OLD VERSION: Number Properties Part II - click the link in the description for an updated video

[@kmkm0529]

Thank you for the wonderful explanation!!!

[@GMATNinjaTutoring]

Thank you for the kind words, and have fun studying !

[@JinghanYun]

For Q1, why we don't need to concern the "is divided by 10" part? Seems like we only need to concern about the last digit of 3 to the power of 37. Thanks!

[@GMATNinjaTutoring]

We do need to worry about the "divided by 10" part. The remainder when a number is divided by 10 is the units digit of that number. So the remainder when 23 is divided by 10 is 3, the remainder when 248 is divided by 10 is 8, and the remainder when 3^37 is divided by 10 is the last digit of the number. I hope that helps!

[@ShaadMulla]

What an eye opener this series is. All I understand is that just remembering formulas will get you nowhere. Its all about finding the shortest and smartest way to get to the answer. Having the flexibility to use the rules in a creative reasoning way to get to the answer.

[@rikhrajghosh9897]

Pls explain me the AD/BCE setup ???

[@GMATNinjaTutoring]

This is explained in full in Video 0 - How to Approach GMAT Quant. I've put a link to that video below. Check that out and let us know if you have any further questions. In particular, have a look at question 2 on how to approach a Data Sufficiency question. I hope that helps! kzbin.info/www/bejne/hHuZnadpi7KBmbc

[@rikhrajghosh9897]

Thank you

[@anuragmishra145]

In last question it is much easier if we focus on 0.48n=12 ( as we can see (x/y=53.48, so remainder is 0.48 multiple= remaining oranges I. e. 12) We will get n = 25 Ans

[@kenyaschwarz6072]

All the Gmat Stuff feels like bashing my head into the wall xD

[@chibuikeonyia3124]

The last question was the only one I was able to solve and within two minutes. Seemed easy to me

[@aayushpokhrel7118]

What range is he talking about? 640s or 740s?

[@pickles8863]

The Gordon Ramsay of Quant. Killer questions and excellent explanations! I'm on week 6 of the GMAT Ninja study plan and I was going to skip this video as Charles recommended --glad I didn't. Thank you, Harry; your other videos (especially the geometry ones) are very helpful :)

[@harryduthie]

I've never heard someone call me "the Gordon Ramsay of Quant," thank you for making me laugh! I'm so pleased you're finding the videos helpful, and thank you for the kind words. Best of luck with your studies and please keep us posted on how you get on.

[@mohsin9907]

@@harryduthie Honestly Im in love with your videos. Thank you for helping

[@GMATNinjaTutoring]

Charles here! Just responding so that @Harry Duthie isn't alarmed: in the study plan on GMAT Club, I recommend against watching this video just because it's more than most test-takers need if they're only studying for 13 weeks. If you have a good reason to push for a super-high quant score -- and don't have any more urgent ways to spend your study time -- this video is great. So yeah: Harry is awesome. I didn't mean to imply otherwise on the study plan. 😃 Thank you so much for taking the time to write lovely things, @Mohsin and @Pickles! And have fun studying.

[@pickles8863]

​@@GMATNinjaTutoring The legend, the glorious, the maestro himself... Apologies for not clarifying that in my previous comment, I wrote it mindlessly... Thank YOU for putting this brilliant plan together! I'm indeed enjoying the process and super happy with my progress. Much love and respect. -Pickles

[@GMATNinjaTutoring]

@@pickles8863 ❤

[@HalfGermany100]

why does m/n equals 2k? Why does it not equal e.g. 4k? I dont get where the questions states that. Thanks for the support! :)

[@GMATNinjaTutoring]

The question tells us m/n is an even number. One way of ensuring m/n will always be an even number in the algebra we use from then on is to say that m/n = 2k where k is some integer. Using 4k wouldn't work so well as we'd miss out on some of the even numbers. If m/n = 4k then we'd be limited to 4, 8, 12, 16..... and would miss out on 2, 6, 10, 14...... I hope that helps!

[@HalfGermany100]

Thank you guys. Appreciate your work!

[@rafaelporto673]

On the second last question, M+6/2, why couldn't M = 6 (EVEN, satisfying all conditions), resulting in 6? Thus, the result could be even.

