GMAT Ninja Quant Ep 4: Beyond Algebra in GMAT DS: Inequalities, Absolute Values, & More
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Күн бұрынDo algebra-heavy Data Sufficiency questions mess with your head on the GMAT and Executive Assessment? Do you struggle with inequalities and absolute values? Or do you spend an eternity on algebra DS questions because you just can't see the "quick way" to a solution? Are you losing tons of time on DS by picking numbers?
In this video, Bransen -- a GMAT Ninja tutor -- will show you how to think about EA and GMAT algebra DS questions efficiently and effectively. He'll help you understand how to blend logic, algebra, and flexibility to maximize your performance on these questions.
This is video #4 in our series of full-length GMAT quant lessons. For updates on upcoming videos, please subscribe!
This video will cover:
➡️ "Hard" algebra DS questions
➡️ When to pick numbers
➡️ Inequalities
➡️ Absolute values
This video is for you if:
➡️ You test cases or guess numbers
➡️ You “know” everything but still struggle
➡️ You don’t know the most efficient tool to use (logic, algebra, or number-picking)
➡️ You don’t have a consistent approach to the “hard” ones
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
03:11 Question 1 - Dividing by a variable
09:21 Question 2 - Inequalities
15:46 Question 3 - Absolute Values
23:15 Question 4 - Push the Question
30:10 Question 5 - Is it an integer?
38:10 Question 6 - Inequalities Part II
48:24 Question 7 - Push the Question Part II
58:02 Question 8 - Absolute Values Part II
1:05:18 Question 9 - Where do I start?
@xAccident Жыл бұрын
Hi Bransen! I just wanted to leave a comment to thank you and the rest of the GMAT Ninja team for providing such a valuable course to solving GMAT questions for free. I really appreciate your efforts and I'm finding your methods helpful to solve quantitative questions on the GMAT, which I'm struggling with. Kudos to you and the rest of GMAT Ninja's tutors for making the videos entertaining as well!
@GMATNinjaTutoring Жыл бұрын
Thanks Gregory for the kind words! Super glad that you find these videos helpful, and best of luck with your GMAT journey!
@pratikraj5364 9 ай бұрын
Hi team, I think there is a mistake in Q2. The value of a-b < 7 should be a-b < 8 instead. Otherwise the solutions seems incorrect
@GMATNinjaTutoring 9 ай бұрын
Thank you for spotting this! We're aware of the error, and the best we could do was put a tiny pop-up banner on the right side of the screen, acknowledging the screwup. The good news is that it doesn't affect the answer, since it's a DS question. But it's embarrassing all the same. Thank you for watching carefully enough to notice that type of detail! We're trying to tell ourselves that it's a good thing whenever somebody sees it. :)
@TheSam984 Жыл бұрын
In the penultimate question i think an alternate way would be to push the option and arrive at the equation as mentioned in the question stem. -2
@houdasrhir3216 Жыл бұрын
Question 6: y can be a fraction or a negative number but it can also be zero. Zero raised to any power greater than 1 as x>1 will equal 0 and in that case also y will be less than x. Thank you for this video, interesting questions!
@daniellee2023 4 ай бұрын
Hello- thank you for your help- quick question- in the algebra & efficiency session, you talk about setting new 0s or setting bounds to help reason through logic. Would you be able to apply that sort of reasoning here to Q2 in any way? Or maybe not because you are dealing with both a and b as variables and unknown bounds for them?
@corrayatom Жыл бұрын
Great video, thanks
@punitmishra6560 2 жыл бұрын
Nice video! Quality questions!
@GMATNinjaTutoring 2 жыл бұрын
Thank you so much, Punit! Glad to hear that you enjoyed it. Have fun studying!
@rahulbasu4539 11 ай бұрын
Thanks a lot for the video. These videos have been extremely helpful, as always
@GRENinjaTutoring 11 ай бұрын
Thank you!! Glad you're enjoying the videos.
@ashishkarki1005 Жыл бұрын
About that last question, I couldn't get why statement 2 was not sufficient..can anyone explain
@HalfGermany100 4 ай бұрын
That is sooooo valuable, thank you!
@GMATNinjaTutoring 4 ай бұрын
Thank you so much for watching and taking the time to write this!
@akshitsingh3752 Жыл бұрын
Hi Bransen, first of all thank you so much these GMAT quant and verbal series. I've a doubt regarding last question. For second statement after solving the inequality I get x>-1. So what I did is I divide it into two parts. If x>0 then we can compare the denominators to check which fraction is larger. If -1
@GMATNinjaTutoring Жыл бұрын
Hi Akshit, Unfortunately, when -1 < x < 0, the fraction with (x + 1) in the denominator is less than the fraction with (x - 1) in the denominator. We can show this by saying when -1 < x < 0, x is negative, x-1 is negative, and x+1 is positive. This means, x/(x+1) is a negative divided by a positive, which will leave us with a negative number, and x/(x-1) is a negative divided by a negative, which will leave us with a positive number. This means x/(x-1) will be greater than x/(x+1). If 0 < x < 1, we could apply a similar argument to the one above to show x/(x+1) is greater than x/(x-1). Since we get two different results, one for -1 < x < 0 and one for 0 < x < 1, statement (2) is insufficient to answer this question. I hope that helps!
@TheChirag11111 Жыл бұрын
I didn't understand Question 6 properly, why was 'B' dismissed? Can you help me with this?
