Two of the Hardest Quant Questions - GRE and GMAT Math

[@Spybuoy]

Gave my GRE today after watching your video. Helped me score 323 (I got 317 on my first attempt.) Just can't thank you enough.

[@TheTestedTutor]

Thank you so much for telling me Chakri. You made my week!

[@EverythingTechWithMustafa]

What was your preparation stratergy ? how much time did you prepare it for ?

[@thisispartaa]

My face when I was in the 11% who got the 2nd question right 😄 definitely really interesting questions. Thanks again Philip, for enlightening us!

[@TheTestedTutor]

Well done!

[@gomz2346]

Thanks for all your help. Your videos helped me get 329 on my test. :D

[@TheTestedTutor]

Thanks so much Gomz, one of my earliest supporters. Do stayed tuned for personal finance videos in December.

[@gomz2346]

@@TheTestedTutor Will be looking forward to it. Very crucial life skill indeed.

[@rish8357]

Gomz give me tips please

[@AshleighGaruz]

Learning that factorial trick is today's highlight. I have wasted so much time on factorials during the practice tests. Thank you!

[@mdrifathossain1575]

I had my gre exam today. Got 317 on overall. 155 in verbal and 162 in quant. The score was almost close to my expectations though a bit disappointed for the quant score expected more from that as it was my strength. I found the first quant section a bit lengthy, there were not much hard questions but some of the questions were of too much unnecessarily lengthy question, while solving those I got panicked about the time management. However, verbal section was quite like the powerprep 2 questions and seemed consistent throughout the two sections. A big shout out to you as some of your videos helped me a lot. keep up the good work.

[@TheTestedTutor]

Thank you Rifat. I think that's a great score, and you can build on it if you retake.

[@mdrifathossain1575]

@@TheTestedTutor I will stick with this and now will prepare for Toefl which is on 12th October.

[@mikiallen7733]

thanks rifat for the feedback , yet would you kindly refer to those videos ( preferably with titles included ) which you have referred to above where you described them as most helpful ? your input is highly appreciated

[@mdrifathossain1575]

@@mikiallen7733 he made a video on solving reading comprehension problem, that was helpful. Also his content on standard deviation was exceptional.. that's the best I can remember now, as it's almost a year since I have taken my exam.

[@thevagabond85yt]

Q1, can also be approached as 18C2 / 20C2 (C = Combination) = (18x17/2 ) / (20x19/2) 20C2 : total possibility of picking 2 balls from the 20 balls sample 18C2 : possiblility of picking 2 non-defective balls from the non-defective lot

[@lizs2456]

This video was so helpful. I think I would have gotten these wrong before watching this but you explained it so well and I feel more confident that I can get these right.

[@adaamm]

Great confidence booster, I’m sitting my GMAT at the end of this year. I failed math at high school but for some reason I find these quant questions really easy

[@anuragsinghraikwar]

I don't know why I found both the questions very easy and did them within seconds.

[@TheTestedTutor]

Nice!

[@anantharamayya4412]

Cause you're indian Go ahead and solve verbal

[@saileshsivakumar1404]

@@anantharamayya4412 lmao

[@saltygamer8435]

Verbal is the bane of Indians I see

[@shuhaoliu5474]

@@TheTestedTutor hello! Do you have some recommendations for practice test resources? I feel like I should take a few simulated tests before the real one. Thanks!

[@piyushmanglani6471]

Thanks man I watched and I knew the answer and that is possible because I saw your probability video and that is how I have learned how to deal with this kind of questions.

[@TheTestedTutor]

Great news Piyush!

[@ihuomaokoro-ebi3837]

Same here 💃💃

[@dhwanipatel3600]

I agree. I saw his earlier video and was able to answer this one! Kuddos ma!

[@anamicaverma8374]

i got them both right!! you're the best teacher ever!!

[@dhwanipatel3600]

You're really doing a great job! I am a 2022 aspirant and these videos are really helping!

