GMAT Ninja Quant Ep 2: Algebra & Efficiency

Рет қаралды 39,109

Күн бұрын

Do you struggle with algebra questions on the GMAT or Executive Assessment? Do you "know" plenty of algebra, but struggle to answer questions efficiently? Do you sometimes get stuck because your avoid algebra and pick number instead?
In this video, Bransen -- a GMAT Ninja tutor -- will show you how to think about GMAT algebra questions efficiently and effectively. He'll help you understand how a flexible, consistent approach to algebra can increase your efficiency and accuracy on quant.
This is video #2 in our series of full-length GMAT quant lessons. For updates on upcoming videos, please subscribe!
This video will cover:
➡️ Simultaneous equations
➡️ Quadratics
➡️ Basic inequalities
➡️ Basic absolute values
This video is for you if:
➡️ You lack efficiency or flexibility
➡️ You need to learn (or review) the basics
➡️ You “know” everything but still struggle
Want more GMAT test-prep tips and advice?
Subscribe to our KZfaq channel: / gmatninjatutoring
For more information about GMAT tutoring: www.gmatninja.com/
For updates on this series and our other projects: / gmatninja
For more on Bransen Vilardo and his ability to answer GMAT questions in Hebrew, Greek, and Arabic: www.gmatninja.com/bransen-vil...
Chapters:
00:00 Introduction
04:27 Question 1 - Simultaneous Equations Part I
12:19 Question 2 - Simultaneous Equations Part II
19:03 Question 3 - Simultaneous Equations Part III
26:11 Question 4 - Algebraic Fractions
34:18 Question 5 - Quadratics Part I
42:17 Question 6 - Quadratics Part II
49:55 Question 7 - Absolute Values
57:21 Question 8 - Absolute Values & Inequalities
1:05:37 Question 9 - Pushing the Question

Пікірлер: 130

@tonyassamoi9688 Жыл бұрын

Q3, isn't it X= -10 ?

@startcomplaining9781 5 ай бұрын

Up Up and away fly Bransens chances for the HBS :)

@miho9453 Ай бұрын

You’re right

@gyanaranjandash5880 2 жыл бұрын

You guys have put together a good team for these online sessions and a proper gmat focused channel. Cheers!

@adki7559 Жыл бұрын

Hi, thanks for the video, really helpful to repeat all learnings once again. In the last question for statement two you only mention that its enough to answer the question but actually never do so. I figured the whole DS question is B, because x according to statement two can still be 0 or positive. Therefore we cannot conclude that it is zero. (as required in the x*(sqrt(x^2)-x)=0) Hope this is helpful for anyone wondering the same. Please correct me if I'm wrong. BR

@ambecksfulful 2 жыл бұрын

I found it really helpfull for the concept of “distance” for solving problem about inequality. Thanks, really appreciate it..!!

@GMATNinjaTutoring 2 жыл бұрын

Thank you so much for the kind words, as always! I'm glad that these have been helpful. About a dozen more quant videos are on their way... ;)

@devadarshinipoovaragan6758 Жыл бұрын

@@GMATNinjaTutoring Please provide the final answer as well for all questions. Loving the series, btw.

@kogurasama 6 ай бұрын

wow using the diagram by using the distance concept really makes the question simple. Thanks

@pinkybae_tech 2 жыл бұрын

Question 3 answer should be negative 10 rather than positive, right?

@GMATNinjaTutoring 2 жыл бұрын

Yes, that's correct! With both statements together, we get that x = -10, and the answer is C.

@sims_ran 8 ай бұрын

Another amazing video, thank you so much Bransen!! The bit about absolute values being represented as distances on a number line and the note on how the square root symbol is considered a positive root on the GMAT are especially helpful takeaways. On a very different note: Love the shirt! It's pleasantly hypnotizing xD Not in a distracting way though

@domenikgerhards7240 Жыл бұрын

Q9: does this mean that if the statement would say root of x, instead of x-squared, that it would also be the absolute value?

@ukamakacyriacus4833 Ай бұрын

After the explanations, why aren't you saying the answers, so that we'd know if it's both sufficient C or statement 2 is sufficient B. That is what is missing in this video. For instance I can't tell what the option answer is to the first question. Is it even E?