@vivianwang3393 26 күн бұрын
hi Ninja team, for the last question we have, can we use the plugging in method to solve
@yazz8079 Жыл бұрын
Hey Bransen! Love the videos, almost finished the whole series. However, I had a question: In Q 8, how come we are able to say that statement (2) is sufficient? Indeed, even if "a" will always be equal to |b-6| + |b+2|, don't we instead need an exact value for "a" and not just a range to be able to answer the question? Thank you!
@GMATNinjaTutoring Жыл бұрын
Hi Yazz, The visual method Bransen used in the video is one way of answering this question, but we could also use an algebraic method that might clear up your doubt. If -2 < b < 6, then we know that b - 6 < 0. From this, we can rephrase |b - 6| as -(b - 6). Similarly, we know that b + 2 > 0, so we can rephrase |b + 2| as simply (b + 2). This means a = |b - 6| + |b + 2| = -(b - 6) + (b + 2) = -b + 6 + b + 2 = 8 This value is the same as the total "distance" Bransen mentioned during his explanation. Since b is in the range -2 < b < 6, the values of b cancel out in a = |b - 6| + |b + 2|. This is how we can go from a range to a definite value. I hope that helps!
@dushyantkanal8675 Жыл бұрын
Hi Bransen For question number 3 I got the correct answer as 'B', but I just wanted to check if what I did is correct Ques : Is |x+2|
@praxis4375 Жыл бұрын
when you're dealing with absolute values, you *DO NOT* square both sides because that isn't how absolute values work. you want to utilize addition and subtraction with these types of problems, not multiplication or squaring. it's good that you managed to get the correct answer using your unique methods, but you should refraid from squaring both sides in the future when you deal with absolute values.
@hundredmillclub3729 6 ай бұрын
Hi! In Q7 if I rewrite the question as “is (x^2)*(y^2) > (x^2 - y^2)*(y^2 - x^2)?” then do some difference between squares, I can get to: (x^2)*(y^2) > (-1)*((x+y)^2)*((y-x)^2). Since all squares are going to be positive, should this not automatically be sufficient?
@GMATNinjaTutoring 6 ай бұрын
The issue with doing what you suggest comes when you multiply both sides of the inequality by x^2 - y^2. At this point in the problem, there is no way to know for certain that x^2 - y^2 > 0, so you may have multiplied the inequality by a negative and need to flip the inequality symbol. Since we don't know whether we get (x^2)(y^2) > (y^2 - x^2)(x^2 - y^2) or (x^2)(y^2) < (y^2 - x^2)(x^2 - y^2), we can't say that we'll arrive at something that's automatically sufficient if we continue working from here. I hope that helps!
@vedantjain2196 2 жыл бұрын
Great video guys! Have a doubt about question 8. -2
@abhishek_pathania 11 ай бұрын
-2
@abdur5908 Жыл бұрын
Hey Branson , I didn't get why we cant cross multiply in the last question ? if you could please clarify
@GMATNinjaTutoring Жыл бұрын
Hi Abdur! We can't cross multiply because we don't know whether the denominators are positive or negative. If they're negative, we'd have to flip the inequality sign. But we don't know, so we can't cross multiply. I hope that helps!
@CarmenHorse Жыл бұрын
i am actually struggling a lot in this episode even with the explanation. is this a sign that i am having trouble applying the math foundational concepts when they are all together in one problem? my quant score has been mid 30s. anyone has suggestions on how i can break through this episode? cant pin point what OG questions i should focus on since this is so broad
@srilanka739 11 ай бұрын
TTP course
@zeynep2287 4 ай бұрын
Hi Bransen! Will data sufficiency problems like these examples be asked in the GMAT Focus Edition?
@GMATNinjaTutoring 4 ай бұрын
The GMAT Focus Edition has moved towards more word-based problems in Data Sufficiency problems. The underlying math covered in this video can still be tested, but it's unlikely you'll see such difficult algebra in the Data Insights section of the new GMAT. I hope that helps!
@dushyantkanal8675 Жыл бұрын
Hi Bransen One more question For the last question, why didnt we cancel x from the numerator? Was it just a choice or we could not do that because we didn't know the sign of 'x'?
@GMATNinjaTutoring Жыл бұрын
Hi Dushyant! The reason that I’d shy away from that is because when we cancel x in the numerator, we’re really dividing both sides by x. Like you said, we don’t know the sign of x, so we don’t really know whether to flip the inequality.
@gauravbadve9692 Жыл бұрын
Is there any video which has just > 700 level questions?
@paulcieri78 Жыл бұрын
Hi Bransen, Not that it would change the answer but in Question number 6 Statement 2 when x>0 why does Y have to be a fraction? If Y=0 then y^x= 0 which is less than 1, or if y= a negative number and x is odd then y^x would be a negative number and thus y^x
@GMATNinjaTutoring Жыл бұрын
Hi Paul! You're actually correct that with statement 2, if x>0, then y must be a fraction or less. Hope that helps!
@prachitabakliwal5207 2 жыл бұрын
@GMAT Ninja Q 2 : a-b |b|, a could be 5 and b -7. If we add these together a+b==>>-2, negative, so I guess answer should be A instead of D.
