Absolute Values in a Nutshell: GRE / GMAT Quant Explained (with official questions)

[@shobbada]

I've always messed up problems associated with inequalities and absolute values. You're a life saver Philip! Can't believe I'm bossing every single one of these questions now!! Hands down THE BEST EXPLANATION available anywhere.

[@TheTestedTutor]

Thanks for this shobbada!!

[@juanamariasolanomesa8671]

Literally a life saver! I am sooo so grateful !

[@anikajabin35]

"If you stay calm, life will be much easier." - Phillip, the tested tutor, 2020. I'll always keep it in mind Sir.

[@TheTestedTutor]

Perfect! :)

[@indian_scouser_ynwa]

It ain't phantasmagorical to promulgate that "YOU ARE THE MOST FINESSE TUTOR ONLINE FOR GRE". Your videos are repleted with cognizance and its jovial to watch.

[@TheTestedTutor]

Amazing comment! Extraordinary vocabulary!

[@kepler3570]

That's obviously a GRE student. Best wishes abbhijith

[@indian_scouser_ynwa]

@@kepler3570 Thanks a lot!. Good luck to you too.

[@frankanin6900]

Ow wow, I gained a lot from your vocabulary. I hope your words all show up on my test. But for sure Philip's synoptic GRE insights, tips and material are by far the best you can find online...… And trust me I have perused quite a number of different tutors out there. GREAT job Philip. Keep them coming.

[@sarahbrock5449]

I'v been doing the Magoosh study plan that I paid for to study for the GRE, but in my opinion these videos are way more helpful and explain things in such an accessible way! Thank you!

[@TheTestedTutor]

Great to hear Sarah!

[@shivanishrivastava4539]

I can see my growth as an individual and that's the greatest gift one can ever get! Gratitude Philip and Thank You So Much Once Again...We need more Human like you, who can explain math's the way that even a child can learn!🥺💯

[@shazigetssober2394]

I'm prepping for the GRE General Test. When I saw an absolute value inequality I didn't even know what it was. Thank you for focusing on the philosophical aspect. It made this so much easier and simpler to understand. THank you very much!

[@soapmactavish7358]

from this video, I only learned this: "Always check the answers when VARIABLE=VARIABLE in ABSOLUTES", which is gold advice. Thanks Philip!

[@salonidoshi8269]

Thank you, Philip! You are a lifesaver, I have understood all of the concepts, and your practice problems have helped me test those concepts as well you are a fantastic tutor.

[@Tilmaamaha_Caafimaadka]

I gained a lot from this inequality video. Different techniques for different questions. Had you not been here, this wouldn't have been possible. Thank you so much Philip.

[@TheTestedTutor]

Thanks so much Hassan. Really glad it has helped. You have been there from early on.

[@PoojaPithva-k8p]

🎯 Key Takeaways for quick navigation: 00:00 🎬 The video covers absolute values and their applications in GRE / GMAT Quant. 01:09 🧠 The output of an absolute value is always positive, regardless of the input's sign. 02:14 📚 Understanding the core essence of absolute values is crucial for solving complex problems. 03:34 🔍 Analyzing absolute value inequalities requires considering both positive and negative input scenarios. 05:44 🤔 A negative number inside an absolute value can result in a larger positive output due to the sign removal. 08:12 🤖 Absolute value questions often involve reasoning about scenarios where variables could be positive or negative. 10:42 ⚖️ Comparing quantities involving absolute values requires considering multiple possibilities, including variables being zero. 12:30 🧮 Solving equations with absolute values involves considering both positive and negative input values. 14:55 🔀 Inequalities with absolute values require solving two separate scenarios, one with a plus outside the brackets and one with a minus. 17:23 📐 Absolute value equations and inequalities often necessitate solving multiple scenarios to account for different input sign possibilities. 22:18 📈 Applying the concept of absolute values in solving inequalities involves analyzing both positive and negative input cases. 25:00 🤯 Handling integer solutions in absolute value inequalities requires considering all possible scenarios for the variable's sign. 25:41 🔍 Solving equations with a variable inside and outside an absolute value requires calculating two scenarios. 26:20 🔄 When a variable equals another variable in an absolute value equation, solving both scenarios is necessary. 26:48 🔀 Replace the absolute value with both positive and negative scenarios, then solve for each variable. 27:28 🧐 Check the solutions by substituting them back into the equation; one of the solutions will be valid. 28:11 🎯 A variable in an absolute value equating a variable outside it often requires solution validation for correctness. 28:51 ❗️ Checking solutions for validity is particularly useful when a variable inside the absolute value equals another variable outside it. Made with HARPA AI

