GMAT Ninja Quant Ep 8: Number Properties I: Methods & Mechanics
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Күн бұрынDo you get lost in the “word soup” of GMAT or Executive Assessment number properties questions? Do you some methods for tackling number properties questions, but you're not sure why those methods don't always work?
In this video, Harry -- a GMAT Ninja tutor -- will help you identify which number properties questions can be solved using a methodical, technical approach. Among other things, he'll show you how to use "quasi-algebra" to answer these questions efficiently under time pressure.
This video covers a wide range of difficulty levels. It starts with some simple questions to cover the foundations of GMAT and EA number properties questions, and the difficulty level builds through the rest of the video. This video finishes with a very tough question that will challenge nearly any GMAT or EA test-taker.
This is video #8 in our series of full-length GMAT quant lessons. For updates on upcoming videos, please subscribe!
This video will cover:
➡️ LCM and GCF questions
➡️ Divisibility
➡️ “Quasi-algebra”
➡️ Formalizing the things that can be formalized
This video is for you if:
➡️ You get lost in the “word soup” of number properties questions
➡️ You feel you don’t have a “method” to approach a question
➡️ You have a “method” but you don’t understand why it works
Want more GMAT and EA 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 Harry Duthie and his penchant for bench-pressing students who refuse to do their homework: www.gmatninja.com/harry-duthi...
Chapters:
00:00 Introduction
02:55 Question 1 - LCM and GCF
11:58 Question 2 - Is x an integer?
17:22 Question 3 - Divisibility
26:09 Question 4 - Divisor or Multiple?
32:11 Question 5 - Which one is an integer?
40:24 Question 6 - Including factorials
46:56 Question 7 - Make it a multiple
52:12 Question 8 - Raised to the 4th power
59:51 Question 9 - Tables and Divisibility
@aneeshabadhwar4882 10 ай бұрын
I usually don't write comments on KZfaq, but the series are amazing! Was literally chewing my brain off with quant, you guys are absolute heroes! Thank you!!!
@user-li7vp1gc1f 7 ай бұрын
This is amazing, I could solve every exercise but it took me a while. These methods and approach to exercises are easier and faster than everything I knew before.
@GMATNinjaTutoring 7 ай бұрын
Thank you for the kind words! I'm so pleased you found the video helpful. Good luck with the rest of your studies, and please keep us posted on how you get on!
@gauravmishra5998 4 ай бұрын
I could do the last question but struggled with initial questions, which I think indicates gaps in my conceptual knowledge. Beautiful lesson as always. Thank you.
@anuragmishra145 Жыл бұрын
A great resource for making strong fundamental of number properties topics. Thanks a lot Harry love from India🇮🇳 ❤
@GMATNinjaTutoring Жыл бұрын
Thank you so much for taking the time to write this, Anurag -- it's very much appreciated. Have fun studying!
@tbt73 Жыл бұрын
Amazing video! Cleared so many of my doubts and refreshed the basics. Thankyou for that.
@BSA77 Жыл бұрын
for question 8 I came to the same realisation after solving for S and ending up with 2 3 5 t with fraction powers. so I said to myself in order for S to be an integer then these fractions must be eliminated. so 1- each fraction then t^1/4 = 2^1/4 x 3^3/4 x 5^3/4 and raised everything to the power of 4 and got the same result as Harry. It took me 30 minutes to make a sense of it so NGMI on the real GMAT :)
@artisticsaurabh 5 ай бұрын
Thanks to your guidance in the initial questions, I could solve the last one. Took about 6 mins though. Not sure if it's worth investing this kind of time during the test.
@karimkaan8700 2 ай бұрын
I m amazed by how much logics this questions involves instead of pure maths and rules
@GMATNinjaTutoring 2 ай бұрын
Welcome to the GMAT! 😃
@user-jt2rc8ri2x 4 ай бұрын
Amazing video! Do you know where I can find resources to read up more about how to solve sums raised to the 4th power? I'm not very clear with that concept
@andreamalison2490 2 ай бұрын
Thanks for your fantastic work on this serie :)
@GMATNinjaTutoring 2 ай бұрын
Thank you so much for watching!