[@GMATNinjaTutoring]

If m could equal 6, then you'd be absolutely right. However, m can't equal 6 in this question. As Harry showed in the video between about 42:50 and 44:40, m must be a multiple of 4. This means m could be 4, 8, 12, 16, 20....., but it can't be 2, 6, 10, 14, 18.... If we limit m to being a multiple of 4 then (m + 6)/2 cannot be even. I hope that helps!

[@rafaelporto673]

@@GMATNinjaTutoring It helped! You guys are fantastic. Thank you.

[@AusGreenLdn]

For Q7 if you know N is even as well why not C as well?

[@GMATNinjaTutoring]

If n is one of 4, 8, 12, 16, 20... then (n + 2)/2 will be odd. However, if n is one of 2, 6, 10, 14, 18.... then (n + 2)/2 will be even. Since we are looking for the answer choice that CANNOT be even and (C) can be even if n is one of 2, 6, 10, 14, 18...., we know that (C) is not the answer to this question. I hope that helps!

[@VidurSeth-b7o]

Thank you so much for your videos. You're the best!

[@NewxToXThisxBiz]

what i dont understand about data sufficient questions is that, sometimes when you can get two answers and its insufficient but sometimes when you can get two answers, it is sufficient. How do i know which one will accept two answers being correct vs its only wanting one answer and it having two will be insufficient.

[@yassineessbai9468]

So for the visibility of n(n+2) by 8 I can put 8 like 2(2+2) so the probability of n(n+2) divisible by 8 it’s like n divisible by 2 and we have n from 1 to 1000 so the probability will be 1/2 since we have half even numbers and half odds numbers

[@sayandeepguha6946]

Question number 7- it was proven that m and n both are even. So when checking answer, m/2 is even that i understood but why we are sceptical about n/2 is even or odd? Because if n is even then it would definitely be divisible by 2. There i am confused

[@GMATNinjaTutoring]

You're absolutely right that n is divisible by 2, but we're not sure whether we get an even or odd number when we divide n by 2. It's possible that n = 4, 8, 12, 16, 20.... and if this is the case, then n/2 will be even. However, it's also possible that n = 2, 6, 10, 14, 18.... and if this is the case then n/2 will be odd. Since we don't know which of the two lists n is in, we can't be sure whether n/2 is even or odd. I hope that helps!

[@JarenScott]

For question 7: if M= 10 then wouldn't answer E result in an even integer - namely 8, thereby making answer E incorrect?

[@GMATNinjaTutoring]

From the information given in the question, we can show that M must be a multiple of 4 (shown in the video from about 43:20 to 44:20). This means M cannot be 10, it can only be one of 4, 8, 12, 16... All of these would give an odd number if we put them into the formula (M + 6)/2. I hope that helps!

[@SuparnaSinha-b7c]

17:30 Self study time stamp

[@1was3im]

Hey Harry ! can you tell me what wrong with this approach? reducing n(n+2)/ 8 to n^2/8+ n/4 which further can be written as (n/4)^2 * 2 + n/4 so basically for this to be integer, i have to find how many n are divisible by 4 since there would be 250 for 1000 , my answer is coming out be 1/4.

[@GMATNinjaTutoring]

You're missing the terms for which neither (n/4)^2 * 2 nor n/4 are integers but they add together to make an integer. Consider what happens when n = 6. In this case, (n/4)^2 * 2 = 4.5 and n/4 = 1.5 so they sum together to make 6. This means that n(n + 2) is divisible by 8 for n = 6 even though 6 is not divisible by 4. I hope that helps!

[@1was3im]

@@GMATNinjaTutoringunderstood ! Thanks

[@sandhyasilotia8533]

Hi Some different version of solution for question 7 & 8 7: m+n -only possible if both terms r even ir odd m/n - only possible if both r even Since both r true, both m and n even, Quick glance through options, we know that only option E gives odd 8. Since rows and columns has to be interger, y has to be factor of 5 or 10, which brings us to answer option C Pls let me know ur opinion abt this approach.

[@GMATNinjaTutoring]

You'll have to go into a little more depth on question 7 to ensure you get the right answer. It's not enough to know that m and n are even as we're not just trying to find an answer choice that gives an odd number, we want the answer choice that CANNOT be even. If we assume m = 6 and n = 4, then all the answer choices give an odd value. We need to know that m must be a multiple of four to ensure that (E) is the only answer choice that CANNOT be even. For question 8, I don't know what you mean when you talk about rows and columns. If you explain what you mean here, I might be able to comment more on this approach. Thank you for posting, and I hope that helps!