@DubCmusicTV 2 жыл бұрын
answer is C a-b>8
@srilanka739 Жыл бұрын
29:19 kzfaq.info/get/bejne/pppkbJBlua6qpo0.html 'a is further to the right of zero than b is to the left of zero' Does this mean for e.g. if a>-b and -b= -2 (for example) then a has to be a>2? therefore (a+b)>0 ? is that what a> |b| means? thank you Prachita - my understanding is absolute value of b = -7 = 7 and absolute valuye of A = 5 is 5 therefore a>-b has been violated remember absolute value means distance from zero if b=-7 then a has to be greater than positive 7 so if b = -7 then a has to be a>7 ---- this satisfies a> | b |
@terapy6198 9 ай бұрын
Hi Bransen, in Q5 for option 2. 3m = n^3-n when you get to (n-1)n(n+1) and if n was 1 then it is not divisible by 3. So would that not mean option 2. is not sufficient and so the answer would be A
@GMATNinjaTutoring 9 ай бұрын
If we substitute n= 1 into (n - 1), we get 0. This means (n - 1)n(n + 1) would be zero as well, since anything multiplied by zero will equal zero. We can also say zero is a multiple of three as 0 = 3*0, so zero is divisible by 3. This means that if we say n = 1 as we look at statement (2) in this question, we get that m = 0. This is an integer and, along with the rest of the explanation Bransen gives in the video, shows why statement (2) is sufficient to answer this question. I hope that helps!
@suyashgoenka6287 11 ай бұрын
Hi Bransen, the logic method is definitely faster and easier, but one quick doubt: For the last question Q9, if we solve algebraically, we get, x(x-1) > x(x+1) => x
@suyashgoenka6287 11 ай бұрын
Ok never mind, I think I got it. We don't know the sign of x so we don't know if we have to flip the inequality as you said.
@vaibhavand 8 күн бұрын
Hi Bransen Really great video, but I have a doubt for the last question. Statement 2 says (x/x+1)>1. Now this statement will be true only for positive values of x, ie, x greater than or equal to 1. Is it because of the "equal to 1" case in this equality that statement 2 is invalid ? Because then x>1 is basically statement 1 again, which is valid and the answer would then be Option D. Thanks, Vaibhav
@GMATNinjaTutoring 6 күн бұрын
Hi Vaibhav, Thank you for the kind words! I'm sure this was just a typo, but statement 2 says (x/x+1) -1. We can then say that if x = 5, x/(x + 1) = 5/6 and x/(x -1) = 5/4, so x/(x + 1) < x/(x -1). However, if x = 0.5 then x/(x + 1) = 1/3 and x/(x -1) = -1, so x/(x + 1) > x/(x -1). This means that statement 2 is insufficient to answer this question. I hope that helps!
@TheChirag11111 Жыл бұрын
Also - in Question 8, if we consider statement 2 where b lies between -2 and 6 -> The value of a could vary with respect to what the value of b is right? But we won't have a conclusive answer right? Then how are we saying statement B is sufficient?
@itsak117 Жыл бұрын
put any value between -2 and 6 in the equation, you will get one unique value that is 8
@caramarie2313 7 ай бұрын
Hi thanks for the video. For Q6, what do you mean by saying if x>0 then y must be a fraction? Is this the same as saying y must be less than 1? And for the case where x < 0, why must y be an integer? Thanks
@GMATNinjaTutoring 7 ай бұрын
I think you're referring to statement 2 in this question, but please tell me if I've got that wrong. Any number greater than one raised to a positive power will remain greater than one. This means that if we want to satisfy statement (2) and we want x and y to both be positive, then 0 < y < 1. In the case where x < 0, y doesn't have to be an integer. I think Bransen meant that y > 1 by that statement as y = 7/2 and x < 0 satisfies statement (2), for example. I hope that helps a bit, but please let me know if you'd like any more explanation!
@caramarie2313 7 ай бұрын
@@GMATNinjaTutoring thanks so much, I get it now! I was forgetting to consider the constraints of the question ie for statement 2, if x is positive and y > x then y must also be positive.
@Paddle_Shifter 7 ай бұрын
Are these types of Data Sufficiency asked in Data Insights of GMAT Focus Edition?
@GMATNinjaTutoring 7 ай бұрын
That's a really good question and, unfortunately, a really difficult question to answer. We don't have a huge amount of information at the moment, so everything I'm about to write here is coming from what we can see in the 2023-2024 Official Guides and from the practice exams we've completed so far. I might have to change my answer in a few months once things become more clear, but here's what we think today (the middle of December 2023): The GMAT could ask you questions on the same CONTENT as the content covered in these questions in the Data Insights section of the GMAT Focus Edition, but it's very unlikely they'll ask you questions in the same STYLE as the questions in this video. It looks like the GMAT is moving more towards a word-problem style of questioning in Data Sufficiency problems. It's difficult to write a word-problem style question that involves algebra-heavy inequalties or absolute values, but it's possible they could find a way. I'd use this video to make sure you understand the mathematical concepts behind each question. If you can do that, you'll hopefully be able to apply those concepts to other questions when they appear. I hope that helps a bit, but please feel free to ask if you have any other questions!
@linus284 Жыл бұрын
Great video and great effort of you guys; I really appreciate it! But I still have a question regarding the last question #9. Why is the second statement insufficient? As I understand it, it has the same message as statement one, that x>1 which would make it sufficient and therefore make D the right answer. Nevertheless, great series.
@GMATNinjaTutoring Жыл бұрын
Hi Linus! With statement two, it doesn't have to be the case that x > 1. For example, it's possible that x = 0 in statement 2, or x could be any sort of fraction. For that reason, we can eliminate (D). I hope that helps!