@Mont_Bomul 2 жыл бұрын
Very helpful
@sunjeevsolomon9973 2 жыл бұрын
The marker flip 🤣
@Alappavan 2 ай бұрын
Time stamp?
@wisamey 11 ай бұрын
If you see an up tick in your views from Saudi Arabia, that would be me! Great videos. Thanks a lot
@GRENinjaTutoring 11 ай бұрын
Thank you!! Glad you are finding the videos helpful.
@user-lv3sj8gv3h 9 ай бұрын
In Q8 I think it must be stated or implied in the question stem that t is an integer
@sauravdevkota6019 2 жыл бұрын
Very informative..
@lauragallon9191 5 ай бұрын
wow. i think i'm in love with harry. great lesson btw
@GMATNinjaTutoring 5 ай бұрын
We're all in love with Harry. :) Thank you for the kind words, and have fun studying!
@AP33781 Ай бұрын
HI Harry- thank you for this series! I have a question I really can't get around. Why for Q7 do you not need to consider integer A part of the factorization of 144 and match LCMs to 6^x like in Q3 and Q4?
@GMATNinjaTutoring Ай бұрын
We could have set this question up in the same way as Q3 or Q4 by saying 6^x = 144*A. By prime factorizing, we'd get 3^x*2^x = 2^4*3^2*A, and the smallest value x could take would still be 4, leaving A = 3^2. However, it's a bit more difficult to see why x = 4 using this method. The reason Harry set the solution up in the way he did was mainly out of convenience and ease of seeing what to do next. It's easier to see how 144 could be a factor of 6^x if we say 144 divides 6^x and leaves an integer with no remainder. I hope that helps!
@lukaalnoch8827 Жыл бұрын
Thank you
@tiyaandrews8397 Жыл бұрын
Hi, for question 9 I'm having trouble with understanding the wording like you've shown. It's said that the gap b/w two tables is 1/3 of the length, and the gap between the table and the wall are identical. I'd assume both the mentioned gaps to be of different lengths; i.e. the gaps in between to be m/3 and the gaps at the end (let's say x) to sum to 2x (identical). Maybe I'm overthinking with how the question's worded.
@harryduthie Жыл бұрын
Hi Tiya, The question doesn't say the gaps between the table and the wall at each end of the room are identical (even though they are), it says there is "an identical gap between a table and the wall at each end of the room." The only gap this part of the question could refer to is the "gap between any two tables of 1/3 the length of each table." This means the gap between the wall and the table at each end of the room is the same as the gap between any two tables, so each space around a table will be 1/3 the length of a table. I hope that helps!
@guilhermecristofani1272 Жыл бұрын
Hi Harry! Thank you for your lesson! In the last question, I believe you assumed the gaps between a tables and the wall are equal to the gaps between the tables (1/3m). But by reading the question I understood that that is not necessarily true, is it? Once again, thank you!!
@harryduthie Жыл бұрын
Hi Guilherme, The question says "Regulations require a gap between any two tables of 1/3 the length of each table. They also require an identical gap between a table and the wall at the end of the room." So the gap between the wall and the nearest table should be the same length as the gap between the tables. I hope that helps!
@TheAmigoBoyz 3 ай бұрын
For Q6, you could actually just test the options by factoring 26 from the get go. In other words just do the n=13x2(19x18... 'without 13 and 2' +1). Akthough we know that 19 would be in the paranthesis, we also know that adding 1 to a number changes the prime factors to completely different ones (because any subsequent number has no overlapping prime factors), and thus we can definitely say that 19 will not be in that number. I hope it makes sense to anyone struggling on that question.
@kartikgosain1896 3 ай бұрын
great video gmat ninja! I just have a doubt in 9th question, in the question line "they also require an identical gap between a table and the wall at the end of the room", i thought it only meant that the gaps between table and wall at either ends of the room are identical and not identical to the gaps between each table. But when i saw you take those two gaps as same as the gap between each table, i paused the video right there and made the equation myself and was able to solve the question very quickly.
@sid99varma 3 ай бұрын
I have the same doubt. Do we just assume that the gaps between table and wall at end of the room are equal to the gaps between tables? It isn't very clear from the question.
