana9776 Nothing is wrong

@adminbusiness4478 3 года назад

I think question framing is wrong.

@basukivenkatpati3052 3 года назад

I want to ask in last question that how can we take -3 and -1 if a, b , c, d are distinct natural numbers

@Rodha 3 года назад

That is 6-a not a

@Pavankumar-sv5fo 3 месяца назад

Last question explanation is not convincing....how can u say the factors of 45 except 1,3,5 can't be used? Conuter example is i will take a=15, b=1,c=5,d=7 the the product will be -9*5*1*-1.. .May be he got the answer right but his logic that we can't use 9,15,45 of 45 sounds unconvincing

@prateekbirthal9649 Месяц назад

True the explanation seems to be bogus.

@sureshshetty9439 3 года назад

For the 10! question, when I have 2^8 3^4 5^2 and 7, why can't I take A/m = B/n form? and I get 45 as the sum then. Is it like, the values should be as close as possible?

@killerlook111 3 года назад

You cant take A/m=B/m form because if you take that the you will get result of addition of factors of a^4(since we have assumed all to be equal) instead of a,b,c,d. which are to be different nd not equal as they are natural no's. Hope you got my point :)

@adminbusiness4478 3 года назад

I think we can't take negative values of 1, 3 and -5 in 2nd question as given constraints a, b, c, and d are distinct natural number. It only possible when we take a, b, c,d are distinct whole number.

@purvapurandare6142 3 года назад

We are not taking values of a,b,c,d negative.. the values of the brackets are negative and not the numbers.

@mrunaldeshpande8972 Год назад

@@purvapurandare6142no it's not that. Values of a,b are taken negative. Solution is wrong.

@saikartheek992 3 года назад

If a*b*c=504 then what is the max sum of a+b+c=?

@AnkitKumar-pm3bh 3 года назад

a=1, b=1, c= 504 abc= 504 (a+b+c)max = 1+1+504 = 506

@AnkitKumar-pm3bh 3 года назад

@Muskan Yadav Although not mentioned in question to take distinct numbers. Lets again try by taking distinct number. a = 1, b = 2, c = 252 abc = 504 (a+b+c)max = 255

@AnkitKumar-pm3bh 3 года назад

@Muskan Yadav Thats ok. btw how you arrived on 24 as answer?

@AnkitKumar-pm3bh 3 года назад

@Muskan Yadav Yeah correct

@AnkitKumar-pm3bh 3 года назад

@Muskan Yadav Yes Muskan. You too?