@HHNYC Жыл бұрын

Thank you so much for these videos

@divyanshharnal5169 Жыл бұрын

HY I have a doubt if its 3^8/3 = it should be 3^7 not 8 if i am correct ?

@anshlaroia9443 2 жыл бұрын

Really helpful as always! :D

@visheshgupta5948 Жыл бұрын

I didn't get the last question. I face extreme difficulty in questions which involve absolute values and that's maybe because my basics for absolute value aren't clear. Is there any other way to solve the last question?

@GMATNinjaTutoring Жыл бұрын

Hi Vishesh! There are certainly multiple ways to solve any question, and we just present one particular way to solve it. That being said, I think that the way that we solved the last question in the video is one of the most efficient paths to a solution. It’s also worth noting that the final question of this video is pretty hard. Absolute value definitely shows up on the GMAT, but it’s possible to get a really good score without having completely mastered all absolute value questions. Don’t get too focused on hard questions that are going to make a difference between a 49Q or 50Q, and instead, focus on the more basic questions that will get you to that range. I hope that helps!

@VedikaHansaria 11 ай бұрын

In question 4, if you solve: 2/x = (3 - 3/y), wouldn't that be easier and faster than the proposed solution? Please suggest if it's the wrong approach

@GMATNinjaTutoring 11 ай бұрын

That would certainly be a possible first step in this question. However, it wouldn't necessarily be an easier path in the end. Notice the next step after that would be to take the reciprocal of both sides. The left side would become x/2, which is quite simple. But the right side would become 1/(3 - 3/y). In other words, we would have a fraction with an expression containing fractions in the denominator -- which isn't a lot of fun! One side note -- sometimes people assume the reciprocal of 3 - 3/y would be 1/3 - 3/y, but notice you can't take the reciprocals of each term in the expression. In fact, you need to take the reciprocal of the expression as a whole -- yielding that ugly fraction 1/(3 - 3/y). I hope that helps!

@patbateman979 9 ай бұрын

for question 4 you can also rewrite both sides of the equation as reciprocals :)

@GMATNinjaTutoring 9 ай бұрын

Agreed! If you don't mind dealing with fractions within fractions [i.e. 1/(2/x + 3/y)], that's an effective strategy :)

@ArshdeepSingh-ek6su Жыл бұрын

in question 3, howcome x=10, shoudnt it be -10 on solving it?

@GMATNinjaTutoring Жыл бұрын

Yes, that's correct! With both statements together, we get that x = -10 (not 10 :) ), and the answer is C.

@guneetpandher3505 Жыл бұрын

Quick question about Number 5: Why can the fact that 505 is being sqaured and 495 is being squared be cancelled out with the square root over both numbers hence cancelling the squares and the square roots. This would leave you with 505-405? Is this not possible to do?

@GMATNinjaTutoring Жыл бұрын

Hi Guneet, You can test this out with much smaller numbers: think about what happens if we calculate sqrt(5^2 - 3^2). If we did as you suggest and find the square root of each individual term, we'd have 5 - 3 = 2. However, if we square the numbers under the square root sign first, we get sqrt(25 - 9) = sqrt(16) = 4. Unfortunately, you can't take the square root of individual terms like that. You can only take the square root of the whole side of an equation or the whole of an expression. I hope that helps!

@balpreetsingh6834 Жыл бұрын

Thank you for the video explanation. For Q4, my approach was since (x+y)² - (x-y)² = 4xy, then find the square root of 4*500*5. Is this efficient enough?

@GMATNinjaTutoring Жыл бұрын

Hi Balpreet! I'm having a bit of trouble following your thought process here. I don't think you're talking about question 4, maybe you mean question 6? And even then, I'm not sure that I follow your process. Would you mind clarifying and explaining a bit more?

@balpreetsingh6834 Жыл бұрын

@@GMATNinjaTutoring Hi, sorry for the typo, I meant Q5, Sqrt of 505² - 495². I assumed (500+5)² - (500-5)² = 4*500*5

@kenny5930 2 жыл бұрын

For Question 6, wouldn't statement 1 be sufficient by applying Pythagoras? Given that x^2 + y^2 = 169 is a Pythagoras triplet 5, 12, 13 therefore x * y = 60?