@visheshgupta5948 Жыл бұрын
For Question 6, can we say that the term that is added (in this case 26) should be divisible by the options to get the answer?
@harryduthie Жыл бұрын
Hi Vishesh, Good question! While your suggestion works in this question, you can't turn it into a general rule. Consider n = 4! + 60, which means n = 84. We can divide n by 7 (84 = 7 x 12), but 60 is not divisible by 7. So the term that is added does not have to be divisible by the divisor for the quotient to be a whole number without any remainder. Now, I can't tell whether the GMAT would use 7 as one of the options if they rewrote the question using n = 4! + 60. They might use 6, 9 & 12, in which case your suggestion would be right *for that question* , but they might use 4, 7 & 10, in which case your suggestion would not be correct. Unfortunately, all you can do is take each question on a case-by-case basis. I hope that helps!
@joshuaraphaelson9007 2 жыл бұрын
For question 8, since it isn't stated that T has to be an integer, couldn't T equal 1/120, which would make s=1?
@harryduthie 2 жыл бұрын
Hi Joshua, Thank you for this -- I think you've got me! If I had a chance to rewrite this question, I'd say that T needed to be an integer which would solve the problem. As it stands, you're right: s =1 is a possibility that would break the question. Thankfully, the questions on the real GMAT have been through much more checking than our questions, so you won't have to worry about these sorts of loopholes when you sit the real exam! Thank you for pointing this out!
@guilhermecristofani1272 Жыл бұрын
@@harryduthie Hi Harry! Thank you for your amazing lesson! :) I might be wrong but while testing condition number (2) there's no indication that A couldn't be 0,5, right? Therefore t, in this case, would be 112,5 and condition (2) would be incorrect...
@sotirisapostolopoulos9257 10 ай бұрын
came here for the exact same question ! i just changed s = 2 and t =2/15. thank you (after factorisation)
@Littman31 8 ай бұрын
You are a great techer Harry! Thanks for the videos! I was wondering about the way I solved Question 5. I solved it by rearranging the statement as you did. Then I instead isolated p and q from the statement -> p=r*B and q=r*C Then I inserted these into the answer choices as substitutes for p and q and tried to cancel out. Answer choice B gave me ((r*B)+(r*C))/r -> Cancel out r and we're left with B+C which we know are positive integers from the statement. two positive integers added to one another gives a positive integer. Then we know for sure it's correct. Do you think this is an effective way of approaching the question or will I possibly get tangled up in other similar questions because of this?
@GMATNinjaTutoring 8 ай бұрын
Thank you for the kind words! I'm so pleased you're enjoying the videos. I think your solution is great! If you can convert each of the fractions to be some function of r, you can see whether you can simplify each expression to check whether it will be an integer. Your reasoning once you get to ((r*B)+(r*C))/r was spot on, and you reached the solution efficiently (and quickly from the sounds of things!) I think this is a great way of approaching these questions IF you're able to convert all the expressions in the question into functions of a single term (in this question, you converted each answer choice into a function of r). If you can't do that, you might have to take the slightly longer route that I took in the video. If you understand both methods and are ready to use either one depending on how the question is phrased, you'll be in a great place to take on these sorts of questions in the real GMAT! I hope that helps!
@Littman31 8 ай бұрын
@@GMATNinjaTutoring Thank you kindly for the quick reply and further clarification! Much appreciated!
@visheshgupta5948 Жыл бұрын
Since the last question is so difficult, can I start my working by looking at the answer choices and picking a number from there?
@harryduthie Жыл бұрын
Hi Vishesh, If you saw a problem like the final question in the video on the GMAT and you didn't know where to begin, your best bet is probably to guess and move on. Since you've only got an average of 2 minutes per question, it's almost certainly not worth the time to try and create equations from the answer choices and work backward to find out whether they work. One of the worst things you can do on the GMAT is to dig your heels in and try to fight one of the tough questions if you don't see a good path through the problem. You just end up burning through time you could have spent on other, easier questions to make sure you got them right. Take a look at this video for more information, especially Myth #5 about tough questions deserving extra time: kzfaq.info/get/bejne/qZ5do8WBldXRcqs.html I hope that helps!
@Simon-dn6cu Ай бұрын
Thank You!