[@kalpeshmaldikar1515]

Hi GMAT Ninja, thanks for the amazing content! I have a quick question related to optimizing problem-solving strategies. When working with constraints like (9x + 4 < 100) and (7y + 5 < 100), I thought about trimming down the possible values by using inequalities. For example:For (9x + 4 < 100), I determined that the maximum value of (x) would be 10.For (7y + 5 < 100), I figured that the maximum value of (y) would be 13.

[@raabiyaalishaq1457]

For Q7, because we know m and n both are even. In choice C: n/2 + 1 would always be odd? so choice C is also correct?

[@harryduthie]

Hi! We know that n is even, but it would need to be a multiple of 4 to guarantee answer choice (C) could never be even. If we assume n = 8, then n/2 + 1 = 8/2 + 1 = 4 + 1 = 5, which is odd. However, if we assume n = 10, then n/2 + 1 = 10/2 + 1 = 5 + 1 = 6, which is even. Since we cannot guarantee n/2 + 1 will always be odd from the information provided, (C) is not the answer to this question. I hope that helps!

[@manuelecreatini]

One doubt on question 7: isn't easier just to think that the (E) is the only answer where you add a odd number (i.e., 3) to something that must be even in order to for the overall result to be an integer (i.e., m/2)? for example, if m was even, then m/2 + 3 would be odd, whereas if m was odd, then m/2 + 3 wouln't be an integer, so it turns out that m/2 + cannot be a even integer. Thank you!!

[@GMATNinjaTutoring]

We don't have to worry about (E) giving us a non-integer value because m can never be odd. The part of the explanation starting from about 42:50 shows why m is not just even, it must be a multiple of 4. This means that m/2 must be an even integer, and adding 3 will always give us an odd integer. I hope that helps!

[@parvindernogi6264]

Did question 8 in 15 seconds by this : 1. Reminder is 12 so y>12, so a and b are out 2. Terminating decimal is given, so divisor has to be only powers of 2 and 5, so d and e are out Answer is thus C by POE

[@harryduthie]

This is an amazing solution! Thank you for adding this, Parvinder!

[@SarthakGupta-il6mt]

@@harryduthie I was thinking of something similar here: we know that we are going to end up with an 'integer' value - so when you multiple y by 0.48, you are going to get a 'whole' number --> only C = 25 gives you this and is thus the answer (we know y > 12 so a and b are already out). Does this thinking also work or is it flawed?

[@harryduthie]

@@SarthakGupta-il6mt this is another great solution! You're in a lovely position if you can come up with alternative methods to answer these questions. The GMAT will try to ask questions that need some creativity and flexibility, so you'll be rewarded if you can come up with new ways to answer questions in the real exam. I hope that helps!

[@JinghanYun]

For Q8, what is the reason of imitating the reminder as r/B, instead of just r? Thank you!

[@GMATNinjaTutoring]

If we take 35 divided by 4 as an example, as shown in the video, 35 can be written as 35 = 4*8 + 3. The remainder in this division is 3, and this is what the GMAT would consider the remainder. However, the division 35/4 can also be written as 35/4 = 8 + 3/4. Nothing has changed here -- this is just another way of writing the same sum. The remainder will still be 3, but as shown in this question, the information might not be presented in the 35 = 4*8 + 3 format. It's helpful if you can see and recognize the format change and be able to work with both. I hope that helps!

[@ashishsinha9035]

Thanks GMAT Ninja for the awesome video !

[@GMATNinjaTutoring]

Thank you so much for watching!

[@aulc3836]

For Q.6, How did 1/5^6 become (2/10)^6, how does the exponent 6 get applied to the numerator?

[@harryduthie]

Hi aulc, 2/10 is an equivalent fraction to 1/5, so we can change the fraction within the parentheses. When the exponent is applied to the whole fraction, it's applied to both the top and bottom of the fraction, so (2/10)^6 = (2^6)/(10^6). We can use some smaller numbers to demonstrate this. Consider (1/2)^3 which we know equals 1/8. However, I could say that 1/2 = 2/4, so (1/2)^3 = (2/4)^3. Then, applying the power to both the numerator and denominator, we get (2^3) / (4^3) = 8/64 which simplifies down to 1/8, the same answer as if we'd just done (1/2)^3. I hope that helps!

