GMAT Ninja Quant Ep 2: Algebra & Efficiency

[@tonyassamoi9688]

Q3, isn't it X= -10 ?

[@startcomplaining9781]

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

[@miho9453]

You’re right

[@nagatopain8453]

You probably do not need the confirmation but your ans is the same as mine

[@gyanaranjandash5880]

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

[@ambecksfulful]

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

[@GMATNinjaTutoring]

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... ;)

[@devadarshini00]

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

[@doniaridane175]

Q9: I think that the first data given is sufficient because if IxI*x is strictly positive and we know that IxI is strictly positive then x is also strictly positive which means that IxI= x so that IxI -x =0

[@pinkybae_tech]

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

[@GMATNinjaTutoring]

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

[@adki7559]

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

[@ukamakacyriacus4833]

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?

[@matheustran8009]

it is E because there are an infinite number number of solutions for x when you consider both statements, so both statements together are not enough

[@JordanDavidson-d1p]

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.

[@matheustran8009]

I feel like there was a much easier way to do question 4: 2/x +3/y = 3 => 2/x = 3 - 3/y => 2/x = 3y/y - 3/y => 2/x = (3y-3)/y => x/2 = y/(3y-3) => x = 2y/(3y-3) => x = -2y/-(3y-3) => x = -2y /(3-3y) I added more intermediate steps so that it is completely clear what I did, but you can skip a lot of these steps in your head I prefer this approach more because you do not create more x variables, and it is much simpler

[@depiction3435]

Q 4 you can flip fractions you just have to change the signs and you still get the right ans.

[@yuriyk8002]

Q9: you’ve mentioned that if the sign is √x then we are interested only in positive value of x, right? So √x^2 will be just x, thus x(x-x)=0? -> x(0) will be 0. So we can answer the question even without statements 1 and 2, no? Apropos is this an official GMAT question, or you came up with it?

[@GMATNinjaTutoring]

If we are finding √x, then x can only be a positive number since (in the GMAT), you can't take the root of a negative number. Also, when presented as √x, the GMAT is only asking for the positive root. So, for example, √4 = 2. If we're looking for √(x^2), however, then x might be negative but √(x^2) returns a positive value. For example, if x = -2, then x^2 = 4 and √(x^2) = 2 which is not the same as x. The way we get around this is to say that √(x^2) = |x|. From this, we can say x(√(x^2) - x) = x(|x| - x). If x is positive then (|x| - x) = 0, but if x is negative then (|x| - x) = 2|x|. I hope that helps!

[@biswadeeproy4019]

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]

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

[@biswadeeproy4019]

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

[@pierof6837]

Hi, first of all thank you. I ve increased my score after studying all these videos. Really grateful for this. I've a question.... For those questions with increases % through parameters like: 1) " the price per share of Stock X increased by k percent " or 2) r percent of the store's revenue was from newspaper A sales In the equation where i will call the price per share or the store's revenue as X, I ve to write: 1) (p/100) * x or p*x ? 2) (r/100)*x or r*x ? I do not still understand if I ve to put 1/100 or not... Thank you!

[@GMATNinjaTutoring]

That's great that you've increased your score, and I'm so pleased our videos could help a little! Thank you for the kind words. Whenever the GMAT says something like "p percent", that means you should have p/100 in your working. 'Percent' means one part of every hundred so if we have 7 percent of some quantity x, we have 7 parts out of every one hundred parts of that quantity. To find this 7 percent, we could divide x by 100 to find the value of one part before multiplying it by 7 to get our answer. Using algebra, we'd write (7/100)*x I hope that helps!

[@pierof6837]

@@GMATNinjaTutoring Ok thank u! A video on these kind of problems would be useful :) . I ve jumped into a lot of different problems on this that follow different approach

[@corrayatom]

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

[@roshdipesh2534]

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.

[@kogurasama]

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

[@ryanhui9135]

I think the answer for Q3 is x= -10

[@GMATNinjaTutoring]

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

[@ajitrajendran63]

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]

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]

@@GMATNinjaTutoring thanks so much for the reply and clarification

[@ArshdeepSingh-ek6su]

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

[@GMATNinjaTutoring]

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

[@RoseAvalonA]

would be more helpful if you had clearly marked the number on the questions and gave the answers

[@sims_ran]

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

[@Khiladii786]

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]

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!

[@Nidhisharma-qs8ll]

For question 3 ans is -10

[@GMATNinjaTutoring]

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

[@somasundaram5744]

Q4 is still easy if you transfer y term to RHS

[@aryank.3860]

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]

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.

[@WillC]

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]

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]

@@GMATNinjaTutoring You are incredible.