@GMATNinjaTutoring Ай бұрын
Thank you so much for watching!
@adityagawhale 2 ай бұрын
I skipped Question 8 as I didn't understand it at all (answer explanation), is that ok ?
@frederickkingjnr 11 ай бұрын
Hello, For question 2, i saw the algebra and all, but the square of a non integer cannot be an integer and no non integer that is squared and divided by 2 can give an integer so shouldn't it be sufficient? This is not merely algebra but a basic impossibility i think
@harryduthie 11 ай бұрын
Hi! The square of *some* non-integers can be integers. For example, if we take the square root of six as our non-integer and square it, we get the integer 6. We could then divide this by two to get 3. In this case, our starting value was not an integer, so the value of x in this scenario is not an integer. However, if we choose six as our starting value, we can square it to get 36 and then divide it by two to get 18. In this case, our starting value was an integer so the value of x is an integer. So, from the information provided in statement (1), we can come up with one scenario in which x is an integer and one scenario in which x is not an integer. This means statement (1) is not sufficient to answer this question. I hope that helps!
@robbitpat Жыл бұрын
love your teaching style. Thanks for the video!
@ekaterinaz9644 Жыл бұрын
Hi! Thank you! For the second question why is statement 1 insufficient? It says x2/2 is an integer therefore x cannot be 7 because (47/2) does not satisfy statement 1? What value of x that satisfies statement 1 would not be an integer? Except.. maybe 1/2🤔? Thanks again!
@harryduthie Жыл бұрын
Hi Ekaterina, I think you might be twisting statement 1 the wrong way around and that's what's causing the confusion. You're really going to struggle (and you shouldn't try) picking values of x to plug into statement 1. The algebraic route through the problem that's shown in the video is the best way I can think of to demonstrate that statement 1 is insufficient. At the final step in that explanation, I could have chosen p to be 2, 8, 32, 50.... and any of those would have given an integer value of x, but if I chose p to be a number not in that sequence, I wouldn't have found an integer value of x. Therefore, we can say statement 1 is insufficient. I hope that helps!
@IIBamboocha Жыл бұрын
Really struggled with that one to. My explanation was that you x could be the root of 6 if statement one holds.
@emawan7396 Жыл бұрын
Hi Harry, thank you for the video! Very helpful. I have a question about Number 6. Why 19 is not an answer? Could not it be 19(18!+1+7/19) = 19!+19+7=19!+26? Appreciate your help. Thank you!
@harryduthie Жыл бұрын
Hi Ema, One of the ways we can know a number is divisible by 19 is to factor out a 19 and see what multiplier is left. For example, 19 = 19(1), 38 = 19(2), and 57 = 19(3). The important thing here is that what's inside the parentheses is an integer. 21 is not a multiple of 19, but we can still say 21 = 19 + 2 = 19(1 + 2/19). While we can manipulate 21 so that we can factor out a 19, 21 is not a multiple of 19 because the number inside the parentheses when we do that factoring is not an integer. When you factor out the 19 and get 19(18! + 1 + 7/19), what's inside the parentheses is not an integer. This means 19! + 26 is not a multiple of 19. I hope that helps!
@radyahhassan 7 ай бұрын
Hi Harry! Thank you for this very helpful video! Realised Number Properties isn't as difficult as I thought. I had one question for number 8. In that problem, t= 2*3^3*5^3*A. Here, can we say that whatever is inside "A" must also have prime factors raised to the power 4? Since on the LHS, s is raised to 4?
@GMATNinjaTutoring 7 ай бұрын
I'll have to be careful with the wording here. If A has any other prime factors in it, they must also be raised to a power that's A MULTIPLE OF four to match the power that s is raised to on the other side. The prime factor doesn't necessarily have to be raised to the power of four, as it could be raised to the power of 8 or 12 or 16 etc. but the power must be a multiple of four because we have s^4 on the other side of the equation. So if A had a 7 as one of its prime factors, we know that it must be one of 7^4, 7^8, 7^12, etc. From the information provided, we can't tell exactly what power the 7 is raised to, but we know it must be some multiple of 4. You could say a similar thing if A had an 11 as one of its prime factors, or a 13, or a 17, etc. I hope that helps!