[@TheTestedTutor]

Glad you like them!

[@lillianburton362]

Thanks! Please keep the videos coming. They are helpful and I appreciate viewing them as well.

[@TheTestedTutor]

Thanks Lillian, appreciated.

[@EverInBloomMusic]

Blessings and gratitude for your work!

[@ibukunoyeleke1470]

Thank you ❤

[@amanuelsidamo4152]

I am in the 11 percent for the second one. I love 💘 the way you teach. It is like drinking my favorite drink.

[@sime96]

Please do more very difficult ones! Like the ones you’ll get 1-2 of each test

[@TheTestedTutor]

Ok!

[@adityabhat5189]

Welcome back Sir! The simultaneously was a bit misleading but the 2nd question was a cake. I am not doing well on the Logic-based Reading Comp questions. If you could make a video on how the author is relying on the assumption, how to make analogies, additional proof to the paragraph kind of questions, it would be very helpful. Thank you for the great content and have a great day Sir! :)

[@TheTestedTutor]

Glad you got them. Assumptions are a great topic to cover...

[@EnkoreTech]

@@TheTestedTutor I would love a video on that also.

[@myjourneywithmybabyginger3901]

Why we have only 10k subscribers?It is the one channel I want to see flourish.

[@anonymouslearner4368]

Please do more such videos sir

[@TheTestedTutor]

Will do!

[@thermite10k40]

What i learned from this video is to not over complicate the questions when you think it is hard, what i did for the first one was subtracting chances of picking 2 bulbs with at least one defective and subtracting the total possible was from it, did it work? obviously but it took me 2-3 times more time to solve than your solution. thanks for the video.

[@pratimas3598]

Very well explained.. I liked the second question. It's challenging

[@SwagggarModale]

Really really helpful

[@TheTestedTutor]

Thanks Sagar! Means a lot.

[@akashmishra3369]

So glad to have watched your Probablity video before this, Phillip :3

[@omi_naik]

Thank you sir very helpful sir can you do different types of questions for data interpretation

[@lavendervvoo2970]

your videos are so helpful! unfortunately, recent GRE questions have gotten much more difficult

[@ihechukwuosuji1503]

Have u written recently?

[@EnkoreTech]

for the first question, shouldn't the 2nd nondefective also be 18/20? since he's picking it simultaneously, shouldn't that mean there are still 20 bulbs in the box?

[@TheTestedTutor]

Simultaneously doesn't make a difference, it's still 19 after the first one has been counted. Good question though.

[@EnkoreTech]

@@TheTestedTutor thanks for clearing that up, do you have any quick tips for logic based RC? my exam is tomorrow and it still messes with my head.

[@mohammedsharikuzama5518]

I had my GRE today and I scored too low that I'm embarrassed to even say that score. I'm retaking the exam in the coming month. I need some tips from your side bro since I follow your videos a lot and they're so helpful.

[@TheTestedTutor]

Thanks Sharik and well done on bouncing back!

[@iDenyTalent]

wait did you really get a 145 on the quant and 148 on the verbal?

[@stephaniebittner9388]

Big confidence boost when I got the first one

[@ishaanapte6570]

can the first question be done in this way? A: select a defective piece p(A) = 2/20 = 0.1 we select one AND then one more to p(of selecting two such) = 0.1 x 2 so P(selecting two non defective pieces) = 1- 0.2 = 0.8?

[@ananyapanda._]

Hello, I have a question. The quant questions in the ETS quantitative book seem really easy compared to the Manhattan 5lb sums. Are the GRE questions going to be of a similar difficulty as the ones on the ETS book?

[@TheTestedTutor]

Somewhere in between. Most questions are like ETS, a handful like Manhattan.