@seanhudson5889 Жыл бұрын
In the last problem why didn't we push the question more by bringing the -x/1-x to the left hand side to get x/x+1 + x/1-x > 0 and then simplifying from there?
@GMATNinjaTutoring Жыл бұрын
Hi Sean! That's definitely an approach you could take, but I'm not sure that it's all that helpful beyond that first step. Things get fairly complicated when you try to get a common denominator, and I'm not sure it gets you all that far. Or at least, I'm not sure whether it's worth the time that you spend getting there for what you get out of it.
@adyasamishra3392 Жыл бұрын
Hi Team In Qns 4, I felt that the 1st option was redundant since in the qns we saw it was given that ax>-bx which means if we simplify a+b>0, hence I eliminated option A because the data was redundant I think I read it in some qns in Gmat club and that kind of got me confused. So my understanding after the solution is that even if the data is redundant but if it helps solve the qns we can consider it? Pls, help.
@GMATNinjaTutoring Жыл бұрын
Hi! In the question stem, we're told that ax > -bx. If we take all the terms onto one side, we get ax + bx > 0. We can then factorise x as a common factor to get x(a + b) > 0. This tells us that either x > 0 and a + b > 0 *OR* x < 0 and a + b < 0. Since we can't divide ax > -bx by x, as we do not know whether x is positive or negative at this point, we *cannot* say that the question stem simplifies to a + b > 0. This means that the information in statement (1) is not redundant. I hope that helps!
@GRENinjaTutoring Жыл бұрын
Great question! If a statement is redundant (i.e. it doesn't add any new information that allows you to solve the question), then we'd have to say that statement is NOT sufficient. But is statement 1 really redundant? If we simplify the inequality in the question, we can arrive at the inequality x(a +b) > 0. However, we can NOT divide by x at that point. Why not? Because we don't know if x is positive or negative. If x were positive, the expression would become a + b > 0. However, if x were negative, the expression would become a + b < 0. Why? Because if you multiply or divide both sides of an inequality by a negative, you have to flip the direction of the inequality. So the first statement is not NECESSARILY equivalent to a + b > 0. That would only be the case if x were greater than zero. Statement 1 confirms that a + b is actually greater than zero. This tells us that x MUST be positive. That's sufficient to conclude that x > 0, so statement 1 on its own is sufficient. I hope that helps!
@adyasamishra3392 Жыл бұрын
@@GRENinjaTutoring Thanks for the detailed response.
@jonaskoch5181 4 күн бұрын
@@GMATNinjaTutoring Hi. Why can we not divide by x? It implicitly states that x cannot equal 0. Reasoning: we have that x(a+b) > 0. If x were 0, then x(a+b) would be 0, but it's given that the term is >0 ----> Ergo, x cannot be zero. Where am I going wrong? Thanks!
@artisticsaurabh 5 ай бұрын
For the a-b
@artisticsaurabh 5 ай бұрын
Please let me know what's wrong in this approach
@GMATNinjaTutoring 5 ай бұрын
Hi @@artisticsaurabh, Statement (1) says b < -13. From statement (2), we know a > -5. That means the smallest value of a - b will be (-5) - (-13) = -5 + 13 = 8. Since this is greater than 7, we know every value of a - b will be greater than 7. This means the answer to this question is (C). I hope that helps!
@artisticsaurabh 5 ай бұрын
@@GMATNinjaTutoring thanks a ton
@usubakunov 6 ай бұрын
Hi! In Q5 when considering the second condition alone, what if b
@GMATNinjaTutoring 6 ай бұрын
Hi! From statement (2), we know a > |b|. From this, we know a must be positive. Even if b is zero, a must be greater than b, so a must be greater than zero. This means we cannot have the situation b < a < 0 because we can't have a < 0. We now know a must be positive and we know a > |b|, but there are still two cases to consider. In the first case, b > 0. This is the easier case because now we know a + b > 0. In the second case, b < 0. We can still show a + b is greater than zero because the magnitude of a is greater than the magnitude of b (we know this from a > |b|). Since we know a + b is greater than zero in both cases, we know x > 0. This means statement (2) is sufficient to answer this question. I hope that helps!
@varun110291 2 жыл бұрын
Hey -13 + 5 will be -8 at 14:22
@GMATNinjaTutoring 2 жыл бұрын
Thank you, Varun! We're aware of the error, and the best we could do was put a tiny pop-up banner on the right side of the screen, acknowledging the screwup. The good news is that it doesn't affect the answer, since it's a DS question. But it's embarrassing all the same. Thank you for watching carefully enough to notice that type of detail! We're trying to tell ourselves that it's a good thing whenever somebody sees it. :)
@varun110291 2 жыл бұрын
@@GMATNinjaTutoring Thank you GmatNinja. I really love all your videos and explanations. Thank you so much for this reply.
@aarshdubey7898 2 жыл бұрын
In ques number 6 - from statement number 2 we can conclude that y is less than 1 in a much simpler manner - y^x < 1 = y^x < 1^x thus y
@GMATNinjaTutoring 2 жыл бұрын
Thank you for the question, Aarsh! From statement 2, we don't actually know that y is less than 1. The problem with your logic is that you can't necessarily take the "xth" root of both sides of an inequality and assume the sign will stay the same. For example, even though (-2)^2 > 1^2, we can't take the square root of both sides and say that -2 > 1. Likewise, if we say that y^x < 1^x, it's possible that x = -1 and y = 2. In that instance, 2^(-1) < 1^(-1) or 1/2 < 1, but y is greater than 1. I hope that helps a bit!