[@insandouts9617]

Your lessons are worth paying for. But for people like me such free classes are a blessing. Thank you.

[@TheTestedTutor]

Thanks so much Arghya

[@AravindSADance]

I've gone through Magoosh, Princeton and their online materials. Nothing is even remotely close to every single topic that you cover and the tips that you provide, hats off to the wonderful work.

[@TheTestedTutor]

Wow, thanks Aravind

[@AravindSADance]

@@TheTestedTutor I know you've done a video on AWA, but could you show us a live example of tackling say an issue task and an argument task

[@mocca4life120]

Thanks again Philip, you are truly "The Trifecta." If you feed them, they will come. I came back to another fruitful video...keep them coming!

[@yatrithoria2309]

As I am progressing towards my GRE exam date, your videos are proving to be a great savior! Thank you Philip!

[@TheTestedTutor]

Happy to help Yatri!

[@shrutiparthasarathy4500]

Honestly, will never be able to fully express my gratitude to you for these amazing videos you post! Thank you so much!

[@TheTestedTutor]

Thank you for that wonderful comment Shruti

[@Enigma700-dp1kv]

Most comrehensive explaination on absolute values and inequalities EVER !!! I used to get baffled everytime, but now I won't be so ! Thank you so much you are the best !!!

[@vr426]

This man out there saving lives. You da real MVP.

[@TheTestedTutor]

Thanks VR!

[@prakharnarang1898]

You are a great teacher, for some reason I have always made mistakes in absolute value questions and you have made most of my doubts go away. I will keep your advice in mind for my exam "stay calm". Thanks

[@pradyumnakumar5628]

Philip, I don't know how I would manage to learn so many concepts without you. Tried so many sources but I was unable to get absolute value but this video has helped me grasp it at once. You are doing so amazing. Please make some fresh videos on reading comprehension.

[@TheTestedTutor]

Hahathank you. I will

[@caroleg1997]

quite helpful, almost gave up studying on absolute value for my GMAT thanks a bunch though you're a lifesaver

[@renn4489]

Now I will use this two solutions approach I know it may be easy to the majority of people but I remember how in school I either missed it or didn't understand this concept and only occasionally saw other using it. Now in my 20s I finaly encountered with it again and understood it! Thank you a lot! I must do practice questions on this

[@victoriamuchiri8551]

Thanks for this video. I have understood where I had not understood.

[@tanvir7781]

this is probably the best video on this topic. love ur energy man. u are a saver.

[@anup_patel]

Last question was a surprise for me. I never checked the validity of the solutions for variable = variable in absolute type of question. Thanks a lot for making this video.

[@shivamjadhav301]

Best explaination for absolute values ques.

[@nataliaromo1613]

Simple, direct and easy to reason explanations, there is great value in this video.

[@TheTestedTutor]

Thanks Natalia

[@riddhidineshoza9182]

These videos are definitely worth making Sir ✨✨✨✨✨ God bless you

[@Xalgozblade]

Whether this video gives me a negative or a positive result on test day, I must say I absolute-ly loved it ;)

[@Anirudh53615]

I really appreciate the way ur working hard for gre aspirants..ur videos helped me alot in improving my vocab... please dont stop making videos

[@TheTestedTutor]

I won't, inshallah.

[@DeepakKumar-rz9wq]

You made it super easy to understand even the complex questions..!!!