@GMATNinjaTutoring 2 жыл бұрын

It's funny: Pythagorean triplets can be useful, but they can easily lead you astray on equations like this one. You're making two huge assumptions here: (1) x and y are integers, and (2) x and y are positive. And the question doesn't tell us that either of those things are necessarily true. That nice Pythagorean triplet jumped into your mind, but that's just one possible set of values for x and y -- and there are actually an infinite number of possible values of x and y here. If it helps, maybe try picking a few random values for x (including negatives), and see what happens with y. That might help you see what's going on with this particular equation. The takeaway: on data sufficiency, if you identify one possible set of values for x and y, you can't just stop there. You'll have to do more to be sure that it's the ONLY possible set of values. And in this case, it isn't. I hope that helps a bit!

@isidoramontefioriherrera5408 Ай бұрын

@@GMATNinjaTutoring Hi! I was wondering in the same question if A by itself is sufficient because: x^2 + y^2 = 169 x^2 -169 + y^2 = 0 And I know that ( x - y)^2 = x^2 -2xy + y^2 =0 So: 2xy = 169 Then xy= 169/2 Myabe I'm making a mistake because of one assumption? In this case, when you have just A, but also both together could be the answer, then which one is the final one? Thanks!!!

@HaraChiaki 2 ай бұрын

Hi, for Q8, for statement 2, why did you take the absolute value of x ?? x^2

@GMATNinjaTutoring 2 ай бұрын

There are two ways we can go from x^2 < 25. We could take the square root of both sides but, as you say, we'd need to include both the positive and negative roots. This means we'd end up with -5 < x < 5. Alternatively, we could follow the route Bransen took in this video and say |x| < 5. Both of these statements are just different ways of saying the same thing. I hope that helps!

@NeuralNewsletters 6 ай бұрын

TLDR: Efficient algebraic techniques, logical thinking, and manipulation of equations are crucial for solving GMAT problems effectively and finding the value of x. 00:00 📊 Algebra tools are crucial for solving GMAT problems efficiently, including simplifying equations, manipulating them to the same format, and understanding when two equations with two variables have no single solution. 11:50 🧮 Substitution isn't always efficient on the GMAT, avoid dividing by variables unless explicitly told, and consider both statements together to solve equations with multiple variables. 22:14 🧮 Efficiency in solving for x on the GMAT involves elimination, not substitution, and requires manipulating equations and answer choices to find the value of x. 32:13 🧮 GMAT questions require efficient techniques and the ability to simplify equations, recognize patterns, and avoid unnecessary arithmetic. 43:59 🧮 When solving for x and y in algebraic equations, consider using the equations together to find multiple solutions and be on the lookout for unexpected quadratics in GMAT problems. 51:38 🧠 Understanding absolute value as distance and using logic instead of guessing numbers can help solve algebra problems more efficiently, making both statements in the question sufficient and the answer d. 01:07:08 📝 Simplify equations by considering the order of operations and the absolute value of x, and use the given statements to determine the value of x. 01:14:26 🧮 Algebra skills are crucial for GMAT, so think logically and use algebra instead of guessing numbers or testing cases.

@user-nz4uw9zm7z 4 ай бұрын

In Q1, I understand why he's saying substitutions are always the way to go but realizing you can isolate x easily in the second equation, a substitution here is very quick.

@SPARSHGANJOO 10 ай бұрын

Hi I Have a doubt- In Q1 since there are infinitely many solutions possible, we can't get the value of x, hence, we mark E. What if the two set of equations were such that there was no solution possible for the system of equations, would I still mark E?

@GMATNinjaTutoring 10 ай бұрын

That is correct. If the question is asking for the value of x, and the information is insufficient to allow you to compute a single, correct value of x, then you should mark E. I hope that helps!

@ajitrajendran63 21 күн бұрын

Hello, I am sorry if the question has been answered but can we use the videos and material in this channel and website to prepare for the new GMAT focus edition? (I know data sufficiency and geometry is not on there, so probably not going to view the geometry video) Are the questions otherwise similar and a good barometer for the new version? Thanks a lot, y'all definitely help a lot of people out there :)

@GMATNinjaTutoring 15 күн бұрын

Yup! We filmed this video series before the GMAT Focus was a thing, so we use language that isn't totally consistent with the new test -- for example, Data Sufficiency is now part of Data Insights instead of quant, and we refer to the old score scale at times. Other than those bits of language, everything we say in our quant series still applies fully to the GMAT Focus Edition. (We deleted the geometry videos, obviously.) We're releasing new versions of all of our quant videos over the next few months, just to avoid any confusion. But the content and advice won't be radically different for the new quant videos. I hope that helps a bit, and have fun studying!