@aarshdubey7898 2 жыл бұрын
@@GMATNinjaTutoring right! That makes sense, thank you gmat ninja team 👍
@corrayatom Жыл бұрын
in Ques : 8 I got that (2) provides us info with values of b. And the ans is B. But, why didn’t work out both statements together. Is it that, a is not possible to be greater than 7 while -2
@GMATNinjaTutoring Жыл бұрын
Hi Tom, If statement (1) does not provide sufficient information to answer the question and statement (2) does, then the answer is (B) and we've finished the question. There is no need to check whether the information in both statements combined is sufficient to answer the question. We know the information in statement (2) alone is sufficient, so adding the information from statement (1) won't make it any *more* sufficient ;-) I hope that helps!
@saeedal-mitwalli2883 6 ай бұрын
Hi everyone, in question 7, in statement one: lx-yl>1 , shouldnt that also mean that x^2 -y2 will also be greater than 1 which shows that the first part of the equation (x^2/x^2-y^2) is positive meaning the statement is true?
@GMATNinjaTutoring 6 ай бұрын
Consider the case where x = 10 and y = 1. In this case |x - y| = |10 - 1| = |9| = 9 which is greater than 1. Also, x^2 - y^2 = 10^2 - 1^2 = 100 - 1 = 99 which is also greater than 1. However, now consider the case where x = 1 and y = 10. In this case |x - y| = |1 - 10| = |-9| = 9 which is greater than 1. However, this time x^2 - y^2 = 1^2 - 10^2 = 1 - 100 = -99 which is NOT greater than 1. This means that just because we know |x - y| > 1, it doesn't mean we can say (x^2/x^2-y^2) is positive. I hope that helps!
@saeedal-mitwalli2883 6 ай бұрын
Thanks for the comprehensive explanation, much appreciated.
@benjamintan5291 6 ай бұрын
Hi, where do I find the MCQ options for the questions?
@GMATNinjaTutoring 6 ай бұрын
The questions in this video are all Data Sufficiency questions, so they don't come with answer choices. They've all got the same process for finding the correct answer, and you can find an explanation of that porcess in Video 0 of this series (link below). I hope that helps! kzfaq.info/get/bejne/hLBmn9dku7Oyk4k.html
@zeynep2287 4 ай бұрын
Hi, I did not get the last question actually. Statement 2 tells us that x/x+1 is not bigger than -x/1-x. So I think the answer should be D. Could you please explain why statement 2 is not sufficient? Thanks a lot !
@GMATNinjaTutoring 4 ай бұрын
This one's complicated! I'll do my best to make this make sense, but it's difficult to do this explanation via text. If you're not sure about anything I write here, please let me know and I'll try another explanation. First, let's take a look at the inequality in statement (2): x/(x+1) < 1 to try to figure out what values of x satisfy this inequality. First, consider x > 0. When x is positive, both x and (x + 1) are positive, and (x + 1) is greater than x. This means x/(x + 1) < 1, so x > 0 satisfies the inequality. Next, we'll look at -1 < x < 0. In this region, x is negative and (x + 1) is positive, so x/(x + 1) is negative which means it's definitely less than 1, so -1 < x < 0 also satisfies this inequality. Finally, consider x < -1. In this region, both x and (x + 1) are negative, so dividing x by (x + 1) will give us a positive number. The absolute value of x will be greater than the absolute value of (x +1), so when we do the division x/(x + 1), we'll get a number greater than 1, so x < -1 does not satisfy this inequality. This means statement (2) can be summarised as -1 < x. From the explanation Bransen gave when he looked at statement (1), we know that if x > 1 then x/(x + 1) > x/(x - 1). However, consider what happens when x = 0: for x/(x + 1) = 0/(0 + 1) = 0/1 = 0 and for x/(x - 1) = 0/(0 - 1) = 0/-1 = 0. Since for x > 1, we have x/(x + 1) > x/(x - 1) and for x = 0 we have x/(x + 1) = x/(x - 1), the information in statement (2) is insufficient to answer this question, so the answer is (A). I hope that helps, but let me know if you have any questions after reading through all this!
@srilanka739 Жыл бұрын
if you did the last question algebraically, how would it work?
@srilanka739 Жыл бұрын
does it become is x>0 ? if you do it with algebra?
@debodootysarkar2 7 ай бұрын
In the last question shouldnt there be a minus sign before x divided by x minus 1.?.
@GMATNinjaTutoring 7 ай бұрын
The right-hand side of the inequality in the question was -x / (1 - x). If you multiply the top and bottom of this fraction by minus one, you'll get x / (x - 1). This is what Bransen did as he was writing the first line of his solution. I hope that helps!
@banafshehz6390 10 ай бұрын
Hi, for Q2 couldn't we solve it much easier? we know that b-5 when we have a-b means their distance as you said previously, so their distance is gonna be more than 7 (if we imagine them on the axis) so the answer is" No" and C gonna be the answer 🙂
@GMATNinjaTutoring 10 ай бұрын
That's absolutely correction -- a - b in this case will give the distance between the two points on a number line. If you can conceptualize the question that way, it's a great way to do it. As you're pointing out, GMAT questions often have more than one path to the answer -- sometimes algebraic, sometimes conceptual/spatial. If you're able to consider different paths and pick out the best one, you're in great shape. Thanks for the insightful comment!
