Algebraic Comparison (aka Inequalities, Quantitative Comparison etc)

[@shreshthsaha8497]

The key takeaway was the 3 golden rules: 1. Substitute with positive and negative integers. 2. Substitute with positive and negative fractions. 3. Take care of the equality/inequality symbols. Thank you for making Math visually appealing.

[@akashmishra3369]

So glad I watched your picking numbers video before this, and the [ -2, -1/2, 1/2, 2] set works mostly all of the time. Thanks Phillip

[@anaanaana44]

Thanks!

[@kwamebflat5087]

Excellent videos, Philip. I'm learning a lot! For the first example, I moved the b2 to the left hand side and equated it to 0. Then I realised the equation is a difference of 2 squares (a-b)(a+b) meaning that a=b or a=-b, making me choose answer choice D.

[@khandakernayeemahaque4274]

The best math teacher on KZbin 👍.

[@bukolaessien7352]

Woohoo.. I got the last one!! I've been so so scared of comparisons for long. Thanks so much again Philip

[@Leonardich30]

Hi, for the last question, it is just C < -1, not that C < -1 and is an integer. Try C = -3/2, otherwise, everything else is the same. A more general approach is to split into four groups as such: --(-1)--(0)--(1)--, so you have four intervals to check because in your case you are not taking into account pos/neg fraction greater/less than +1/-1.

[@prabeshkhanal5273]

Thank you so much Philip. You've been of great help. Love from Nepal.

[@IbiyeTam-George]

I got the last question! I’m so happy. Thank you Philip

[@snehashisnag2411]

If we consider a=1 in the third question, then also the inequality doesn't hold ground. So we can't say that all positive integers work.

[@MrMcfire2]

A very useful technique indeed - GRE really are always looking to trick you! The way I think about it is if the question looks too easy, then there is almost always a trap somewhere...

[@sigurdlongva]

Great video, as always. Just a small correction regarding the last question: c does not necessarily have to be a negative integer. It can be any negative NUMBER smaller than -1 (like negative 3/2). It does not make any difference for the solution to the question, but it can be important to bear this difference in mind for other questions.

[@bradleygoronson9698]

I got the last question right! Thanks for all your videos Phillip! This framework for thinking through these questions is great.

[@TheTestedTutor]

You are very welcome

[@lubainabhori8651]

Your videos are favourite part of my preparation..

[@TheTestedTutor]

Thank you so much 😀 Lubaina

[@prajaktachavan9329]

You are just brilliant! why did'nt I see your videos earlier😪

[@ishanpathak2526]

Super helpful

[@-Rishikesh]

16:25 Please Clarify, How is c a negative integer ?, we can chose c as -2.5 and the equality c< -c < c^2 still holds. The answer is D nonetheless but wanted to clarify this.

[@bupechikumbi3082]

It's negative to satisfy the statement C

[@puneet.fitness1729]

Dear Philip can you please go through the below question If g(x)=3x+√x​, find g(d2+6d+9).

[@51Nazish]

Since c will be a negative integer and every -ve integer satisfies, except -1 where -1

[@iyanuoluwaaliu5539]

🕺🕺🕺 I got everything right. Thanks a lot, Philip for making me a better student 😊👏🏿👏🏿

[@yashwaingankar9149]

I wish our Engineering professor taught like the way you do...my GPA would have been above 3.5 🙂

[@TheTestedTutor]

Thanks Yash

[@msk27vlogs]

Great work Philip!! You will never disappoint with all your analysis. Thanks for being our Virtual Professor 🤗

[@dimpledhillon169]

Great job Philip

[@hansiwelangoda1895]

Thank you very much Philip for your excellent teaching style.youre the best🙏

[@TheTestedTutor]

😁

[@juancaballero5687]

Hey Philip, your videos are by far by the best to prep for the GRE and grasp the concepts easily! I wanted to ask you about the last question. How can we assume that c is an integer? Couldn't it be 1.5 or any greater than 1 decimal, and therefore not an integer?