@radyahhassan 7 ай бұрын
@@GMATNinjaTutoring Thank you! This really cleared up my query 😃
@anashwarapillai4228 3 ай бұрын
@GMATNinjaTutoring Question 9 , it says that there is an identical distance between table and end of wall , doesn't it mean that 1/3 m is maintained across all three ends , that is , bottom , top and side ? Kindly help me understand this
@GMATNinjaTutoring 3 ай бұрын
In this question, we don't have to consider the top or bottom of the table. We can think of this situation as if we're looking down on the line of tables from above, as in the diagram drawn on the board from about 1:02:15 There is a gap of 1/3 the length of a table between each pair of tables in the line, and there's a gap of 1/3 the length of a table between the wall and the table nearest the wall at each end of the room. That means the number of gaps will be one greater than the number of tables. I hope that helps!
@Ssrssj Жыл бұрын
For question 8, why can't T be a fraction? This way when s^4 = 120t, t can be anything ranging from 1/120, 16/120, 81/120 etc. If this is the case, none of the answer choices can be integers right? My issue is t hasn't been clearly defined like s.
@harryduthie Жыл бұрын
Hi Ram, You're right, I slipped up when I wrote the question and didn't define t carefully enough to make sure it had to be an integer. If I had a chance to rewrite this question, I'd be a bit more careful about defining the terms. Thankfully, the questions on the real GMAT have been through much more checking than our questions, so you won't have to worry about these sorts of loopholes when you sit the real exam! Thank you for pointing this out!
@shirleyeriko6012 4 ай бұрын
can anyone help me generalize question 3? thanks.
@datvuk2 3 ай бұрын
@GMATNinjaTutoring Question 9, it says "an identical gap between a table and the wall at the end of the room". I'm just being dumb and assume that there is only a gap between 1 table and 1 end of the room, not both ends. But i'm curious, if that was the case, what would be the answer to the question?
@GMATNinjaTutoring 3 ай бұрын
This is a very difficult question, and you definitely weren't the first person to make that mistake! Unfortunately, the question would fall apart if we changed the parameters in the way you're suggesting. I haven't done the calculation fully, but it's likely that the numbers would get very messy and we'd end up with a non-integer answer. This question uses very specific numbers and any slight deviation from those numbers would make the calculations go haywire. It would be great if we could play around with the question easily, but that's just not the case here. Sorry I can't do more here, but I hope that helps a bit!
@srilanka739 Жыл бұрын
in Q6 how did the 13*2 cancel down to become + 2? is it because we took the 13 out of N= 19 factorial ?
@harryduthie Жыл бұрын
Hi Sri Lanka, The 13*2 didn't cancel down to become a +2. In that line, the 13*2 was factored and brought into the parentheses with the rest of the 19!. If those lines had been written out in full, they would have said: n = 19! + 26 n = 19! + 13x2 n = 13(19x18x17x16x15x14x12x11x10x9x8x7x6x5x4x3x2x1) + 13x2 n = 13(19x18x17x16x15x14x12x11x10x9x8x7x6x5x4x3x2x1 + 2) I hope that helps!
@srilanka739 Жыл бұрын
@@harryduthie UNDERSTOOD. thank you so much
@Kee1993 5 ай бұрын
Hi for the Q6, since the question says x is the power of 6 and not 2 or 3 wouldn't x=3 be the least value of x to make 144 a multiple of 6^x? Going by 144 = (2*2*6*6)
@GMATNinjaTutoring 5 ай бұрын
If we let x = 3, then 6^3 = 216. 216/144 does not give us an integer (it's 1.5), so 216 is not a multiple of 144 and the correct answer is not x = 3. The problem with your suggestion is that you've not prime factorized 144 as far as you can. 6 = 2*3, so 144 = 2*2*6*6 = 2*2*(2*3)*(2*3) = (2^4)*(3^2). As explained in the video from about 49:45, we need the power of x to match the largest power in the denominator. In this case, that's 4, so the answer to this question is x = 4. I hope that helps!