@ajitrajendran63 4 күн бұрын

@@GMATNinjaTutoring thanks so much for the reply and clarification

@pbs201 Жыл бұрын

in the question 4, i did 2/x= 3- 3/y and solved it that way and got answer c. what is wrong in my approach?

@GMATNinjaTutoring Жыл бұрын

Hi! It’s hard to know exactly where you went wrong without seeing your entire process, but I suspect that you misplaced a negative somewhere in your process. The correct answer (A) can be written as 2y / (3y-3), which is easy to confuse with (C) if you drop a negative somewhere.

@Amine-fo2qw 6 ай бұрын

Hi!, why the correct answer A can be written as 2y / (3y-3) ?@@GMATNinjaTutoring

@Amine-fo2qw 6 ай бұрын

OK I'm sorry, you explained it in the video. Thanks a lot!

@jessicaechegile2476 2 жыл бұрын

For question 6, is the answer A? Because we know that x^2 +y^2 = 13^2 meaning that the square of x and y must be 169 and the only way that's possible is 12^2 + 5^2 ? This makes statement 1 sufficient

@GMATNinjaTutoring 2 жыл бұрын

Ah, I think I see where the misconceptions are happening. First, it looks like you're assuming that both x and y are integers. So yes, x and y could be 5 and 12, but there are actually an infinite number of solutions for statement #1 by itself. For example, x could be 11, and y could be √48. Or x could be √99 and y could be √70. We could go on literally forever with examples, which is why Bransen says that statement 1 has infinite solutions, and isn't sufficient by itself. But even if you assume that x and y are integers, there's no reason why they need to be positive integers. So even with the numbers you chose, x could be -12 and y could be 5, for example. If you learned algebra visually at all, you might consider graphing that equation on a coordinate plane (either by hand, or with an online graphing calculator) to see what's going on. The graph is a circle, and there are an infinite number of points on that circle, which means that there are an infinite number of possible solutions. I hope that helps a bit!

@jessicaechegile2476 2 жыл бұрын

@@GMATNinjaTutoring Oh yes, I see it now. I assumed x and y were integers. Thanks for clearing that up.

@supratikparajuli9660 4 ай бұрын

For Q5, not sure but since the equation doesn't actually have x and y variables but instead numbers we can actually quantify, can't we 505-495=10 and 10^2 = 100 so sqt of 100= 10? Are we breaking a law while following this?

@GMATNinjaTutoring 4 ай бұрын

Sadly, you are breaking a law when you do this. The 505 and 495 are both, separately, squared. We can't ignore the exponents, do the subtraction, then bring the exponents back in. To provide a simple example so you can see this in practice, what we'd be saying if we were to follow that process is that 4^2 - 3^2 = (4 - 3)^2 = 1^2 = 1. However, 4^2 = 16 and 3^2 = 9, so 4^2 - 3^2 = 16 - 9 = 7 which is definitely not the same as 1. The rules still apply, whether you're dealing with numbers or variables. The GMAT does a great job of mixing these two up in ways you probably don't see very often, but the rules still apply no matter which of the two they throw at you. I hope that helps!

@AnthonySamson-wl3gw Жыл бұрын

Q4: I am confused why you cannot subtract 3/y from both sides.

@GMATNinjaTutoring Жыл бұрын

Hi Anthony! You definitely can subtract 3/y from both sides, but ultimately you’re going to want to get the variables out of the denominator. For that reason, it makes sense to get a common denominator for your fractions and multiply both sides by that. I hope that helps!

@WillC Ай бұрын

Q9 - 01:09:46 If we are taking the positive square root on GMAT, why are we introducing the concept of absolute value (the possibility of negative integer)?

@GMATNinjaTutoring Ай бұрын

We need to use an absolute value here because we don't know the original value of x. If we take a positive integer, square it, and then take the positive square root, we'll end up with the original integer. However, if we take a negative integer, square it, and then take the positive square root, we'll end up with something different from the original integer. Using an absolute value symbol gets around this issue, so we can say that sqrt(x^2) = |x|. I hope that helps!