@devamshidinesh4132 3 ай бұрын
hi your method sounds simpler , could you please tell me how you figured out the distance is more than 7 ? this is my first time hearing distance method
@jennert_ 7 ай бұрын
Hi! Q3: is B sufficient, because 14 < x < -8 is already out of the range of the question? So that you can conclude that the answer of (2) to the question is not true?
@GMATNinjaTutoring 7 ай бұрын
From the work Bransen did at the start of the solution, we can rephrase the question to be: is - 8 < x < 4? From the information in statement (2), we can say x < -8 or 14 < x. This means we can guarantee that x is not greater than -8 and less than 4, so the information is sufficient to answer the question which means (B) is the answer. I hope that helps!
@jennert_ 7 ай бұрын
Thank you!@@GMATNinjaTutoring
@SalutCCharlie Жыл бұрын
Doesn’t multiplying by -1 change the inequality sense in question 9?
@GMATNinjaTutoring Жыл бұрын
Hi Salut! Multiplying by -1 on both sides of an inequality does change the sign. But simply moving the negative sign from the top to the bottom of a fraction on one side of the inequality doesn't change the sign.
@randyorton9863 9 ай бұрын
Hey guys. Q2 at approximately 13:41, is it not b-a
@GMATNinjaTutoring 9 ай бұрын
Yes that's absolutely correct -- thank you for catching that. Our apologies for any confusion!
@aveeshsingroha2512 10 ай бұрын
Dear all, I am a bit confused about question 8. I used the algebraic method to solve, and I get a>=8 in every possible case. So that should make the correct answer to be D. a= 2b-4 for b>=6 a =8 for -2
@GMATNinjaTutoring 10 ай бұрын
There's absolutely nothing wrong with your algebra! You've manipulated the absolute value signs perfectly to reach the three cases you've listed, but I think your error might come just after that. You say you get a >= 8 in every possible case (which is totally correct) but that doesn't tell us exactly what a does equal. In this question we're asked to find the value of a, so we need to be able to find *one and only one* value for a for us to say the information provided by one, the other, or both of the statements is sufficient. Statement (1) tells us that a is an integer greater than 7. If we look at your first case: a = 2b - 4 for b >=6, we could say that a = 10. This means 10 = 2b - 4, so 14 = 2b and b = 7. This satisfies both the information in statement (1) and the restriction of b >= 6 we need to stay in the first of your three cases. However, we could also say that a = 12 which means that 12 = 2b - 4, so 16 = 2b and b = 8. This potential solution also satisfies the requirements for a and b. Since we can come up with at least two values of a that satisfy the information provided in the question stem and in statement (1), the first statement is not sufficient to answer this question. The information in statement (2) limits us to the second of your three cases, so the value of a always equals 8 and cannot equal any other number. Since statement (2) provides sufficient information for us to reach one and only one value of a, the answer to this question is (B). I hope that helps!
@lavanyajain9315 11 ай бұрын
In Q7 statement 2- |x| y^2, so (2) becomes insufficient right
@GMATNinjaTutoring 10 ай бұрын
It's true that numbers between 0 and 1 get smaller when you square them. Nonetheless, given statement 2, we can still conclude that x^2 < y^2. Because even if x and y were between 0 and 1, their relationship to each other won't change once you square them. To prove that, consider the following numbers: x = 1/10 and y = 1/5, which would satisfy statement 2. Notice that in this case (and all cases like this) x^2 is still less than y^2, because 1/100 is less than 1/25. I hope that helps!
@srilanka739 Жыл бұрын
29:19 kzfaq.info/get/bejne/pppkbJBlua6qpo0.html 'a is further to the right of zero than b is to the left of zero' Does this mean for e.g. if a>-b and -b= -2 (for example) then a has to be a>2? therefore (a+b)>0 ? is that what a> |b| means? thank you
@GMATNinjaTutoring Жыл бұрын
Yes, that's correct if b is to the left of zero. But it's also possible, with just statement 2, that b is positive, in which case a would just have to be greater than b.
@vinhngo93 8 ай бұрын
For the last question why can we do x/(x+1) < 1 ==> x < x+1 ==> x-1 < x ?
@GMATNinjaTutoring 8 ай бұрын
Did you mean to ask why we *cannot* do that? If we know x + 1 > 0 and so x > -1, then we can do what you suggest. However, if x + 1 < 0 and so x < -1, we'd have to flip the inequality sign as you go from x/(x + 1) < 1 to x > x + 1. The reason I'd try to avoid doing that altogether is that you don't know whether x + 1 > 0, so you don't know whether you need to flip the inequality sign. I hope that helps a bit, but please let me know if I misinterpreted your question!
@johnybrave78 8 ай бұрын
In the 2nd last question Range of x is -2 to 6 Addition of any number in this range is 8 This statement bounced over my head. How does this statement gives us the answer of what will be value of x.
@GMATNinjaTutoring 8 ай бұрын
If -2 < b < 6, then b - 6 will be less than zero. That means we can say |b - 6| = -(b - 6) from the way the algebra of absolute values works. Similarly, if -2 < b < 6, then b + 2 will be greater than zero. This means we can say |b + 2| = (b + 2). Combining these, we get a = |b - 6| + |b + 2| = -(b - 6) + (b + 2) = -b + 6 + b + 2 = 6 + 2 = 8. I hope that helps!