[@ananyapanda._]

@@TheTestedTutor Where does one prepare data interpretation questions from? Some people told me to stick to ETS for quant and verbal but I'm already done with most lessons for quant from the 5lb book. I haven't done data interpretation, percents and sequences and series from that book. Would you suggest I do them or leave these chapters out? Especially sequences and series? Also, data analysis from ETS seemed too easy. Should I do that part from Manhattan 5lb?

[@thedialogues9435]

got right both but yes good question and got help from probability videos from your channel

[@Bee-lieve623]

I added instead of multiplying on the first one. I got the second one right ✅

[@verdaarif140]

Hi Phillip! So I have a small question: on Q1, I did 1- p(DD) where D is defective pick. This meant P(DD) = 2/20*1/19 and then our answer that neither picked bulbs are defective : 1 - 1/190 = 189/190. This is not the same as what you have got with the more direct approach. And in theory they should be. Could you tell me what I am doing wrong?

[@parthragadwala4141]

Same

[@THEULTIMATUM]

same, you got idea now?

[@wassupr.7930]

Thank you

[@Shaykhah]

This is just awesome!

[@TheTestedTutor]

Thanks Shaikha

[@eyaqubhossain9135]

Very smart teacher

[@jeffrey4785]

thanks phil u rock :)

[@omi_naik]

18C2÷20C2 probability

[@TheTestedTutor]

Great spot! This also works!

[@omi_naik]

@@TheTestedTutor hello sir if I have finished with Manhattan 5lb quants part should I go for any more books or start the test series

[@TheTestedTutor]

@@omi_naik Start practice tests for sure. Aim for a minimum of 10-12

[@omi_naik]

@@TheTestedTutor sir Manhattan 5lb book is done is it enough for GRE do I need to solve some other book also like ETS quants book or start with test series directly ??

[@AnsImran]

Thanks

[@victoremmanuel3632]

Thanks for your videos, I am just wondering why I cannot also use 1-Pr(defective bulbs) to solve it also..

[@TheTestedTutor]

You can!

[@mubinchowdhury3956]

Wow!! Why don't you make more videos on GMAT verbal? It would be very helpful.. Thanks!

[@TheTestedTutor]

Will do soon

[@rasheedkibria1027]

Very Good Explanation....Thank you a lot....

[@TheTestedTutor]

:)

[@user-zg8mx8wm4h]

Hey! Very helpful video. However, when I try to do the probability question the other way (that is find the opposite probability and subtract it from 1) I get a different answer. Probability of both being defective: (2/10)*(1/19) = 2/380 => 1 - 2/380 = 378/380 = 189/190 What am I doing wrong?

[@joannwatu7603]

You made an error in the denominator of your first probability by writing 2/10 instead of 2/20

[@SweetComputing]

​@@joannwatu7603 Even after correcting the error the answer still computes to 189/190. What am I missing? (1/10) * (1/19) => 1/190 Probability => 1 - 1/190 which is 189/190...

[@yashdoshi961]

@@SweetComputing you are not accounting for the possibility for one defective and one non defective bulb in this case so the answer contains the probablity of these cases too

[@sarthakmaharana2877]

I breezed through the second question. I got the 1st one wrong. What's up with the 1-x strategy?

[@anonymouslearner4368]

Hey huge concept coverage ,cheers to ur recovery sir .learnt a lot For first u can also try with 18 Choose 2/ 20 Choose 2

[@TheTestedTutor]

Thanks AL! And great spot! This also works!

[@ishansingh8759]

I was able to solve both these questions comfortably at 1st attempt

[@Soniasisi_]

I have a question. Can you find the probability of picking the the two defective bulbs and then subtract them from 1? I tried solving it that way and I didn't get the right answer. Thank you

[@TheTestedTutor]

Yes, it should work...

[@Soniasisi_]

@@TheTestedTutor thanks for the reply. Yeah I figured it out eventually.

[@chessologypak786]

Hope you are fine. is this the most difficult level in GRE quantitative level?

[@TheTestedTutor]

Could get a tiny bit harder but yeah...