[@kmaximilian]

@@harryduthie Hi Harry, I get that 1/5 is equal to 2/10 but how did you get from raising just the denominator (5) to the power of 6 to raising both the numerator (2) and the denominator (10) to the power of 6?

[@GMATNinjaTutoring]

Hi @@kmaximilian, we can show how this works in the sequence below, as long as we know that 1^6 = 1*1*1*1*1*1 = 1. 1/(5^6) = (1^6)/(5^6) = (1/5)^6 = (2/10)^6 = (2^6)/(10^6) I hope that helps!

[@kmaximilian]

Yes it does! Thank you very much@@GMATNinjaTutoring

[@kenyaschwarz6072]

@@GMATNinjaTutoring I still dont get this, i mean yea 1^6 would be 1 for sure. But we dont know if it's 1^6. The power could only be in the denominator. We just suspect this at this point. But if we rise both sides to 2/10 wouldn't this change the fraction if i apply the ^6 to the nominator? Normally it's not common that if the denominator has a power, that this also applies to the nominator.

[@srilanka739]

for Q 5 if you change the question to - 1-1000 inclusive whats the probability N is divisible by 8 ? how would you solve for that? Would it just be 120/1000?

[@harryduthie]

Hi Sri Lanka, I might have misunderstood your question, so please let me know if I haven't interpreted what you're asking correctly. If your question says what I think it says then we could just say every eighth number is divisible by 8, so the probability will be 1/8. Alternatively, if you'd prefer a full calculation: we could divide 1000 by 8 to give us 125. The probability would then be 125/1000 which we could simplify to 1/8. I hope that helps!

[@srilanka739]

@@harryduthie thank you so much for the response That is what my question was Thank you guys

[@cateatfood]

Hey. Below is what I did for the last question - x/y = 53.48 This also means number of oranges per box in 53.48. Since oranges per box should be a whole number, there is 0.48 oranges extra in each box. Now we are given that over all 12 oranges remain. So 0.48 X (Number of Boxes) = 12 . Because the extra 0.48 orange from every box will add up to make the remaining 12 oranges. So... 0.48Y=12 Y=1200/48 = 25 Let me know if this makes sense. Also, I somehow manage to get the more difficult questions right but miss out on the easier ones like Q5. Some advice on what to change in my prep would really help! Thanks :)

[@harryduthie]

Hi Brijnandini, Your method looks good to me! For your other question, without knowing much more about your preparation to date, I don't necessarily think I'd suggest any changes to your prep. The problems in this video are all about pattern spotting, so you might find them really easy if you've seen the pattern before. However, if you haven't seen the pattern before, you might find these questions really difficult. It's possible that all you need to do is keep practicing so you see more of these patterns and are able to identify them when they appear in other problems. I hope that helps!

[@linus284]

Brilliant! Due to the answer choices, you could even estimate with your method here. And be done in no time

[@lavv2379]

for the last question, I elliminated all options except 25 cause none of them will give an integer when multiplied by 53.48…is that a correct approach too?

[@fukurogaming3818]

i did the last question as the following: x and y both needs to be integers accurately speaking x = 53.48(y) the only y for which x is an integer is 25 but if the question has one more option let us say 50 i would need to figure the same out.

[@shrihari3306]

In Question 8, can we take 12 as 0.48% of y and directly gives us 25. The method being that that 53 is the whole no. And thus the decimal should be equal to the remainder.

[@GMATNinjaTutoring]

Absolutely -- that's a great way to solve this one!

[@Hrushi190]

Hey the 2nd last question about m and n being even or odd... Last option could result in odd OR even result right? 2+6 / 2 = 4 4+6 / 2 = 5 Could be odd or even no?

[@GMATNinjaTutoring]

In this question, m must be a multiple of 4, so it cannot be 2. It can only be one of 4, 8, 12, 16, 20... If m is a multiple of 4, then (m + 6)/2 will always be odd. For an explanation of why m must be a multiple of 4, check out the explanation in the video starting from about 42:50. I hope that helps!

