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Unfortunately, we can't equate 20 trucks with 36 days and we can't equate 16 trucks with y days. However, we can use the units of each quantity to try to simplify the question a little. At the start, the company has enough fuel to run 20 trucks for 36 days, so instead of saying 20 = 36, we can multiply these numbers to get 720 truck-days of fuel. Here, we're saying that the total amount of fuel the company has in its stock is equal to the number of trucks multiplied by the number of days the company can keep that truck running. To represent this figure, we can use the made-up unit of a truck-day, where one truck-day represents the amount of fuel one truck uses per day. This means we can divide the number of truck-days of fuel we have available by the number of trucks we want to run. If we think of the units as variables, we'd be doing truck-days / trucks and we could cancel the trucks on the top and bottom of this fraction to leave us with the number of days. Doing this with the numbers involved in the question means we'd do 720 truck-days / 16 trucks to get 45 days of fuel available. I hope this helps!

This is a great question, and it all comes down to the notation you use. For the purposes of the GRE, when you go from x^2 = 4 to finding x, you'll get two answers: +2 and -2. However, when you're presented with sqrt(4), in the same format as in Q2, then it's implied that you're looking for the positive root. So, you can think of sqrt(4) as +sqrt(4), and it's only when you want to go from x^2 = 4 to x = ±2 that you need to find both roots. I hope that helps! For more information, check out this page: en.wikipedia.org/wiki/Square_root

@@GRENinjaTutoring Thanks

We can say that because the sum of the items in list A divided by 5 is equal to the sum of the items in list B divided by 4, the sum of the items in list A is greater than the sum of the items in list B. The sum of the items in list A is 9 + 5m + n and the sum of the items in list B is 9 + 4n, so we can say 9 + 5m + n > 9 + 4n, which simplifies to m + n > 0. From this, we can't say whether n is greater than 4. It's possible that m is -5, so n needs to be greater than 4 to make m + n > 0 work. However, it's also possible that m could be 5, so n could be less than 4 and we still satisfy m + n > 0. All this shows that the algebra that Charles used in the video explanation is, sadly, necessary to reach the answer to this question. I hope that helps!

Thank you so much!

Sadly, you can't do this. Let's use another example to demonstrate why: if we were trying to find the square root of 16, we could set this up as 16^(1/2) which equals 4. However, if we were to do what you suggest, we would say that 16^(1/2) = 16^1 / 16^2 = 16 / 256 = 1/16 which definitely does not equal 4. It's a nice thought, and it would be lovely if it worked out, but your suggestion breaks a few rules of algebra. I hope that helps!

In this question, there are four possible outcomes: 1. We could choose two Americans 2. We could choose two Europeans 3. We could choose an American and then a European 4. We could choose a European and then an American Even though #3 and #4 leave us with the same final outcome (we chose one American and one European), they're counted as two different outcomes when we think about calculating the probability. If the number of Americans in the group is x, then the number of Europeans is (10-x). This means the probability of outcome #3 occurring is (x/10)*((10-x)/9) and the probability of outcome #4 occurring is ((10-x)/10)*(x/9). Even though the order of the numerators is reversed in these two options, they give us the same final outcome (x(10-x))/90. This means that to figure out the total probability of either one of outcomes #3 or #4 happening, we can calculate the probability of one of them and then double it. I hope that helps!

@@GRENinjaTutoring Hi, thanks for replying back so quickly and with lots of details. I am starting to grasp it. I remember watching a previous quant video where a tutor mentioned that order doesn't matter when selecting people in a group or in a team, I am wondering how we are able to discern between these cases where order does and doesn't matter. I know in this example, there are two outcomes for the same group. But are we assuming or matters? Are there keywords? Thank you!