@puneetsonpal5340 10 ай бұрын
Hi the answer to question 9 should be D, since we can infer that x>1 from statement B as well. Please let me know if my understanding is wrong
@GMATNinjaTutoring 10 ай бұрын
While we can definitely say that x > 1 from the information provided in statement (2), we can go further and say that x > -1 from this information. If x > 1, then we can say that x/(x + 1) is less than -x/(1 - x) as Bransen explained in the video. However if x = 1/2, for example, x/(x + 1) is greater than -x/(1 - x). Since we cannot say for certain whether x/(x + 1) is greater or less than -x/(1 - x) from the information contained in statement (2), this information is not sufficient and the answer to this question is (A). I hope that helps!
@siddharthshukla222 11 ай бұрын
In question no. 1 : x is a cubic equation. So it can have 3 solutions, then why we said that x can have only one solution ?
@GRENinjaTutoring 11 ай бұрын
Based on statement 1, x could be either 0, 5 or -5. Statement 2 rules 5 and -5. So taking statements 1 and 2 together, we see that x must be 0, and the answer is C. I hope that helps!
@rockygamey 5 ай бұрын
Hi! for the second problem isn't 13-5 = 8 ?
@GMATNinjaTutoring 5 ай бұрын
Thank you! We're aware of the error, and the best we could do was put a tiny pop-up banner on the right side of the screen, acknowledging the screwup. The good news is that it doesn't affect the answer, since it's a DS question. But it's embarrassing all the same. Thank you for watching carefully enough to notice that type of detail! We're trying to tell ourselves that it's a good thing whenever somebody sees it. :)
@srilanka739 Жыл бұрын
can we think of |b| as either 0 or positive since it is an absolute value, therefore a has to be greater than 0 or any positive value, therefore a+b>0, and therefore x>0?
@GMATNinjaTutoring Жыл бұрын
Hi! I think that I may be missing something in your line of thought because the fact that, with statement 2, a is positive (by itself) does not mean that a + b is also positive. It's possible that b is more negative than a is positive. We do know that is not the case because a > |b|, but simply knowing a is positive does not tell me that a + b is positive.
@srilanka739 Жыл бұрын
@@GMATNinjaTutoring sorry question 5 Statement 2 if a>|b| does that mean a+|b| will be greater than zero?? a+|b| since |b| is either 0 or positive and since a>|b| , we can say tha a+|b|>0?
@GMATNinjaTutoring Жыл бұрын
Hi! That's correct: if a>|b|, then a + |b| > 0.
@pratsyprats Жыл бұрын
What if Y is an improper fraction with denominator less than the numerator?
@GMATNinjaTutoring Жыл бұрын
Hi Prateek! I’m not sure that I 100% understand your question. Could you be more specific about which question you’re asking about and what you’re asking about in that question?
@yatibansal6654 Жыл бұрын
@@GMATNinjaTutoring It's about question 6, for statement 2, bransen said If x>o then y has to be fraction but what if it something of the sort 6/5 or 25/13 where N>D?
@GMATNinjaTutoring Жыл бұрын
@yati bansal if x>0, then y has to be a fraction less than one. If y = 1 (or anything greater than one) and x = 6/5, then y^x >= 1 and statement two would not hold true.
@yatibansal6654 Жыл бұрын
@@GMATNinjaTutoring Makes sense, thankyou!!!
@johnrider9801 9 ай бұрын
In Question 6 why can't x be negative fraction? -1/8 > -1/4, hence making the answer E.
@GMATNinjaTutoring 9 ай бұрын
From the information in statement (1), we can demonstrate algebraically that x must be greater than 1 (Bransen does this in the video from about 44:30.) If we combine the two statements, we can show that x > 1 and y < 1, meaning we can show y < x and the answer to this question is (C). Check out that section of the video and let us know if you have any further questions. I hope that helps!
@itsak117 Жыл бұрын
great video but in question 5. if n=1 then we'll have 0x1x2 divided by 3 i.e 0/3 so basically m will not be an integer so answer should be A Please reply to this as i am confused
@GMATNinjaTutoring Жыл бұрын
Hi! 0 / 3 = 0, and 0 is an integer, so m would be an integer. That's similar to how I could say that if n = 2, then I have 1 * 2 * 3 / 3 or 6 / 3. Because 6 / 3 = 2, m would still be an integer.
@itsak117 Жыл бұрын
@@GMATNinjaTutoring thanks a lot for replying. I was curious about if 0/3 is considered as an integer or not.
@aulc3836 Жыл бұрын
I dont understand q4. How can we tell that if a+b > 0, then x must be > 0? Even if a+b > 0, can't x still be 0? x(a+b) > 0.
@GMATNinjaTutoring Жыл бұрын
Hi aulc, If x = 0, then x(a + b) also equals zero. This contradicts the result x(a + b) > 0 that we found by pushing the question. So before we look at statements 1 and 2, we know that x cannot equal zero. From pushing the question, Bransen showed that if we know x(a + b) > 0 then either x and (a + b) are both positive or they're both negative. Statement (1) tells us (a + b) is positive, so we now know that x must also be positive. This is why statement 1 is sufficient. I hope that helps!
@ukamakacyriacus4833 2 күн бұрын
Data sufficiency questions really confuses me. In question 8 for instance, statement 2 shows that there'll be many values for a. So why is B still the answer.