[@shivamsinghal4848]

In the last question, 4 12 and 48 can't be the answer since the number of oranges left are 12. 53 can't be the answer because x/y = 53.48 (0.48 left which is again a multiple of 12). Hence the answer is 25

[@radyahhassan]

The question about chocolate bars got me hungry so I got myself a chocolate bar mid session xD. Jokes apart, thank you so much for these questions and explanations! I actually watched videos on number properties before by others but they weren't as helpful. But your explanations made it so easy! Algebra and logic can be used to solve most of these questions. Though I do struggle with time, I'm working on solidifying my concepts and then pick up my pace. Your videos have been of great help! Hoping I'll get my target score in less than two months.

[@GMATNinjaTutoring]

Thank you for the kind words! I'm so pleased you're finding the videos helpful, and it sounds like you're doing all the right things. Good luck with your studies, and please keep us posted on how you get on. Now, I'm going to find a chocolate bar...

[@harrybrar9094]

hi harry, for 2nd last que. M+N = even. we proved that m=2 x sth that means M is even. also m+n is even, from this can't we infer that N is also even. therefore, n/2 should also be an even. Can you pls explain what i am getting wrong here?

[@GMATNinjaTutoring]

It's the final step in your process that isn't correct: if we know N is even, we can't say for certain whether N/2 will be even. If N is 4, 8, 12, 16... then N/2 will be even, but if N is 6, 10, 14, 18... then N/2 will be odd. I hope that helps!

[@daniellee2023]

Would you be able to solve Q5 piecemeal at all? Like probability of n then n+2? My thinking no because multiplying the two probabilities would give us even smaller- rather than bigger- numbers, but trying to see if there's an alternative, potentially equally prescriptive way to solve this using probability tools. Thank you!!

[@GMATNinjaTutoring]

This question asks for the probability that n(n + 2) is divisible by 8. We can't find the probability that n is divisible by 8 and separately find the probability that (n + 2) is divisible by 8 and multiply the probabilities together. For example, if n = 8, then n(n + 2) = 8 * 10 = 80. This is definitely one example of a value of n that means n(n + 2) is divisible by 8 and it would count using the method you suggest because n itself is divisible by 8. However, if n = 4, then n(n + 2) = 4*6 = 24. This is also divisible by 8, but it wouldn't be counted if we were only looking for numbers where either n or (n + 2) is divisible by 8. We are suggesting you solve this question using probability tools, it's just that probability doesn't come into the question until after you've done the calculation and know the value of n(n + 2). I hope that helps!

[@navneetarora6369]

Hi Harry, great video. Had a slight tweak in logic to Q4- After reaching the Eq- 0.19L + 0.35C = 2.35, I assumed that first off C, L > 0 because he bought at least 1 of both items (implied by the statement that he only buys 2 items but still does buy both) secondly, since 0.35 x 7 = 2.45, the number of chocolates will be 6 or lower. (0.35 x 6 = 2.10, which even leaves room for 1 L) After this, we can take C = 1 through 6 and find our answer. which happens to be C= 4. But since this is a DS question, we just need to know if we can get the solution or not, so we can answer that both together are sufficient after reaching the Eq. and the 2 assumptions, Please let me know if this logic is correct. Also once again love your videos, they help a lot!

[@harryduthie]

Hi Navneet, I think your logic looks good, and I think you could say both statements are sufficient by the time you have the equation and your two assumptions. Whether you are comfortable enough to say that information is sufficient, choose (C) as the answer, and move on before you've calculated that C = 4 depends on how confident you are with the process. While I think you're right that you could click (C) and move on before doing the calculation, I suspect most people would want to KNOW if they can get an answer for the number of chocolate bars before moving on. I hope that helps!

[@varun110291]

Hello, in this question 20:00, what I did was this: 7785/360 173/8 168/8 + 5/8 So the dial would be 5 places from the current position which is 2. Is this also correct way of doing?

[@harryduthie]

Hi Varun! Your method is definitely correct and is an alternative way of doing this question. However, it probably wouldn't be the way I'd recommend because of the arithmetic you've had to complete to go from your first line to your second line. I don't think I'd be able to see that 7785 was divisible by 45 and I'd worry I'd make a mistake in the arithmetic making that division. If you're comfortable doing the arithmetic in big jumps like this, then go for it! However, I'd be far more confident dividing 7785 by 5, then by 3, then by 3 again. Doing this calculation in stages would make me more confident I was doing things correctly and avoiding errors. I hope that makes sense! Thank you for posting an alternative way of doing things!