@WillC Ай бұрын

@@GMATNinjaTutoring You are incredible.

@user-oz4uo4hh4k Жыл бұрын

I didnt understand last step of Q.4 how did you change signs?

@GRENinjaTutoring Жыл бұрын

Good question! At the second to last step, we have the expression x = (2y)/(3y -3). But the answer choices don't have that expression in that exact form. So...we can change our expression by multiplying it by (-1)/(-1). Notice that (-1)/(-1) = 1, so we won't change the expression by doing this. However, we will change the form of the expression. The top becomes - 2y. The bottom becomes -3y + 3 (OR 3 - 3y). This leads to the correct answer of (A). I hope that helps!

@user-oz4uo4hh4k Жыл бұрын

@@GRENinjaTutoring Thanks got it

@DubCmusicTV 2 жыл бұрын

For the last question, the prompt becomes: is x >=0? and Choice D is the answer?

@GMATNinjaTutoring 2 жыл бұрын

Yes, that's correct! Let us know if you have any other questions!

@Silverdrift 2 жыл бұрын

@@GMATNinjaTutoring I have the same question. If x>=0 is asked then statement 1 just says x>0 and statement 1 tells x>=0. Then typically it should be answer B. Can you please help me where my understanding is wrong?

@GMATNinjaTutoring 2 жыл бұрын

Hi Surya! I'm not 100% sure that I've understood what you're asking, but I think that you're saying that because x>0 from statement 1 is different than "is x>=0?" from the question, statement 1 is not sufficient. But if we know from statement 1 that x>0, then we also know that the answer to our question "is x>=0?" is yes. We know this because anything that is greater than zero is also going to be greater than OR equal to zero. Does that answer your question?

@Silverdrift 2 жыл бұрын

@@GMATNinjaTutoring Yup, thanks a lot for clarifying my query

@Analyst2019pro 2 ай бұрын

Question 4 is insane

@ggas33dfdf 7 ай бұрын

Q6: I don't understand the solution. x^2 + y^2 = 169 than x + y = 13; statement two says x+y = 17; so statements give me different answer so there is no solution to xy. Please explain how you can just plug in the x+y from statement one into statement two although the variables are completely different in their solution. Does not make sense to me. Based on that i could plug in just any number instead of the variables, bc why bother with the variables if i can just put in any number...

@GMATNinjaTutoring 7 ай бұрын

When you're doing algebra, you can't take the square root of individual terms on each side of an equation, you can only take the square root of the whole side of an equation. It might be easier to see why this is the case if we do the inverse process first. If we have x + y and we square it, we don't get x^2 + y^2, we get x^2 + 2xy + y^2. So, if we take the square root of x^2 + y^2, we shouldn't expect to get x + y, instead we get sqrt(x^2 + y^2). An alternative route to the solution that Bransen provided in the video could show that in statement (1), we cannot say that x + y = 13 for the reasons given in the previous paragraph. We could say sqrt(x^2 + y^2) = 13, but that doesn't help us get to a solution very easily. Instead, we could say x^2 + y^2 = (x + y)^2 - 2xy. Since we know x + y = 17 from statement 2, this means x^2 + y^2 = (x + y)^2 - 2xy = 17^2 - 2xy. So we can say 17^2 - 2xy = 169, and that will give us enough information to find xy, meaning (C) is the answer to this question. I hope that helps!

@aryank.3860 5 ай бұрын

For Q5, why does the root symbol matter?, even if square root of 100 is asked, it is supposed to be 10 (not -10).But if some questions is x squared & asked for value of x, then it could be +/ - 10. Correct me if am wrong.

@GMATNinjaTutoring 5 ай бұрын

I'm not 100% sure I understand your question, but let me take a shot at answering it. The root symbol matters for the question because it changes the answer. The answer to 505^2 - 495^2 is very different to the answer to sqrt(505^2 - 495^2). If you were asking why Bransen took the time to discuss the symbol, it's because there's a very common misconception among our students that says that sqrt(100) = +/-10 when in fact sqrt(100) = +10. Your understanding of the square root symbol is totally correct, but many of our students think of it slightly differently. Bransen was aiming to highlight and correct that misconception. I hope that helps a bit, but please let me know if I've misinterpreted your question.

@kelvincheng3103 Жыл бұрын

In Q4, square root of 505^2 - 495^2, why couldn't we have taken them as individual numbers and eliminated the square root with the power of 2 and ended up with 505-495?