@Kee1993 5 ай бұрын
Okay got it. Thank you for the reply.@@GMATNinjaTutoring
@PranjalAwasthi Жыл бұрын
I had a doubt in Question 2 and Question 7 - Question 2 - If x^2 / 2 = Integer then X^2 = 2* Integer (also an Integer). Therefore x^2 = Integer. And if the square of a number is an integer then shouldn't that number be an integer to ? Question 7 - The question says there's an identical gap between the table and each of the two end walls of the hall. Is this table-to-wall gap "identical" to the inter-table gap or just identical to each other (I assumed the latter and ended up with an extra variable).
@harryduthie Жыл бұрын
Hi Pranjal, If you take your working and say that x^2 = 2 * integer, then I could have chosen the integer to be 2, 8, 32, 50.... and any of those would have given an integer value of x, but if I chose the integer to be a number not in that sequence, I wouldn't have found an integer value of x. Therefore, we can say statement 1 is insufficient. I hope that helps!
@ichhajain3738 2 жыл бұрын
Hi team! Is the last question discussed in the GMAT club forum? I got down the approach but couldn't understand why 4t+1 has to be equal to 37. Another (time-consuming) way is to put in the options and arrive at the answer, which is not feasible
@chethanmohan 2 жыл бұрын
Dunno if you've figured it out by now. We have : 2^3 x 3 x 37 = m(4t+1) Here we are splitting terms m and 4t+1. With 4t+1 , 4t will be a multiple of 4 and then you add 1 to it the only factor which satisfies this is 37 = 36 + 1
@user-lv3sj8gv3h 9 ай бұрын
In the last question I tested 9 & 24 and found out they give the same result, hence excluded 3 & 8 as they are factors of 24 already (I don't know why I did that) and was left with E, how you see my approach? with your eyes? hhh
@srilanka739 Жыл бұрын
for question 2 x^2/2 = integer any number you pick for x has to be divisible 2 by? isnt the statement telling you x has to be an integer? confused :(
@harryduthie Жыл бұрын
Hi Sri Lanka, I advise my students to stay away from picking numbers as it can often go wrong and make the question take far longer than it needs, but we can choose a couple of numbers here to illustrate what's going on. If we said x^2/2 = 8, then x^2 = 16 and we find x = +/- 4, so x is an even integer in this scenario. However, if we said x^2/2 = 7, we're still using an integer and satisfying the condition provided in statement (1), but now we get x^2 = 14 and x = +/- sqrt(14) which means x is not an integer in this scenario. Since we can create two different situations that satisfy statement (1) with one showing x can be an integer and one that x can be a non-integer, statement (1) is insufficient to answer this question. I may be totally wrong here, but I think your difficulties are coming from your choosing values. of x. In this explanation, I chose values of the integer mentioned in statement (1) (this is P in the algebraic solution in the video) because that's the only thing we've been given any information about. I hope that helps!
@srilanka739 Жыл бұрын
I think I see where the mistake is assume x^2 = 12 12/2 = 6 but x = square root of 12 - this is not an integer as this would be 2 root 3 is this correct?
@harryduthie Жыл бұрын
Hi @@srilanka739, Your example works for one side of the process to show statement (1) is insufficient. You've found an integer value of x^2/2 which means x is *not* an integer. You'll need to find another integer value of x^2/2 which means x *is* an integer to complete the process, but what you've done so far is correct. I hope that helps!