[@lucasennouchi7060]

For the last question, my approach was: x and y must be integers, and so x=53.48y and the only solution for y to make x an integer is 25. (5*8). Hopefully this is correct :D

[@muhannidmm8453]

So the information provided to us in question 4 was clearly not enough so we couldve ruled out C and chosen E. I mean it makes sense we assume and get the answer but the whole point is of if the statement is sufficient enough or not. kindly elaborate im confused

[@GMATNinjaTutoring]

When you combine the information given in statements (1) and (2) of question 4, this information is sufficient to answer the question. The explanation from about 23:49 shows how we can conclude there is one and only one solution to the problem using the information provided without making any assumptions. Check that out and let us know if you have any further questions. I hope that helps a bit!

[@chanavijarutas809]

For Q4 can he bought 0 Lolipop?

[@GMATNinjaTutoring]

Alejandro cannot buy 0 lollipops in this scenario. From statement (1), we know he spent $2.35 in total. From statement (2), we know each chocolate bar costs $0.35. If Alejandro only bought chocolate bars, he could have spent: $0.35 if he bought 1 chocolate bar, $0.70 if he bought 2 chocolate bars, $1.05 if he bought 3 chocolate bars, $1.40 if he bought 4 chocolate bars, $1.75 if he bought 5 chocolate bars, $2.10 if he bought 6 chocolate bars, $2.45 if he bought 7 chocolate bars..... From this, we can see that there is no way Alejandro can spend $2.35 by buying ONLY chocolate bars. The solution in the video shows at about 27:00 that he must buy 5 lollipops and 4 chocolate bars to spend $2.35. I hope that helps!

[@chanavijarutas809]

@@GMATNinjaTutoring thank you for super fast response!

[@salvador4512]

Hey, I loved the approach in the last response. I was surprised I caught it myself while solving. However, don't you think you could have provided more options with, let's say, unit digits of 5? Initially, in GMAT questions, if this situation arises, I'd immediately mark 25 as the answer since 5*8 can only result in 'X' being a whole number. Also just to make things quicker for everyone for the last question: Since 53 is a whole number and 0.48 is a decimal - you can decipher that y times 53 divides x with some remainder which is leading to the decimal 0.48 - so just turn that into a fraction and boom you have the answer 48/100 leading to 12/25

[@henadoshi8120]

Hi, My doubt was for the second last question- when I take m as 6, 6+6/2 gives me 6 (an even number) - If E was the correct answer shouldn't it be true no matter what the case, even if I don't split the denominator.

[@harryduthie]

Hi Hena, By the conditions given in the question, we can show that m is a multiple of 4. This is shown in the video at about 44:15. This means that m can't be 6, it must be one of 4, 8, 12, 16, etc. If we split up the fraction in (E), we'd get m/2 + 3. Since we know m must be a multiple of 4, m/2 must still be even. We're then adding 3 to an even number which means we definitely have an odd number, so (E) cannot be even. I hope that helps!

[@henadoshi8120]

@@harryduthieIt does help, thank you so much!

[@tarynharalson1181]

For the second to last question, I don't understand how/why you chose "2k" for m/n = 2k. If I'm forgetting fundamental math, I blame it on my fried brain haha

[@GMATNinjaTutoring]

In this question, we're told that m/n is an even number. If we want to represent an even number, we can do that by taking an integer and multiplying it by 2. In this case, k represents any integer. To ensure m/n is an even integer, we can multiply k by 2, giving us m/n = 2k. I hope that helps!

[@guille7497]

Hi Harry, great vid. I dont understand the explanation for Q1. Where does the 10 play a role? We don't care about it? How would the answer differ if instead of 3^37 /10 we had 3^37 / 7 or any other number for that matter?

[@GMATNinjaTutoring]

Asking for the remainder when a number is divided by 10 is the same as asking for the units digit of that number. The remainder when 23 is divided by 10 is 3 because 23 = 10 x 2 + 3. Similarly, the remainder when 175 is divided by 10 is 5 because 175 = 10 x 17 + 5. So, if we can find the units digit of a number, we know what the remainder is when that number is divided by 10. The process would change entirely if we were asked for the remainder when 3^37 is divided by 7. This would be a much more complex question that, thankfully, wouldn't be asked on the GMAT so we don't have to worry about it. I hope that helps!