[@TheTestedTutor]

Yes, technically it could be anything greater than one. Just for simplification I use integers for my examples

[@loopm1599]

in case of a decimal you have to consider it a positive fraction & if you check the 2nd expression, for ex c = 1.5 (as per your suggestion) doesn't satisfy the condition.

[@amithasan946]

Excellent Video to Crack Hard QC Questions! Thanks!

[@TheTestedTutor]

Glad it was helpful!

[@ganiyatwahab1927]

Thank you 😊 Very insightful

[@sreejasree7427]

So glad , I found this video Thankyou ❤

[@nitesh8900]

Last example is fun 😉

[@nikitachaudhari9167]

Thanks, Philip for your assistance. :)

[@TheTestedTutor]

Any time!

[@abdulmuneeb454]

Thanks phillip you are really a great teacher i love the way you teach. I have confusion In the last problem you said that C is a negative integer but you didn't tried -1 as it is also the negative integer but if we put -1 we get ......-1

[@TheTestedTutor]

Yes, so c is a negative integer but not 1. Either way, we still don't know the value, so answer D

[@priyanandinibose2104]

4th question at 12:23 the answer will be D. Because b= 0.5 so it can be that a= 0.1 and c= 0.9 then Quantity A is becoming greater. Hence it cannot be determined

[@ahmedelsayed342]

Very helpful great 👨

[@SweetComputing]

My question is regarding negative fractions. Even though they are getting bigger will they ever surpass to be a positive number since it is an odd power? If not, can we be sure then that the answer will be C?

[@BiomathematicsKnight]

when you taught the third thing to remember why cant we just use 1 as an example and that doesn't satisfy the equation hence move to 3? and -1 for lower than 0.5?

[@althamashsheikh7807]

Hi, could you please make video on tricks & tips to crack "weakening & strengthening the argument"

[@adhingopuj6739]

In last section ( Algebraic Comparison), C < -1.

[@Rose-db6vy]

Hey Philip Thankyou so much for these videos.I had a doubt on que 4 if b is in between 0 and 1 then why did you choose the possibility of a negative no?As in can we assume a=0 and c=1 and then plugin values in a^3 and c^2 because even that way I got Opt B. Awaiting a feedback..

[@TheTestedTutor]

You're right that wasn't even needed

[@hannahforsythe3847]

Hi Philip theses are greats. Do you have any videos on Quadratic equations in GRE?

[@TheTestedTutor]

Yes somewhere in the Quant playlist!

[@SWASTIKB306]

Philip can you make one on word problems please And how are you doing ,hope cases are dipping .

[@lubainabhori8651]

Yeah, word problems are pretty tricky...

[@TheTestedTutor]

Cases are still dipping, thank you Swastik

[@joykhan3407]

Thanks a bunch 🙂

[@TheTestedTutor]

No worries!

[@mohammedrizwankhan3313]

Deep concept

[@ankyr2791]

Hey Philip For the last question, can't we directly say CND because no relation given between b and c.... Thanks for all the videos 😊

[@naunhoc92]

No you cant, what if the Quantity A is positive and Quantity B is negative. So even there's no relationship between them, the answer cannot be D here.

[@Koomar_18]

Hi, thank you for making these videos.. can we work on the question stem at all in QC questions?

[@TheTestedTutor]

Yes, always try to simplify the question stem. I did a video on this about 3 weeks ago! :)

[@Koomar_18]

@@TheTestedTutor Thank you :)

[@jawaadzulqernine2146]

Excellent video, can we have a part 2 on this? :D

[@TheTestedTutor]

Yes!

[@giuliahayes9252]

You are so awesome, thank you for this!! I recently did a practice test and really struggled with an algebra question. If you happen to see this and can direct me to one of your videos that would help me, or explain in a reply, I would appreciate it! The question was: If ((x+1)/6x) + ((x+1)/2x) = 1, what is the value of x? I get 0.2 every time I try to solve it, but the correct answer is 2. I read the explanation but it did not make sense to me.