@srilanka739 Жыл бұрын
@@harryduthie thank you so much. I can see why S1 is insufficient now. if you chose a value for x^2 first and then work back to see what x would be you'd see S1 is insufficient. ,but if you chose an x and then say x^2 =... you will incorrectly chose S1 as sufficient which is the mistake I made
@user-lv3sj8gv3h 9 ай бұрын
In question 2 we can say since x^2 / 2 = integer then x ^ 2 = integer and from this we can conclude nothing
@chandlerbing5437 7 ай бұрын
Wowww
@andycampo6624 Жыл бұрын
dont get question 8 and why 3 and 5 were cubed to begin with
@hitteshkumar5518 Жыл бұрын
Ques 8- how you found value of t, could understand the power of 3 there. Please simplify here in comment, thanks
@harryduthie Жыл бұрын
Hi Hittesh, In this question, we know s^4 = 120 * t and we can find the prime factorization of 120 to give s^4 = 2^3 * 3 * 5 * t. Since s has been raised to the fourth power, the powers of each of the prime numbers in the prime factorization of s^4 must be a multiple of 4. They could be 4, 8, 12, etc. but they must be a multiple of 4. In order to make that happen, t has at least one 2 in its prime factorization so the powers of 2 in the prime factorization of s^4 are a multiple of 4. For the same reason, we need a 3^3 and a 5^3 in the prime factorization of t. There might be more numbers in the prime factorization of t, but this is the minimum required to make sure the powers of each of the prime numbers in the prime factorization of s^4 are a multiple of 4. This means t = 2 * 3^3 * 5^3 * A, where A represents any additional numbers in the prime factorization of t. A could be 1, but it could also be 2^4, or it could be 2^4 * 3^4 -- A represents additional numbers that *could* be in the prime factorization of t but don't *have* to be there. We don't need to figure out the value of A and can use t = 2 * 3^3 * 5^3 * A to complete the rest of this question. I hope that helps!
@sriramasokan 3 ай бұрын
In Q3, If the statement 1 was " 81 is a factor of x" Will the answer be C ? I think the answer would be still be D, as we still have unknown variables B and C( as mentioned in the explanation). Can you pls clarify ?
@GMATNinjaTutoring 3 ай бұрын
If statement (1) told us that 81 was a factor of x instead of 24, then the answer to this question would be (C) instead of (E). In order to know whether x is divisible by 405, we need to know that it has 3^4 * 5 in its prime factorization. It can have other numbers, but it needs to have 3^4 * 5. If statement (1) tells us 81 is a factor of x, then we know x has 3^4 in its prime factorization. Statement (2) then tells us 15 is a factor of x, so we know x has 3*5 in its prime factorization. Combining these two by finding the lowest common denominator, we know that x has 3^4 * 5 in its prime factorization, so both statements combined are sufficient. It doesn't matter whether the unknown variables add anything to this list, as long as we know that x has 3^4 * 5 in its prime factorization, we know x is divisible by 405. Those unknown variables could add anything to this list, and x would still be divisible by 405, so we don't have to worry about them as we go through this process. I hope that helps!
@sriramasokan 3 ай бұрын
@@GMATNinjaTutoring Got it.Thanks for the clarification
@pranilpawar6540 11 ай бұрын
In q2 if x^2/2 is an integer then x can only be 2,4,6,8….. It cannot be any fraction or decimal number so we can say yes x is an integer…am I missing something or what?
@harryduthie 11 ай бұрын
Hi! Statement (1) tells us that x^2/2 is an integer, but it doesn't tell us whether x is an integer. As shown in the video from about 14:33 to 15:05, if we say x^2 / 2 = P where P is an integer, then x = sqrt(2P). This means x is an integer when sqrt(2P) is an integer. This will happen when P is 2, 8, 32, 128... as these values of P will give a square number when they're multiplied by 2. However, if P is given any other value then x will not be an integer. P could be 1, 3, 4, 5, 6, 7, 9, 10... and this would give a non-integer x value. You can also look at it from the other direction (but I think this would be much harder to do in the middle of the exam): if x is 2, 4, 6, 8... then x^2/2 will be an integer. However, x^2/2 will also be an integer if the value of x^2 is an even number. This could happen if x was the square root of 2, the square root of 6, the square root of 8, etc., none of which are integers. Since we can find one scenario in which x is an integer and one scenario in which x is not an integer, statement (1) is not sufficient to answer this question. I hope that helps!
@vaibhavbhatia4641 2 ай бұрын
S and t both need to be integer for the given explanation to work. What if s = 1 and t = 1/120. Still the given equation would be satisfied and then none of the options would be an integer
@GMATNinjaTutoring 2 ай бұрын
You're absolutely right. As it stands, you're right: s =1 is a possibility that would break the question. We'll fix this issue when we film a new quant series. Thankfully, the questions on the real GMAT have been through much more checking than our questions, so you won't have to worry about these sorts of loopholes when you sit the real exam!