@GMATNinjaTutoring Күн бұрын
If we approach the information in the statement a bit more algebraically, it might help you see why there is only one value for a. If 2 < b < 6, then b - 6 will be negative. This means that we can treat |b - 6| in the same way was -(b - 6). Similarly, if 2 < b < 6, then b + 2 will be positive, so we can treat |b + 2| in the same way as (b + 2). This means that if 2 < b < 6, then a = |b - 6| + |b + 2| = -(b - 6) + (b + 2) = -b + 6 + b + 2 = 8. Since we only get one value of a when we use the information in statement (2), this statement is sufficient to answer the question. I hope that helps!
@ukamakacyriacus4833 Күн бұрын
@@GMATNinjaTutoring thank you very much for the explanation
@user-hq7jr3xu1p Жыл бұрын
Q7, Statement 1, Why can we take for granted that our absolute values are positive and we are not multiplying by a negative number?
@GMATNinjaTutoring Жыл бұрын
Hi Marco! I'm not sure that I fully understand your question, but by definition, an absolute value is the non-negative version of a number. So, an absolute value could only be zero or a positive number.
@dushyantdahiya 11 ай бұрын
hey, this might be a fairly silly brainfart when i look at the comment in the morning but in question 2, -13+5=-7. but thats like, wrong, wouldnt it be = -8. either ways answer is c but just wanted to know if im missing something obvious here.
@GRENinjaTutoring 11 ай бұрын
That's correct -- thank you for catching this! The answer is still C, but -13 + 5 should be -8.
@honest_bishop5905 2 жыл бұрын
Are these the hardest level inequality questions that could appear in the exam?
@honest_bishop5905 2 жыл бұрын
I can solve these fairly easily but I'm struggling on gmatclub
@GMATNinjaTutoring 2 жыл бұрын
@@honest_bishop5905 There are only about nine questions in the video, and I don't want to pretend that such a small sample size could possibly represent the breadth of GMAT inequality questions. But if we focus on the tougher questions in the last half of the video, I think it's unlikely that you'll see anything that's too much harder on the actual exam. If you're solving these easily, you're in great shape, and your study time is probably better spent elsewhere. No disrespect to the absolutely lovely question-writers at GMAT Club, but some of their quant questions are wildly excessive. As much as possible, try to gauge your progress with official questions and practice tests -- not the GMAT Club tests. A lot of GREAT quant test-takers struggle on the GMAT Club tests, so always take those with a huge grain of salt. I hope that helps a bit, and have fun studying!
@ritamroy2202 Жыл бұрын
Can anyone explain how -13+5 equals 7 and not 8
@GMATNinjaTutoring Жыл бұрын
Hi! -13 + 5 should equalt -8 and not -7. It was a small calculation error, but the best we could do to highlight it was put a tiny pop-up banner on the right side of the screen, acknowledging the screwup. The good news is that it doesn't affect the answer, since it's a DS question. But it's embarrassing all the same. Thank you for watching carefully enough to notice that type of detail! We're trying to tell ourselves that it's a good thing whenever somebody sees it. :)
@siddharthshukla222 11 ай бұрын
I calculated-13+5 twice on seeing -7😂
@corrayatom Жыл бұрын
in Ques : 3 you wrote, |x|>3 means x >3 or x |b| means a>b or a>-b This is kind of not clear to me. If someone could explain simply, it would've been helpful
@GMATNinjaTutoring Жыл бұрын
Hi Tom, In Q3, we were aiming to find information about where x is on the number line. Finding the actual value of x (or at least a possible range of values) was important. From x^2 > 9, we were able to say |x|>3, and this means we can say x > 3 or x < -3. By the time we were looking at a > |b| in Q4, all we cared about was whether x or (a + b) or both were positive. We don't know whether b is positive, but we know |b| is positive. This means we can say a > b and a > -b as it doesn't matter whether we take the actual value of b or take its negative, a will be greater from a > |b|. This means we can say for certain that (a + b) > 0 which is what we needed to answer this question. The two statements were not trying to say the same thing. They were focused on the information required to answer that particular question. I hope that helps!
@TheTellMeMore 6 ай бұрын
he looks like tom hanks
@ukamakacyriacus4833 2 күн бұрын
I didn't understand Q3
@wisamey 11 ай бұрын
at 14:11 there is a mistake. -13 + 5 = -8 and not -7
@GRENinjaTutoring 11 ай бұрын
Hi! -13 + 5 should equal -8 and not -7. It was a small calculation error, but the best we could do to highlight it was put a tiny pop-up banner on the right side of the screen, acknowledging the screwup. The good news is that it doesn't affect the answer, since it's a DS question. But it's embarrassing all the same. ...
@saahilbansal2280 10 ай бұрын
Thanks a lot for the video series, can't thank you and your team enough but I have a doubt I need help with - I think I'm missing something conceptually in Q9 If I look at Statement 2 - Can't I do this - x/(x+1) - 1 X - (x+1) < 0 (since x+1 =/ 0) Then I get X < X+1 And if I move the 1 I get X> X-1 So on the LHS I have numerator smaller than denominator and on the RHS I have numerator greater than denominator so can't I say LHS
@GMATNinjaTutoring 10 ай бұрын
Hi! The problem is in the second step where you multiply each term by x + 1. Since we don't know whether x + 1 is greater than or less than zero, we don't know whether we need to reverse the inequality symbol. We might get x - (x + 1) < 0 but if (x + 1) < 0, we might get x - (x + 1) > 0. Since we don't know which of these two cases we'd end up with, we can't say statement (2) is sufficient to answer this question. I hope that helps!
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