[@ktmgr7]

Hello, why didn't it work with 1 - (2/20 *1/19) in the first question.? We were selecting defective and then find the probability of finding non defective. Please correct me. Thank you

[@TheTestedTutor]

Because the opposite of 'Both' is not neither. It could be just one defective. Three options, Both, Neither and 1 only. So 1 - Both won't work.

[@narayankhanal9662]

That's Awesome!

[@shounakkulkarni6731]

I found both Questions quite easy and solved within 30 secs each. strange or they were really easy?

[@helpinghands9485]

Hello Gmat tutor , thank you for your videoes , well in the first question , i went about this way . So to get the probablity that both are not defective , how about get the probability that both are defective and subtract that from one . so p ( both defective ) = (2/20 )*(1/19)=1/190. so subtract this from 1 = 1-(1/190)=189/190. Do let me know where i went wrong

[@stefanwolf7772]

Hey Mate! At first i was wondering the same thing. The problem with your calculation is that you are now including the probability of having one of the light bulbs being defective. If you wanna calculate it like this, the right calculation would be: 1-(2/20)*(1/19)+(18/20)*(2/19)+(2/20)*(17/19)=(153/190)

[@sanskartewatia4320]

there's 4 cases in all, Def, Def; Nd, Nd; Nd, Def; Def, Nd, so you're missing out on 2 values that need to be subtracted

[@awaisahmad22]

Awesome video broher

[@la8309]

just leaving a comment to make sure youtube metrics shares the content across the world.

[@farhanakthar4492]

Hi I have a doubt in the first one, why can’t I take it as 1/20*1/19 and then subtract it with 1, that’s how the usual method goes right? Please help

[@muhibmishu9597]

(18C2)/(20C2) 😊

[@mubinchowdhury3956]

why don't you make videos for whole GMAT and GRE? It would help millions!! As always..Thank you! :)

[@TheTestedTutor]

What do you mean exactly? I do already!

[@mubinchowdhury3956]

@@TheTestedTutor i meant in more organized way..like there are some channels that helps with IELTS.. i have seen they make individual playlist like ielts writing, ielts reading, ielts listing, and ielts speaking with practice.. i found it very helpful.. I know it is so much to ask..but then again, it would help millions..and of course you are so nice..thank you for not asking to open some premium account..xD

[@ibrahimahmed3176]

hey I had a slight confusion for the first one. why cant we instead find the probability of defective which is equal to 2/20 and then second pick 1/19. multiply them we get 1/190 and then subtract from one to get 189/190.

[@oderaonyechi1074]

Not sure if the GRE got harder or different people just find different things difficult because these were so easy to me but I saw a bunch of hard questions on the GRE last month 😪

[@rutvikkachchhi7826]

🔥

[@TheTestedTutor]

😀

[@ankitakhadka1336]

I am generally confused with these sorts of questions.. why do we get different answers when we do the probability of getting defective bulbs first and then subtract it from 1?

[@TheTestedTutor]

You should get the same answer, you may be forgetting to remove 1 from numerator and denominator

[@quackqq]

Well that's because you must be doing (2/20)*(1/19) which is the probability that both the bulbs are defective simultaneously. To find the correct answer also add the cases when the 1st bulb is defective and second is not and the 2nd is defective and 1st is not. Hope this helps! Best of luck from India

[@beelikebunny]

I took a diff route. 18c2/20c2. thanks for the trick though.

[@jaannashinsingh9523]

How combination can be applied in this could you please let me know.? And how formula works . Are we creating groups here or order doesn't matter here . Why combination not permutation? @The Tested Tutor @ Abir Sur

[@saharfarhat9239]

Probablity, YES!!! Factorization :(

[@TheTestedTutor]

A video on that coming up soon!

[@TheRedPillMan97]

Great video!

[@TheTestedTutor]

Thanks!