@rohansrinivas9946 Жыл бұрын

505^2 - 495^2 would be (505-495)*(505+495). Similar to x^2-y^2=(x-y)*(x+y) which means you cannot cancel the root here...

@GMATNinjaTutoring Жыл бұрын

Hi Kelvin! Rohan is right above here, but the idea is that sqrt(a^2 - b^2) ≠ (a - b). And for what it’s worth, 505^2 - 495^2 ≠ 10 either. But we can use difference of squares to solve without a calculator. I hope that helps!

@karimkaan8700 2 ай бұрын

Good work, thanks

@GMATNinjaTutoring 2 ай бұрын

Thank you!

@afterburnerfox 11 ай бұрын

for Q6 can the answer be A? xy = 84.5 because x^2 + y^2 = 169; hence, x^2 + y^2 - 169 = 0; hence it looks like the identity (x-y)^2 = 0. now 2xy = 169 and xy = 84.5

@GRENinjaTutoring 11 ай бұрын

The fact that x^2 + y^2 = 169 on its own doesn't tell us much about the values of x and y. In fact, there are many different values of x and y that would fit that equation, and many of them would give different values of xy -- so we couldn't conclude from statement 1 alone that xy = 84.5. For that reason, statement 1 on its own is insufficient. I hope that helps!

@afterburnerfox 11 ай бұрын

Thank you, that makes sense

@daniellaofer1712 Ай бұрын

I got x=10 for q2 and now i'm confused and dont know where i went wrong.

@GMATNinjaTutoring Ай бұрын

Hi! If you let me know what you did in this question, I'll try to help you figure out where you went wrong. I'm struggling to do that with just your answer to go off, but I might be able to help a bit more if you showed me how you reached that answer. Thanks!

@063_arijitaroy3 Жыл бұрын

what is the ansb for question 7 ? why arent you guys telling t he ans after each question

@GRENinjaTutoring Жыл бұрын

The answer to #7 is (E) -- i.e. 121. Thanks for the question, and apologies for any confusion!

@biswadeeproy4019 8 ай бұрын

For question 5, I disagree that (500+5)^2 - (500-5)^2 isn't the efficient way to solve because straightaway we know (a+b)^2 - (a-b)^2 =4ab. Here, a=500 and b =5. Clearly, a*b= 2500. Sqr root of 2500 is 50 and sqr root of 4 is 2. Hence, 50*2= 100. It hardly takes 30-40 seconds to arrive at this answer. It may not be THE EFFICIENT way, but definitely one of the efficient ways for sure.

@GMATNinjaTutoring 8 ай бұрын

You're right, that's another great way of answering this question. Thank you for sharing!

@biswadeeproy4019 8 ай бұрын

@@GMATNinjaTutoring Pleasure is all mine!! Thank you to the GMAT Ninja team for creating these superb videos!! 🤗

@ryanhui9135 Жыл бұрын

I think the answer for Q3 is x= -10

@GMATNinjaTutoring Жыл бұрын

Yes, that's correct! With both statements together, we get that x = -10 (not 10 :) ), and the answer is C.

@Nidhisharma-qs8ll 2 жыл бұрын

For question 3 ans is -10

@GMATNinjaTutoring 2 жыл бұрын

Yes, that's correct! With both statements together, we get that x = -10 (not 10 :) ), and the answer is C.

@Khiladii786 13 күн бұрын

In Question 9, What we essentially finding is x>= 0. statement 1 shows that x>0 but we need to find whether x >= 0. This lead me to think that statement 1 is not sufficient for us to deduce it. ( Because for x=0)

@GMATNinjaTutoring 5 күн бұрын

We don't need the information from the statement to exactly match the question in order to know whether the information provided is sufficient to answer the question. For example, if we were asked whether x >= 10 and statement 1 told us that x > 20, then we know that x could be 21, 22, 25, 45, 100, 432, 20.1 or any other of an infinite number of options -- x could be anything as long as it's greater than 20. If we know this then we definitely know that x >=10. This means that the information provided in this statement is sufficient to answer the question. In the question in the video, we're asked whether x >= 0. If we know that x > 0 then we know for sure that x >= 0, so this information is sufficient to answer the question. I hope that helps!