[@ferozmohammad5841]

You made the concept so easier Philip! Kudos

[@suellabritto5761]

Your videos on quants are really helpful to people like me who are really afraid of this section. Ever since I got a hold of your videos a couple of weeks ago, my level of confidence has really increased and I am able to solve even difficult questions. Thank you so much Phillip! Your videos really have to reach people who are in search of good GRE/GMAT content and I will try my best to help you with that. Thanks again and have a great day!

[@TheTestedTutor]

Wow thank you so much Suella. So glad your confidence is higher!

[@jasonelder6531]

this dude is the GOAT! thanks so much for the help

[@shibanisabnis790]

If I do well in the quant section of GRE, it’ll be only because of your videos. I haven’t done maths in over 12 years! Love your work and effort :)

[@TheTestedTutor]

That's lovely Shibani. Keep going!

[@santhiyatheanraj8436]

Somehow I ended up watching one of your video and I am watching all videos !! Thanks to KZbin for suggesting your video at a very crucial time. You really need a big shoutout. Kindly keep up good work!

[@veniswar]

phillip you are the best ........... period

[@iluvGinger0214]

thank you SOOOO SO much for explaining that last point!!! i could not figure out why i kept getting the wrong answers when i thought my methods and formulas were all right i literally thought i was going crazy. i cant believe no gre test prep book ive come across has explained that and in literally 2 mins you just cleared up all the confusion in my head. you're the best :)

[@TheTestedTutor]

You are so welcome Lily!

[@nusairashahab3764]

This video is great. I always struggled with absolute values and inequalities. Please keep uploading tutorials. It really helps.

[@TheTestedTutor]

More to come!

[@murtalaa]

I can't believe this content is free!

[@esraamansour3405]

very helpful videos, thank you for teaching us

[@ayeshareza5614]

the greatest teacher of GRE.

[@TheTestedTutor]

Haha thanks Ayesha :)

[@OyindamolaOAjala]

Thank you for this video. I had little knowledge on this topic before and now I am more confident.

[@TheTestedTutor]

Wonderful!

[@chaitanyaturankar9512]

Ineffable video!! It just solved all the doubts and struggles I was going through while tackling such questions..Thanks a lot Philip!!

[@abdurrasheed2938]

The last question of variable=variable really saved time.. Thanks Phillips

[@Tarannum_Kalam]

This video really helped me understanding absolute value which was giving me much trouble lately. Thanks from Bangladesh 🇧🇩🇧🇩

[@TheTestedTutor]

You are most welcome Tarannum

[@bahmantahani2537]

Learn to love mathematics again with Philip!

[@rishiksarkar62]

Thank you so much sir! This video was really helpful. You are a legend and your explanation is fabulous. This channel is so underrated and I really wonder how come you have so less subscribers? Keep growing and may god bless you!

[@sanikathakur9344]

Your videos made a lot of problems easier for me!

[@TheTestedTutor]

Glad to hear that sanika!

[@nikilsettipalli5045]

I'm clear with absolute values. Thanks a ton.

[@reax9314]

Hey! Great Video. I Have my GRE on 28th September. Your videos really help understand the different scenarios. Very Useful. Great Work!!

[@thomasgilfix1166]

your content is preternatural tested tutor! kind regards from Florida!

[@disnadon2672]

Such a fantastic teacher you are! You explain so well and I only wish I had found your videos sooner! I am on your 4th video and can’t wait to get to the others as I have a less than 3 weeks for the exam! Also I love the way you explain things so clearly yet calmly! Keep up the brilliant work you do!

[@joycenyancheramakoriyoutub3017]

This is priceless! Thank you so much Philip!!!

[@megank707]

These videos are worth making 🙏🏻.

[@kabitakhanal3299]

I am in love with your videos😍😍 Math now seems interesting ❤️❤️

[@TheTestedTutor]

Thank you so much Kabita

[@sabaaref6025]

Math is just like grammar. Just when I think I know it all, there appears an exception! Thanks, Philip, for clearing things up for us!

[@likachishi7200]

Thank you so much for making our lives easier with your hard work. Really enjoy learning from you. learning has never been this fun.

[@amandagezahegne7038]

Thank you Philip! you are the best!!

[@TheTestedTutor]

Thanks Amanda!