@user-lg1rq1ih9j Жыл бұрын
1:02:05 Personal time stamp (Important)
@alfredoherrera7812 Ай бұрын
About Q2, I think you are wrong, since the first statement is also sufficient. As you said, the equation is X^2 = 2K This means that X^2 is an even number because it is twice an integer. For X^2 to be even, X itself must be an even number (since the square of an odd number is odd). Therefore, X is an integrer, so the statement is sufficient. Am I wrong?
@GMATNinjaTutoring Ай бұрын
If we know that x^2 = 2k, then as you say, we know that x^2 is an even integer. From there, we can say that x^2 could equal 4, 16, 36, 64, or 100 and in that case, x would be 2, 4, 6, 8, or 10. This pattern can continue and there are an infinite number of integer values of x that would satisfy the conditions we've outlined so far. However, if x^2 = 6, 8, 10, 12, 14, 18, 20..... then x will not be an integer, even though these numbers satisfy x^2 = 2k. Since we don't know whether x will be an integer or not, statement (1) is not sufficient to answer this question. I hope that helps!
@caroleg1997 5 ай бұрын
I hope to get a response on question 2 at the very beginning because is x=q^1/2 then what is q is a fraction then x is not an interger just like you checked statement 1🤭🙄 I would go for E
@GMATNinjaTutoring 5 ай бұрын
I think you're asking about statement (2), but please let me know if I've got that wrong. In this question, we're trying to determine whether x is an integer, and statement (2) tells us that the square root of x is an integer. For now, let's say this integer is b, so we know sqrt(x) = b and we know b is a whole number. From here, we can square both sides, so we now have x = b^2. We get another integer when we square an integer, so we know that b^2 is an integer. This is why statement (2) is sufficient to answer this question. I hope that helps!
@purin586 Жыл бұрын
Scary thing is my GMAT dealine coming soon and I have no idea how to do any of these 😂
@GMATNinjaTutoring Жыл бұрын
Good luck on your exam, Purin! It's very possible that you're doing better than you might think, but if you end up struggling with quant... well, our videos are designed for students who have a pretty decent command of the basics, but could use some help applying those fundamentals in a GMAT context. If you're struggling more deeply on the basics -- and if you're a long way from the quant score you're looking for -- you might consider diving into something like Khan Academy for help with algebra, arithmetic, and the basics of things like percents, ratios, exponents, or divisibility. Our videos might be more useful once you have a chance to brush up on all of that stuff. But hopefully you crush the GMAT and all of this is moot. :) Have fun studying, and I hope this helps a bit!
@passionpreneur9740 Жыл бұрын
@@GMATNinjaTutoring kzfaq.info/sun/PL3EF88D8D529A562E , Did u mean by this playlist of khan academy?
@srilanka739 Жыл бұрын
@@passionpreneur9740 Nope I think he means for each topic check the basics for algebrea, roots, exponents etc.
@john.8805 7 ай бұрын
Question 5: It asks: „what number MUST be an integer?„ So you can actually literally chuck any number at it and get the answer ;) If any answer choice does not work out, no matter what number combination you use, it can be eliminated
@GMATNinjaTutoring 7 ай бұрын
You can almost just do that ;-). As long as the number you choose for r divides the number you choose for p, and the number you choose for p divides the number you choose for q, then your method will work! Thank you for posting!
@aloperafan 7 ай бұрын
For question 8, we need the question to explicitly state that T is an integer. Otherwise, let's say that S = 1, and S^4 = 1 and T = 1/120, none of the answers would be correct.
@GMATNinjaTutoring 7 ай бұрын
You're absolutely! If I had a chance to rewrite this question, I'd say that T needed to be an integer which would solve the problem. As it stands, you're right: s =1 is a possibility that would break the question. Thankfully, the questions on the real GMAT have been through much more checking than our questions, so you won't have to worry about these sorts of loopholes when you sit the real exam! Thank you for pointing this out!
@phillipkvile5040 7 ай бұрын
How come I got the easy questions wrong but got the last question right? xD
@ashishsinha9035 3 ай бұрын
Thanks a lot GMAT Ninja! I liked the way you pronounced ‘hall’ (sounding as hole). Even in my country, people from a certain state pronounce like that when they say ‘We were sitting in a hole (hall) having snakes (snacks).
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