@harishprasad9925 Жыл бұрын

For question 3, shouldn't the answer be -10. Because -12 and +2 is -10. So x=-10

@GRENinjaTutoring 11 ай бұрын

Yes, that's correct -- x should be equal to -10. Thank you for catching that! Nonetheless, the answer for this one would still be C.

@hussainhassan2018 9 ай бұрын

For Q5, why doesn’t it work to “move the number line” like in the arithmetic video? Let’s say we make 500 = 0 so 505 = 5 and 495 = -5, following the logic we would get 0 which we would then “realign” by adding 500 to the end, making our answer D which is incorrect.

@GMATNinjaTutoring 9 ай бұрын

Good question! There are some instances when shifting the number line is allowed, and some when it isn't. Generally speaking, you can make it work for addition and subtraction, but not for multiplication or division. For instance, if I wanted to find the value of 95 - 71, I might find that a bit annoying. So I can shift both values up by 5 and get 100 - 76. That's a bit easier to eyeball (i.e. it equals 24), and I get the same value as I would for 95 - 71. Alternately, if I wanted to add 95 + 71, I could add five to both, get a sum of 176, then subtract 10 and get 166, which is the correct value. However, once multiplication comes into play, you can't shift the number line. To see why this is the case, consider an example where I shift the number line up by 2. For instance, 3 x 5 yields a very different result than 5 x 7. And I can't just subtract 2 to get back to my original value. Bottom line - shifting numbers up and down the number won't change their difference, and it's fine for addition if you "realign." But it distorts expressions with multiplication or division, which is why it doesn't work here. Let us know if that helps at all!

@hussainhassan2018 4 ай бұрын

⁠@@GMATNinjaTutoringYes that helps! But then why is realigning the number line a good method to use for Question 8 of the Arithmetic video? In that video, a number is getting realigned then it’s getting multiplied and divided by different numbers.

@user-wl9gc8ns7g 10 ай бұрын

Hi , for Q9 how can we say x > -13, i understood the logic behind it but how do you show it mathematically? cause when we solve it for the negative value of 9 i.e x+4 x

@GMATNinjaTutoring 10 ай бұрын

Hi! If we start from |x + 4| < 9 and solve it algebraically, we get the first of the two solutions by examining what happens when x + 4 > 0. This means we don't have to do anything to (x + 4) to ensure it gives a positive value, so the modulus signs are redundant in this case, and |x + 4| < 9 becomes (x + 4) < 9. This simplifies to x + 4 < 9 or just x < 5. The second solution comes when we consider what happens when x + 4 < 0. Since (x + 4) is negative, we'd have to multiply (x + 4) by -1 to ensure we have a positive value that satisfies the modulus sign. This means |x + 4| < 9 becomes -(x + 4) < 9. To solve from here, we can multiply both sides by -1 but we have to remember to flip the inequality sign to give x + 4 > -9. Finally, this simplifies to x > -13. I hope that helps!

@sahithyadevaraj144 10 ай бұрын

what is the answer of question 3 , 10 or 100?

@GMATNinjaTutoring 10 ай бұрын

The answer to question 3 is (C) since we need both statements in order to find the value of x. If you were wondering what the value of x is in this question, it should be -10 (and not 10, that was an error!). I hope that helps!

@akshaygupta4529 9 ай бұрын

Q6: Can we not solve with eq 1: (a - b)^2 = a^2 + b^2 - 2ab ---> x^2 + y^2 -169 = 0 --> 2xy = -169

@GMATNinjaTutoring 9 ай бұрын

It's a great thought but we can show the problem with using that method by asking why you chose to square a - b and not a + b. We could just as easily do: (a + b)^2 = a^2 + b^2 + 2ab ---> x^2 + y^2 + 169 = 0 ---> 2xy = +169 Since we'd get two values for xy and not know which one is correct, we can't say that the information in statement (1) is sufficient to answer this question. I hope that helps!

@user-wp7zk8sk8d Жыл бұрын

Question3 Ans should have -ve sign

@shivamsinghal4848 11 ай бұрын

what is the answer of Question no. 9 ? D??

@GMATNinjaTutoring 10 ай бұрын

Hi! That's correct, the answer to Question 9 is D. Let us know if you have any other questions!