[@Jeeban96]

Loved the way you taught. Especially the 'pace' .

[@umariddirisu4473]

I needed this thanks to your relentless help you keep giving us till this we appreciate it

[@kritidahagam]

Thank you so much for this video, I really appreciate all the hardwork that went into it

[@ActivionsonTheriver]

This videos are worth making, sir, love'em

[@saahildama9437]

All of your videos are so high value. Thank you so much!

[@chandrasagar9224]

Cheers to learning!!! Great work Sir, thanks for making learning interesting.

[@shivamshukla9486]

Philip The LIFESAVER! Thank you soo much for making such informative videos. Keep'em coming! We owe you a lot brother 🙌

[@TheTestedTutor]

More to come!

[@priyadudhe7996]

Your videos are helping me a lot to boost my quants as well as verbal knowledge. I have scheduled my GRE exam for next month. Looking forward to get more videos on some last minute tricks for exams

[@TheTestedTutor]

All the best

[@nikhilrathod1096]

Your score?

[@aditidixit4424]

Hey, absolutely brilliant video. Just a request though, could you please share the answers to all the questions in the description or comments, please?

[@ArsheeVerma]

Best resource for GMAT

[@gg3675]

another banger, came out knowing much more than i did coming in :)

[@anup_patel]

I always struggled with absolute values questions. This video helped me clear the clutter and to have a better understanding about the concept .

[@varun_MRG]

I always got confused with inequalities and abs values,but now I can understand concepts. Wish I could give multiple likes

[@varun_MRG]

Thank you so much for these well explained topic wise videos, I was able to score well in gre because of these

[@kennethlandin3341]

I loved your video. Absolute values are more "valuable" than we realize (pun intended). They are essential to the algebraic formula for a square, which you never see in math courses. |(x+y)+(x-y)| = r is the formula for a square centered on (0,0) with sides of length r. On more thing. The reason -1 doesn't work in your final equation, |x| = 4x+3, is that an absolute number can NEVER be negative!

[@edwardblack9263]

Awesome video, with lots of examples!! Thank you so much Philip!!

[@louishanekom9761]

Hi, I'm writing my GRE/GMAT (I haven't decided) in a month or so. I absolutely love your videos. I have been preparing for almost a month and a half now, and only recently discovered your content. It is really great. I like that you keep your videos short and I all the tips you give helps me a ton in understanding the material. Hope you keep it up, and I think you should do a video that tells us a bit more about your background, where you're from, what you do, etc.) Kind Regards, big fan, Louis Hanekom from South Africa

[@TheTestedTutor]

Will do so in future videos!

[@hansiwelangoda1895]

I really really appreciate your great work Philip.you are such a wonderful and talented teacher

[@TheTestedTutor]

Thank you so much Hansi

[@ebenezerseesi55]

Your videos helped me a lot. God bless you

[@ranveerchavan3439]

Best videos ever!

[@mansib2228]

Great video yet again! This is the best thing about your videos, you know exactly where would the students be struggling and you give the most logical explanations to them and they no longer seem so difficult.. thank you 👌

[@TheTestedTutor]

Thanks Mansi! I used one of your questions!

[@mansib2228]

@@TheTestedTutor yes! Was able to solve the rest of the questions I had sent u easily after this video..

[@TheTestedTutor]

@@mansib2228 That's great news !

[@Jack_Omush]

Awesome concepts, you are helping in getting the basics right. Cheers!

[@aminaseini6563]

Your videos are always so thorough!

[@TheTestedTutor]

I try Amina

[@reddaxtor5662]

Thanks a lot! I've greatly benefitted from your video series. Really grateful!