[@doniaridane175]

Q1: I thought it's a one solution system since it can give us x=4 and y=0, am I wrong? I couldn't understand why you said it's an infinite number of solutions

[@GMATNinjaTutoring]

You're not wrong to say that x = 4 and y = 0 is a solution to this system. However, we could also say that x = 1 and y = -2 is a solution to this system. Or we could say that x = 7 and y = 2 is another solution to this system. Since the two equations are really just the same equation written in different ways, we have one equation with two unknowns. When we have one equation with two unknowns, an infinite number of combinations of x and y values will satisfy the system. In this case, that means we cannot find one single value for x, so the answer to this question is (E). I hope that helps!

[@doniaridane175]

@@GMATNinjaTutoring I understand, thank you!!

[@balpreetsingh6834]

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]

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]

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

[@supratikparajuli9660]

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]

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!

[@afterburnerfox]

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]

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]

Thank you, that makes sense

[@harishprasad9925]

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

[@GRENinjaTutoring]

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.

[@Analyst2019pro]

Question 4 is insane

[@domenikgerhards7240]

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?

[@ggas33dfdf]

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]

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!

[@HaraChiaki]

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

[@GMATNinjaTutoring]

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!

[@pbs201]

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]

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]

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

[@Amine-fo2qw]

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

[@akshaygupta4529]

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]

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!

[@HHNYC]

Thank you so much for these videos

[@kenny5930]

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]

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]

@@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!!!

[@visheshgupta5948]

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]

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!

[@DubCmusicTV]

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

[@GMATNinjaTutoring]

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

[@Silverdrift]

@@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]

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]

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

[@anshlaroia9443]

Really helpful as always! :D

[@lucianopavarotti-yq3pf]

Damn look at question 3 , I would have calculated the p right there

[@SPARSHGANJOO]

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]

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!

[@AnthonySamson-wl3gw]

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

[@GMATNinjaTutoring]

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!

[@hussainhassan2018]

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]

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]

⁠@@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.

[@guneetpandher3505]

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]

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!

[@nikhitaragam3692]

For question 1, I used substitution and got x = 4. Why would this be wrong?

[@matheustran8009]

because there are an infinite amount of solutions. for every x value, there is a y value, so you can not find the value of x using those two statements alone

[@patbateman979]

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

[@GMATNinjaTutoring]

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

[@divyanshharnal5169]

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

[@VedikaHansaria]

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]

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!

[@karimkaan8700]

Good work, thanks

[@GMATNinjaTutoring]

Thank you!

[@jessicaechegile2476]

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]

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]

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

[@amandeepoberoi6166]

41:40 56:40 1:03:00 1:15:00

[@063_arijitaroy3]

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

[@GRENinjaTutoring]

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

[@kelvincheng3103]

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]

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]

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!

[@NeuralNewsletters]

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.

[@daniellaofer1712]

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

[@GMATNinjaTutoring]

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!

[@DhvanilChavda]

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

[@GRENinjaTutoring]

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!

[@DhvanilChavda]

@@GRENinjaTutoring Thanks got it

[@guille7497]

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]

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!

[@Adhbutham]

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

[@GMATNinjaTutoring]

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.

[@shariqueanwar-n6g]

Question3 Ans should have -ve sign

[@sahithyadevaraj144]

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

[@GMATNinjaTutoring]

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!

[@TanujKhosla]

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]

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!

[@shinchannohara6098]

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

[@GMATNinjaTutoring]

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

[@shivamsinghal4848]

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

[@GMATNinjaTutoring]

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

[@shivamsinghal4848]

@@GMATNinjaTutoring Thanks

[@futbolenlacancha5907]

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

[@GMATNinjaTutoring]

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.

[@whyaaron1]

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

[@GMATNinjaTutoring]

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: kzbin.info/www/bejne/gHKrdH-FZ9-BZq8 Have fun studying!

[@allwindsouza9595]

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

[@shirsendumaiti5682]

more like 500 to 650

[@Analyst2019pro]

Beyond me in question 6 how he got 2XY

[@GMATNinjaTutoring]

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!

[@pranavmalik6242]

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]

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!

[@ryanbhatnagar]

q3 isn't it x=-10?

[@GRENinjaTutoring]

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

[@ritamroy2202]

What's the answer for q1? Wtf please be clear

[@GMATNinjaTutoring]

The answer to question 1 is (E). I hope that helps!

[@pallavid4855]

The value of x in the simultaneous equations part III is -10 and not 10 as given in the video. Please cross-check. @gmatninja

[@GMATNinjaTutoring]

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).