Inequalities 2 | CAT Preparation 2024 | Algebra | Quantitative Aptitude

Advance Algebra by Ravi Prakash | Quantitative Aptitude for CAT 2024
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[@bhagirathsharma7505]

The quality of this content is unmatched on any platform

[@AshwiniSingh-yu6pv]

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]

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

[@dchakraborty79]

Then how is this solution possible?

[@pranjalgupta_stxaviersuniv616]

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

[@sportivetech279]

But why can't you take all four negative factors

[@doyelpal1846]

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.

[@ashishsingh7165]

Is this inequality or max nd min value?

[@priyankakumar7387]

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

[@VishvajeetSuryawanshi]

Good work bro

[@nehaagarwalla617]

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]

Numbers must be unique. This doesn't satisfy that

[@yashasharma9963]

Thanks for such quality questions! 🤯🤯

[@vk9401]

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]

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

[@itssaurabh18]

Super quality questions. Thanks!

[@chanchalbhargav5227]

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

[@saksheemalik6773]

Right

[@arnabde5654]

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

[@kush8806]

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]

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.👍

[@muhammedfasil9036]

Great 👍

[@tejaswinidaware7395]

thank you sir

[@_cat_aspirant_99.9percentile]

Thank you guruji ❤

[@rishimukherjee2118]

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]

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

[@anuragsahu7794]

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

[@Calculatorshubhamsir]

U r grt ❤

[@sammy.3152]

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]

bro these questions dont seem of inequalities ? are they ?

[@arshiya56]

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

[@adarshraj638]

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

[@GokulJS-vb2rd]

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.

[@Shivam_General_Fitness]

Thanku sir

[@Ankurp148]

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]

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

[@kvivek3474]

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]

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

[@rishitripathy11]

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

[@pranavgaganan5595]

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

[@divyanshgarg8352]

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

[@priyankagudivada8190]

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]

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

[@charumittal4813]

dosen't natural numbers mean +ve @@shubhamchaudhary2481

[@Cipher0503]

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

[@VishalKumar-hx7qo]

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]

6-a

[@satishchodisetti7896]

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

[@natwarkalwani4184]

@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]

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.

[@mansisingh3042]

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]

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

[@safalmittal4226]

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

[@garimasahu193]

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

[@manzaralam903]

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

[@sanidhyasetu6480]

natural number cannot be negative

[@krishnamouryapathapati1712]

Super sir thank you

[@novikasharma7883]

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]

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]

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]

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

[@mansidabhi6016]

@@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)

[@shivacharan944]

at 20 min min value should be 172.8.?

[@bewithpallabi3120]

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

[@Rodha]

All the best

[@bewithpallabi3120]

@@Rodha thank you! ✨

[@madhumitharajinikanthan1007]

@@bewithpallabi3120 how did the exam go?

[@AyushKumar-wl8cx]

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

[@shubhamkhandelwal1111]

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

[@komalisaigaddam1093]

Can any one provide a link to attend free mock tests

[@priyanshikushwaha4048]

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

[@Aaditya2k03]

Need of gejo sir varc?

[@deepikagurjar135]

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

[@prashikgajbhiye3386]

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

[@rakeshkonkumalla5405]

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

[@prakhargalgale5048]

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

[@thegreat672]

Distinct kaha h ? 🤨

[@prakhargalgale5048]

@@thegreat672 Que m positive and distinct solutions puche h

[@rupalichaudhary7128]

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

[@prakhargalgale5048]

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

[@harshgupta-kt7kp]

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]

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]

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

[@shantivaranasi231]

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

[@user-tm8wy1hx7n]

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

[@titikshaanand8362]

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

[@amitchoudhary2821]

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

[@Kanishma658]

Same doubt

[@vins686]

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

[@asmitasehgal6135]

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]

@@asmitasehgal6135 oh there you go! Thanks

[@niyatichauhan]

I think this is not the content under inequalities.

[@AshishPal-sh2yo]

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]

look at ur product value

[@vineetdubey2063]

The product of your numbers is way higher than 45.

[@janmejaypanda5414]

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]

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.

[@user-ws2rj4vb5z]

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]

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

[@varunjain2622]

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

[@Kanishma658]

Same doubt

[@fuzailqureshi369]

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

[@AyushKumar-wl8cx]

obviously it is releveant

[@akhilsingh1349]

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

[@RAVIKUMAR-lv2qn]

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]

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

[@satishchodisetti7896]

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

[@jatingupta4912]

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

[@nikhiljohn369]

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

[@vinaygupta609]

Can anyone explain how sir wrote 10! In power?

[@Kastrom_]

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

[@safalmittal4226]

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

[@anshul4385]

Times se ho na ? xD

[@kanantrivedi5537]

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]

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

[@heystalkers]

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

[@AagyaJain-kh6xz]

watch number system playlist facorials part

[@shubhamSingh-ly2kl]

@@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.

[@Kastrom_]

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

[@Kastrom_]

nvm got it

[@aarthisris5103]

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

[@Kastrom_]

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

[@aarthisris5103]

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

[@saptarshimozumdar1657]

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

[@satishchodisetti7896]

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

[@VedaMithra-]

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

[@tonymartial1211]

we need produvt of 45

[@MDMotivatorHD]

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

[@krishnagarg226]

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

[@vinodluhana9776]

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

[@vinodluhana9776]

@@krishnagarg226 something is wrong in question 2

[@arunadityarajjain1129]

@@vinodluhana9776 Nothing is wrong

[@adminbusiness4478]

I think question framing is wrong.

[@adhilmohammed1581]

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

[@manzaralam903]

How can -45 max brother

[@sockyali7551]

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..😊

[@sidhantsachdeva_0209]

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

[@vaidikgupta111]

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]

1 , 1 same ho jayenga na

[@basukivenkatpati3052]

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]

That is 6-a not a

[@hamzahaider4553]

6:49

[@adminbusiness4478]

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]

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

[@mrunaldeshpande8972]

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

[@sureshshetty9439]

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]

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 :)

[@mrunaldeshpande8972]

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

[@Rodha]

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

[@mrunaldeshpande8972]

@@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]

​@@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

[@saikartheek992]

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

[@AnkitKumar-pm3bh]

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

[@AnkitKumar-pm3bh]

@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]

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

[@AnkitKumar-pm3bh]

@Muskan Yadav Yeah correct

[@AnkitKumar-pm3bh]

@Muskan Yadav Yes Muskan. You too?

[@neetkrackers-biology7540]

Unless you already know the answers, these type of questions are meant to leave in the examination.

[@swalehashaikh607]

Anyone interested in studying online in gc

[@Pavankumar-sv5fo]

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]

True the explanation seems to be bogus.

[@cumulusmusic100]

Thank you sir