[@alirezaershadi7035]

I think I know the thing, however, watching the video I just figure out how hasty I do the test. I realy appreciate your videos man. 🤝

[@bisolaajibola7967]

Inequalities made easy!! Brilliant

[@physicsnovice656]

Decent video. Here's bunch of examples I've encountered in different places (my highschool, forums, textbooks, other videos) that might be helpful. I'll skip the definition and list some properties. The proofs can done by cases or some tricks using previously proved properties, they are available online. a) |ab|=|a||b| b) |a|=b b>=0 and (a=-b or a=b) c) |x| < a -a < x < a (when a is negative also works) d) |x| > a x>a or x =0 and (a=-b or a=b) (check that 2x+2 is above 0) or by cases x>=1 and x-1=2x+2 => x =-3 but contradiction with previous assumption x x = -1/3 fine note squaring (x-1)^2=(2x+2)^2 only works when we assume 2x+2 >= 0 2. |x-1| -1/3 and x > -3 x > -1/3 3. |x-1| -3 or x < -1/3 (all x) and -|2x+2| < x-1 |2x+2| > -x+1 2x+2 > -x+1 or 2x+2 < x-1 x > -1/3 or x < -3 so x > -1/3 or x < -3 4. |x| + |x-1| = 2 (when sum of distances from 0 and 1 is equal to 2) cases x >=1 2x-1=2, x = 3/2 ok 00 => because x+y>0, then x-y>0 x>y 7. Graph |x|+|y|=1 By cases or properties or squaring |y|=1-|x| or x+y=1 and noticing it's symmetrical to the lines x=0 and y=0 8. ||x|-|y||0 what's the other side? Pythagorean theorem 4a + x^2 = a^2+2a+1 x = sqrt((a-1)^2) = |a-1| 12. If there are two lines m:2x+y+1=0 and n:x-2y+3=0, what are the bisector lines(divide angles of lines crossover by two)? Points (x,y) on bisector lines are such that their distance is equal from lines m and n so (distance formula |Ax+By+C|/sqrt(A^2+B^2)) |2x+y+1|/sqrt(5)=|x-2y+3|/sqrt(5) |2x+y+1|=|x-2y+3| Now either solve by cases, or recall |a|=|b| a=b or a=-b, or square |a|=|b| a^2=b^2 a^2-b^2=0 (a-b)(a+b)=0 (2x+y+1-x+2y-3)(2x+y+1+x-2y+3)=0 13. When the line going through point (2,0) is perpendicular to circle x^2+y^2=2 Line a(x-2)=y ax-y-2a=0 Now either x^2+y^2=2 and ax-y-2a=0 equations have to have one solution or distance from line to point (0, 0) is equal to circle radius. |a * 0 - 1 * 0 -2a|/sqrt(a^2+1)=sqrt(2) |-2a|=sqrt(2)*sqrt(a^2+1) 4a^2=2a^2+2 a^2=1 a=+-1

[@TheTestedTutor]

Wow most detailed comment I have ever read. Super extensive examples and commentary, thank you so much PN!!

[@oladipoojo1688]

Thank you, Philip!

[@tommyshelby2020]

Great strategy! Highly appreciate your efforts!

[@T.Green.]

Brilliant lesson! Thanks Phillip

[@parthakre7779]

keep up the good work

[@deboraaquino2158]

An absolute gem! ;D

[@hammedtukur]

Great explanation

[@umairahmed1773]

Brilliant stuff

[@ITS_KCM]

Thank you for this!

[@silkinaraha6496]

Very useful topic!! Thankyou for teaching 🙌

[@salsabilahmedshrestho960]

Fantastic Man. Thanks for the structured summary. I'm watching it all. Positive criticism 1. You always just get to the point so THANKS! 2. Your videos are very structured and easy to digest. Negative criticism: 1. In your playlists of week 1 to week 5, could you make the chronological order like mahattan 5lb or your own priority? It would be really really helpful to skip those we are strong in and watch the ones that we are weaker in.

[@hassaanraza1090]

Love watching your videos Philip, big fan.

[@TheTestedTutor]

Thanks so much Hassaan

[@olasubomigiwa8470]

This video was helpful. Thank you

[@fatimaakram9602]

Thankyou so much fro making these videos for us! I feel so much more confident now! Love your content

[@TheTestedTutor]

I'm so glad!

[@sreedeviatp4732]

last lesson is simply hilarious!!!!!!

[@Kirstenmarshall]

The best videos!!!!!

[@luiz6041]

Great tutor