@shivamsinghal4848 10 ай бұрын

@@GMATNinjaTutoring Thanks

@shinchannohara6098 9 ай бұрын

won't the question 8 be |x+4|

@GMATNinjaTutoring 9 ай бұрын

If we start with 2|x + 4| - 3

@allwindsouza9595 Жыл бұрын

Would u say that these are 650 -700 range questions ?

@shirsendumaiti5682 Жыл бұрын

more like 500 to 650

@futbolenlacancha5907 10 ай бұрын

Q3, isn't it X= -10 ? Please, comment

@GMATNinjaTutoring 10 ай бұрын

Yes, that's correct -- x should be equal to -10. Thank you for catching that! Nonetheless, the answer for this one would still be C.

@Adhbutham 8 ай бұрын

In question 3, x = -10 is the correct result

@GMATNinjaTutoring 8 ай бұрын

Yes, that's correct -- x should be equal to -10. Thank you for catching that! Nonetheless, the answer for this one would still be C.

@corrayatom Жыл бұрын

Ques 1 : E Ques 2 : C Ques 8 : D Ques 9 : D right?

@roshdipesh2534 Жыл бұрын

yep, all are correct, for question 9 both statements are sufficient, as even for 2nd statement bot x=0 and x>0 are able to answer the main question/statement.

@whyaaron1 5 ай бұрын

How do they expect us to do all this on a whiteboard with just a mouse...in the time alotted...

@GMATNinjaTutoring 4 ай бұрын

Apologies if I'm misunderstanding your comment, but are you referring to the digital whiteboard for the online version of the GMAT? If so, you're correct that it's really hard to do much with a digital whiteboard under time pressure -- personally, I struggled enormously with that thing. The good news is that you don't need to use the digital whiteboard at all. You can just bring a physical one instead. Details here: support.mba.com/hc/en-us/articles/14025516613147-GMAT-What-Kind-of-Whiteboard-Can-I-Use-for-the-Exam If you're worried about time management in general, that's a whole other kettle of fish, but this video might help a bit: kzfaq.info/get/bejne/gKd4dq-Al-CyYIE.html Have fun studying!

@ryanbhatnagar 11 ай бұрын

q3 isn't it x=-10?

@GRENinjaTutoring 11 ай бұрын

Yes, that's correct -- thank you for catching that! Nonetheless, the answer for this one is still C. Thanks again!

@Analyst2019pro 2 ай бұрын

Beyond me in question 6 how he got 2XY

@GMATNinjaTutoring 2 ай бұрын

Using statement (2), if we start with x + y = 17 and square both sides, we get (x + y)^2 = 17^2 which gives us x^2 + 2xy + y^2 = 289. The 2xy comes from the expansion of (x + y)^2. I hope that helps!

@guille7497 6 ай бұрын

Q9 answer should be A I think. Statement 1 tells us that x is positive therefore it is not zero or negative, answer is sufficient Statement 2 tells us x can be zero or positive. In any case, not a definite answer. Not sufficient

@GMATNinjaTutoring 6 ай бұрын

You're absolutely right in what you say about statement 1, but the information contained in statement 2 is also sufficient to answer this question. This makes the answer to this question (D). From pushing the quesiton between about 1:10:07 and 1:12:20, Bransen showed that we can reduce this question to asking if x is greater than or equal to zero. Statment 2 tells us that x^3 is not negative, which means x is either positive or x = 0. In both of these cases, we know x(sqrt(x^2) - x) = 0, so statment 2 is sufficient to answer the question. I hope that helps!

@pranavmalik6242 2 жыл бұрын

About the last question : Doesn't the question get simplified to x>0 and not x>=0 ? Because if you input x=0 in the question, it becomes 0(root(0) - 0) which becomes 0x0 which is undefined? Even root(0) is undefined. So, how can 0 be a solution for x? I'm very confused as to when the gmat considers 0x0 =0, and not 0x0 = undefined. Mathematically, 0x0 should be undefined, right?

@GMATNinjaTutoring 2 жыл бұрын

Hm, I wonder if you're thinking about dividing by 0? That's always undefined. But when you multiply any real number by 0, you just get 0. So 0x0 = 0, and root(0) = 0. If you've run into an official GMAT question that implies that 0x0 or root(0) is undefined, let us know. But we've never known that to be the case, either in GMAT-world or elsewhere. :) I hope that helps a bit!