@@JennyLiang-oi9zc I'm sorry if I've misinterpreted your question here, but I think you're getting a little mixed up between finding the number of ways a thing can happen and finding the probability that a thing will happen. In a probability question, you consider the selections as taking place one after the other even if the question just says something like "you choose two people". This means we need to consider all the possible outcomes: - American and American - American and European - European and American - European and European However, in a combinations question, all we care about is the composition of the final group, so the order they were chosen in doesn't matter. The final option is that you're asked a permutations question which asks about the number of ways you can select a group, but the order of the selection does matter. For more on the distinction between combinations and permutations questions, check out our Combinatorics video. For example, let's say the Americans are labeled A, B, C...and the Europeans are labeled Z, Y, X.... If we were looking for the number of ways you could choose one American and one European, then the order wouldn't matter as picking person A then person Z gives you the same group as if you were picking person Z then person A. However, if you need to find the probability of picking one American and one European, then we have to consider picking person A then person Z as a different outcome to picking person Z then person A, even though you end up with the same group at the end of it. This is a really tricky thing to wrap your head around, but I hope that's helped a little. Please let me know if you have any other questions, and I'll do what I can to help!

Hi! I'm not sure I understand what your doubt is about Q6. You're absolutely right that the only value of x that satisfies the given equation is x = -3. This means the answer to this question is (B), and that's the answer Charles reached when he answered this question in the video. If you let me know what problem you're having with this question, I'll do all I can to help. Thank you!

​@@GRENinjaTutoring Yes I am sorry. He answered right. I got wrong there I skipped the part of the video where he was explaining why x=2 should not be possible. So, I thought he was wrong. I am wrong here. Thanks for taking time to reply on my query. You guys are doing a great work. Even to the courses online which I have paid no one replies to queries this fast. Keep doing this great work.

@@ramachandrarao6469 No problem! I'm so pleased you're finding the courses helpful. Good luck with the rest of your studies!

Thank you so much!

That all depends on whether t is positive or negative. If t is positive, then it does have to be greater than 1 to satisfy that statement. However, it's also possible for us to satisfy the problem statement if -1 < t < 0. For example, if t = -0.5, then t/|t| = -0.5/|-0.5| = -0.5/0.5 = -1 which is less than t = -0.5. This means the initial problem: t/|t| < t is satisfied if -1 < t < 0 or if 1 < t. Since we can't tell whether t is greater than or less than 1, the answer to this question is (D). I hope that helps!

Thank you for watching and taking the time to write this! Have a wonderful time studying, and please let us know how things go for you.

Thank you for enjoying them! :)

Thank you so much! I'm honored that they've helped a bit. Have fun studying, and please keep us posted on your progress!

In terms of the content itself, yes: you can think of this as a complete, free GRE video course that covers everything you really need. The hitch, of course, is that you'll still need to put everything we teach into practice. So you'll need to do plenty of practice questions and exams, ideally from official GRE materials. You'll need to figure out how to execute with consistency -- for example, careless errors or bad time management can demolish your score, even if you "know everything" already. But yeah: we'll teach you everything you really need on this channel. It's just that it's up to you to use all of the information effectively on test day. :) I hope that helps a bit, and have fun studying!

Haha, thank you! Is there anything in particular you'd like to see in future videos? We cover each GRE question type and topic in some depth already, but if there's something that you'd like to see more of, just let us know, and we'll do our best to accommodate.

@@GRENinjaTutoring well sir i need the videos regarding analytical writing

@@GRENinjaTutoring Hello, great videos...Kindly, make longer videos on text completion and equivalence (I seem to only get one answer or two on the questions with a lot of blank spaces) ...Desperately need your help. Thankyou.

🐐!

for the problem @25:00

Thank you! Noted -- you're not the first person to ask for that, so it's very possible that we'll produce more. Thank you again, and have fun studying!

This is one of those situations in which you need to be very careful with the wording of the question. We're asked "For which of the following regions is the ratio...smallest." This means we're limited to looking at the regions mentioned in the answer choices and only those regions. We can (and should) ignore any other region mentioned in the table. There's no reason why Sub-Saharan Africa was left out. However, the fact that it is not one of the options means it cannot be the answer to this question, even though you're absolutely right that Sub-Saharan Africa has the lowest value for the ratio of all the regions in the table. I hope that helps!

Thank you so much!

Like, how do you know absolutely for sure that the line AB would be perpendicular to the height?