[@TheTestedTutor]

If you multiply everything by 6x to eliminate the denominators, you get ((x + 1) + (3x + 3) = 6x. This is the key step (notice how second fraction the 6x cancels with the 2x denominator to leave x3 for numerator). Solving this you get 4x + 4 = 6x, or 4 = 2x, x = 2. Hope this helps and thanks for the kind comments!

[@giuliahayes9252]

@@TheTestedTutor The part that always confuses me is multiplying (x+1)/2x by 6x, because why is 6x(x+1) not equal to (6x squared + 6x)/2x?

[@amnaammar5288]

@@giuliahayes9252 because 6x/2x cancels to form a simple 3. hence only 3 is multiplied with the second term

[@giuliahayes9252]

@@amnaammar5288 thank you!

[@amnaammar5288]

@@giuliahayes9252 anytime

[@Redcrown77]

I will need to practice this a while

[@anudeepsanpala5357]

Hey can u do vedios on fraction and decimals word problems!!

[@kittehLORDZ]

For the last problem, i noticed that B could be between (-0.5 - 0), and A could be between (-1 - 0), so there is an overlap on the number line. Does this overlap means the answer will always be D cant tell which is bigger?

[@TheTestedTutor]

Overlap does mean that yes!

[@selvakumarmunusamy5901]

Dear Sir, a < a cube, the condition works only for positive integers but not for negative integers and fractions. Then, How can I conclude the answer?

[@koi4004]

Philip The Great!!

[@sushanttimalsina4099]

I think you should not just recite the calculations. Rather show the calculations you're doing on screen. Apart from that everything is perfect

[@lilamayi1289]

Why don't you use zero as one of your categories? Or roots?

[@TheTestedTutor]

Takes too much time usually

[@AnsImran]

Thanks

[@ethanbates3484]

excellent vid!

[@Msdrmanish]

Thank you, Sir

[@TheTestedTutor]

Any time

[@shritisingh2382]

Got all five of them correct :D

[@dnd3757]

Thanks a lot for this! Wouldn't it be easier in the last question to select D because the question doesn't give us any idea about how b and c are related? How could be really compare anything between two unknowns if there's no relation shown between them? (apologies if I'm being mathematically incorrect here):)

[@TheTestedTutor]

A great idea but not true unfortunately. I could say, for example, that b is a negative integer and c is prime. You would still know c is bigger than b, even if there is no direct relation between them.

[@1327]

thank you

[@kirthanalp612]

If algebraic comparison occur in GRE test, its automatically assumed that the answer can't be determined as the possibilities are many?

[@TheTestedTutor]

Not that simple alas, have to check every time Kirthana

[@iremharmancik5321]

thank you!

[@TheTestedTutor]

Welcome Irem!

[@dimpledhillon169]

Couldyou please share the schedule of maths to follow 15 days prior to Eda

[@dimpledhillon169]

Exam*

[@tinycircle3068]

very nice

[@TheTestedTutor]

Thanks 🔥

[@sabaaref6025]

thanks!

[@nimranoor3766]

So, the Ans of second last question is B?

[@SISANHLABATHI]

This is tough Phillip

[@siddheshpatil5877]

the answer to last question will be quantity a is bigger .if B=0.2 and C= -2. please let me know?how can you say d is right.

[@arukshitasood5758]

how is it that i was able to solve last ques which was hard but couldn't solve 2 and 3rd- ugh

[@nisthabhandari-t7o]

i would pick d for the last ques if this ques came in my gre just cause it feels D. , and i would be correct then haha that's why they say luck is also a factor in gre .

[@ruchitaasalpara7953]

👍

[@nezsa628]

wow that last one was HARD

[@farahhariri9427]

Funny thing is, I got the first 4 wrong then the last one right.

[@AnsImran]

Thanks