[@sanskartewatia4320]

I'm not gonna lie man, i did both of these under 5-7 seconds without any calculator or pen-paper. Maybe the concepts are tough but I have seen trickier questions that have taken minutes to solve... Being an Indian, where I'm literally doomed is the verbal section so that's that

[@sypherop]

I find them easy. Did both within a minute only my mind.

[@williamwallace4080]

I solved the first one using a tree diagram (just to be sure). For the second I just factorised each number and found out that 58 = 2*29. 29 is prime so it can't be made by any factors of 25! = 24*24*23*.....*3*2*1

[@akashparashar9883]

I came here for find most difficult questions of quants and I had got two very simple questions.

[@TheTestedTutor]

I came here looking for a most interesring comment and I got a silly one.

[@nabiyabano9929]

@@TheTestedTutor haha nice one

[@maxvolmer1896]

56 = 7 *8, both of which are contained in 25! Why isn't 56 the correct answer?

[@jaannashinsingh9523]

Hi , please help me out here @TheTestedTutor. In 2nd question isn't the answer A 26 ?. Because its asking for least + ve integer . Lets say 25! has factors 25*24*23*22*......*1. 26 is not a factor of 25! as 26 has factors - 1,2,13,26 - 26 is out of bounds means greater than 25 so 26 is least integer that is not prime and not a factor of 25 ! .All the options are not factors of 25! but least is 26 -A . Why you are considering only prime factors ?

[@pratikthorat3480]

26 is not a factor but 26 has prime factors 2 and 13 which can be found in 25 factorial. Hence 26 is not an answer. Now 58 is not a prime number and one of it's prime factors is 29 which is outside the scope of all numbers within 25 factorial. Hence 58 is the right answer. 26 was a lucrative answer even I almost choose that in a rush.

[@jaannashinsingh9523]

@@pratikthorat3480 Yeah , Thanks for the clarification. However why we are just considering prime factors . Why 1 and number itself is not under our consideration. If 58 was not in the options then , we still had seen only prime factors? That was my concern actually!

[@pratikthorat3480]

@@jaannashinsingh9523 so see, the question stated, a number which is NOT a factor and NOT a prime number. So to circumvent this problem we have to think of a smallest prime number that us greater than 25. So that is 29. Now the number 29. So any multiple of 29 will most probably satisfy the conditions. And as far as considering 1? We do consider 1 as a factor as well. To understand better, read more about prime numbers and number theory from Khan Academy videos

[@rish8357]

Got the first one right. Q2- 58 contains 2 which is a factor of 25... im confused here

[@gomz2346]

whenever they ask 25! you should think of prime number just above 25.. that is 29. Since they told it cannot be a prime number just multiply that by 2 for making it non prime and thats your answer. You multiply by 2 so that you can get the least value after multiplying with a positive integer(excluding multiplying by 1 which does not change the number at all)

[@calchiat4103]

3:55 The question says simultaniously, but you say we make the choices one after another -how can that be right?

[@TheTestedTutor]

It's just a good way of calculating. Doesn't make a difference to result.

[@calchiat4103]

So can every simultanious pick be broken down that way?

[@TheTestedTutor]

@@calchiat4103 Yep!

[@Revboiuk09]

I got the first question right within 30 seconds and second one took me 1.5 minute to solve it. In short I got both of them right. 💯, Both were logical I loved the questions. Thanksssss

[@TheTestedTutor]

Wow nice!

[@harshjoshi6257]

Who else was surprised that only 11% got the second question right

[@TheTestedTutor]

A bit harsh!

[@pratikthorat3480]

@@TheTestedTutor Pun game strong. No wonder you had a perfect score on the verbal

[@daminivadrevu3027]

Feel kinda dumb to ask, but aren't 25, 5, and 1 factors of 25? 66 is not divisible by 25.