Hi @@JennyLiang-oi9zc, This is based on a property of isosceles triangles. We can draw a line that bisects angle AOB and that reaches the side AB. Since AOB is an isosceles triangle, we know that the angle between the line we've drawn and AB will be 90 degrees. You can find a proof of this property through the following link: www.nagwa.com/en/explainers/973164576417/#:~:text=Corollary%20of%20the%20Isosceles%20Triangle%20Theorems,and%20is%20perpendicular%20to%20the%20base. I hope that helps!

You've got the correct solution for X. There must be a problem after that stage, and I suspect this issues is that you've lost a negative sign somewhere. Once you substitute X = -5/3 into 3^(3X + 3) you should get 3^(3(-5/3)+3) = 3^(-5 + 3) = 3^(-2) = 1/9. I hope that helps!

Haha, I'm glad that you enjoyed it. Have fun studying!

Thank you so much!

Thank you so much for watching!

This is incredibly kind -- thank you so much for taking the time to write this. I'm glad that the video resonated, at least a bit. Have fun studying, and please keep us posted on your progress! We like good news around here. :)

Yes, definitely! The "new" GRE isn't all that different from the old one -- it's just shorter, but the quant content is completely identical. So all of our quant videos apply equally to the old and new versions of the exam. I hope that helps a bit, and have fun studying!

That last one is indeed pretty hard. :) Have fun studying, and please keep us posted on your progress!

You've got to be careful when you multiply both quantities by a constant. Let's consider the scenario in which Quantity A = 5 and Quantity B = 6. If we multiply both of them by 2, Quantity B will still be greater than Quantity A. Similarly, if we multiply them both by 1/2, Quantity B will be larger. However, we'll run into some problems if we multiply both values by -2. If we do that, Quantity A = -10 and Quantity B = -12, and now Quantity A is greater. Similarly, if we multiply both by -1/2, Quantity A = -2.5 and Quantity B = -3, and Quantity A is greater here, too. Multiplying both values by a negative constant reverses which value is greater. While we COULD multiply both values by a negative constant, it's usually safer to only multiply both values by positive constants. This means we won't change which value is greater than the other and won't have to remember to reverse our answer at the end. I hope that helps!

Thank you so much!

Haha, thank you! And yes: that one isn't the most enjoyable question ever. :) Have fun studying!

You're awesome, thank you so much for the kind words! We're starting to see a really nice upward trend in our overall views, so hopefully word is starting to spread...? Have fun studying, and if there's anything specific you'd like to see on our channel, please let us know!

Thank you so much! I'm glad that it's all helping a bit. Have fun studying!

Yes exactly!! Thank you so much, please keep going , thank u guys you’re doing great work

Thank you so much for the kind words! We'll keep releasing these as long as somebody out there is watching. :) Have fun studying!

@@GRENinjaTutoring Thanks a lot sir 🙏

The 5-lb. book is absolutely wonderful if you want tons of extra practice, but keep in mind that it was published by a third party -- not by the creators of the GRE. Personally, I think Manhattan Prep did a lovely thing by making that book so comprehensive, but what gets lost in the shuffle is that some question types are exceedingly rare on the GRE, but still (very understandably) get plenty of attention in that book. When we examine every official GRE question that's been published by the test's creators -- along with questions we've seen when we take the exam ourselves -- we just don't see all that many compound interest problems. We can easily count them all on one hand, for better or worse. Is it worth practicing compound interest problems for the GRE? Sure, if you're trying to scrap and claw for every little point -- there's always a chance that you'll see a question or two on the exam. The more likely outcome is that you won't see any at all, so if you don't have much study time, I wouldn't invest too heavily in that particular question type. I hope that helps a bit, and have fun studying!

@@GRENinjaTutoring Thanks so much! I was considering including the compound interest formula on my list of important formulas to know, but I'm glad I do not have to worry! I love your videos, they have been so helpful!!

Thank you, Michael! And wow, you're quick. :) Have fun studying, and please keep us posted on your progress!

@@GRENinjaTutoring Hi, in general, what resources would you recommend for someone who wants to score 167+ on the quant portion of the actual test?

And after doing a whole lot of bench presses, I guess? 😆