[@TheTestedTutor]

They are factors. But 66 is higher than 58

[@naomihoriuchi7592]

Heh...I knew the first one, and was quite pleased with myself, then you got to the second one and I went....😐😅 lol Just wanted to say thank you, great quality video (first one I’ve watched) and I will definitely be subscribing and watching more!

[@TheTestedTutor]

Thanks so much Naomi!

[@bilalansarkhan3008]

The second one was trickyyy

[@muhammadawais1696]

did both wihin 10-15 seconds

[@oluchinwade2442]

56 is = 2*28. Why didn't it work?

[@TheTestedTutor]

Not sure Oluchi!

[@adithisrinath9830]

Because 28 can be written as 14*2. 56 can hence be written as 4*14 (both are factors of 25!) but 29 cannot be broken down this way

[@himanshutiwari5695]

I got both correct within 10 sec, still when it comes to actual mock I don't even cross 60 percentile of the quant 😞

[@SweetComputing]

I tried to solve the first question by taking the probability of finding a defective piece and subtracting it by one. (2/20) * (1/19) => 1/190 Then substracting it by 1 gives me 189/190. What am I missing? :(

[@glennquagmire9572]

You are missing the possibility that only one of the two lightbulbs, wich were selected, is defect. So you have to add (2/20) * (18/19), the first lightbulb is defect, and (18/20) * (2/19), the first lightbulb is defect. So in total the possibilities to select a defect lightbulb are: (2/20) * (1/19) + (2/20) * (18/19) + (18/20) * (2/19) = (2/20) * (1/19) + 2 * (2/20) * (18/19) = 37/190. And 1 - (37/190) = 153/190.

[@alicebajpai3337]

I got both the answers right, I'm ecstatic lol! (I'm bad at math so....)

[@TheTestedTutor]

Well now you are officially good at Math. I have declared it.

[@alicebajpai3337]

@@TheTestedTutor thank you!

[@RahulSharma-oc2qd]

Why the first one can not be done in this way 1-((2/20)*(1/19))?.. considering that I am choosing both the defective one and then subtractic it from the total probability of the case.

[@ninaricci7643]

Well if you do that you will get cases, where one of them could be defective and the other one non-defective You strictly want the situations, where both of them are non-defective

[@anthonyjohnson9544]

Great explanation but you need to write this so people can visualize it, a lot of people are hearing numbers but not seeing it

[@TheTestedTutor]

Agreed! I changed it to that style for future videos

[@anujabiyani5944]

I found both the questions easy ... My real nightmare is verbal🙄

[@SinghCharan]

These are low difficulty GMAT questions.

[@onurylmaz3798]

these are primary school level questions

[@emmanueladeoluwa737]

I'm a little surprised because your method of solving the opposite that you taught in an earlier video didn't seem to work here. When I tried to instead solve for the probability of both selected lightbulbs being defective, I came up with 2/20 and 1/19. The product of that is 2/380 or 1/190. Taking that out of 1 to get the probability of neither being defective didn't quite get to the point. My question then is, how do I know when this method works and when to not use it?

[@TheTestedTutor]

It's because the opposite of both is not neither. You forgot the possibility of one only. It is not just NN or DD, there is also DN and ND. So the 1 - opposite is not wise here.

[@saadman920]

@@TheTestedTutor thanks !! I was going to ask the same question why 189/190 is not the answer.

[@Hassan.sohail1992]

nice

[@user-jm6gp2qc8x]

how is the first question one of the hardest? Isnt it obvious that it is 18C2/20C2 edit: holy shit second was also easy. ok now i am thinking that Phillip is downplaying the difficulty level in GRE.

[@Vibhu_g621]

Bruh... These are literally the easiest for me.... I'll just say walla habibi , please give JEE😅

[@MrMcfire2]

Quick one on fractions: I believe that the GRE technology will accept non-simplifed fractions (maybe a more time effective method vs. simplifying)

[@megank707]

Sorry, But I didn't find these questions to be HARD.