[@guille7497]

makes sense. cheers! @@GMATNinjaTutoring

[@VamsiChivukula]

Hi Harry! Thank you for yet another amazing video. As far as the last question is concerned, this is how I approached it: The fraction x/y is giving me the number of oranges per box, which is 53.48. Since I can't put 0.48 oranges in a box, I am left with 0.48th of an orange per every box that I fill with 53 whole oranges. Given that there are 12 oranges left over, the question can be reframed to "How many 0.48th's of an orange are there in 12 whole oranges?", which is basically 12/0.48 and that gives 25 boxes. Would you agree with this logic?

[@harryduthie]

Hi Surya, You're very welcome! It's so good to hear you enjoyed the video. Your logic looks good to me -- that's a great way to solve this question. Thank you for adding it to the comments!

[@VamsiChivukula]

@@harryduthie Appreciate you taking the time to comment!

[@kilianbuchgraber5546]

Would also work at Q4 to look for the lowest common multiple of 19 and 35? I think it should be sufficient as long as it is below 235, but Im not 100% sure.

[@PriyankaGupta-en6cq]

Hey Harry, in the penultimate question, if n is even n/2 should be even then why are considering it as some digit that could be even or odd after division in first example. Also in option c ie n+2/2 since n is even and divided by 2 we are getting and even number and then adding 1 to add, doesn't that make it odd itself? Can you plz guide me here I might be wrong. Thanks!

[@GMATNinjaTutoring]

Hello! The problem here is that it's not true that if n is even then n/2 will also be even. If n is 6, then n/2 is 3. Or if n is 10 then n/2 is 5. I hope that helps!

[@amyr8539]

Hi, I have a doubt. For the question at 8:49 you say that there is no way of solving it using algebra. I tried solving N=9X+4 and N=7Y+5 by equating them as 9X+4=7Y+5 and got 9X=7Y+5-4 ie 9X=7Y+1 So I just found the multiple of 9 that was one greater than some multiple of 7. Is this the wrong way of going about it?

[@GMATNinjaTutoring]

Your comment put a smile on our faces, Amy! Harry and I spent some time discussing this, and between us, we've probably challenged literally hundreds of private tutoring students to find an algebraic solution -- and basically none have succeeded. Plenty start with something similar to your initial two equations (N=9X+4 & N=7Y+5), but run into trouble from there. Often, they'll include just two variables instead of three (which isn't correct, because the quotients X and Y are different), or else they'll have no idea what to do with two equations and three variables. And then there's the REALLY hard part: if you can get to that final equation (9X=7Y+1), it's hard to make sense of it. Your interpretation is 100% correct. And out of the hundreds of students we've challenged over the years with versions of this question, I can't remember seeing a single one get to that interpretation. So take a bow, you've done a very cool thing here. The small hair I would split is that your solution is heavily algebraic, but it's not purely algebraic, just because you still have to use some logic to interpret that final equation. So this is pretty academic, but I would agree with Harry that there really isn't a strictly algebraic solution to that question. But you're spot-on: algebra can get you a long way here, as long as your algebra is strong (yours clearly is) and you can add in that final layer of logic required to make sense of the equation. Those things are hard for most GMAT test-takers (which is why we advocate a different path for most students), but you nailed both parts. Sorry, this turned into a very long-winded response, but hopefully it helps a little bit. Nice work, Amy! - Charles

[@tanvi471]

@@GMATNinjaTutoring Hey man! for the same question, why is the answer Choice C? My argument against C is that for 9x=7y+1, there's also a value of 99 that fulfills the equation for x=11 and y=14, which leaves us with two values of N implying the answer is still ambiguous. You can't decide that if N = 40 or N=99 and hence E. Am I missing something?

[@harryduthie]

Hi @@tanvi471, The problem is that N doesn't equal 99 in your solution. You're absolutely right that x = 11 and y = 14 is a solution to the equation you found, but that doesn't tell us what N is. From the first piece of information, we can find N = 9x + 4, so if x = 11, then N = 103. We can follow a similar process using the second piece of information to show that N = 103 if y =14. Since the question stem tells us that the delivery contains fewer than 100 boxes, x = 11 and y = 14 cannot be part of an answer to this question. Since we needed both pieces of information to find that N = 40 is the only solution to this question, we can say (C) is the answer. I hope that helps!

[@tanvi471]

@@harryduthie Oh yess! In my head, N was 99. Missed it to sustitute in original equations. Thanks for the detailed explanation.

[@socialcommentator21]

i am confused. For the first question, why do we need to know the units digit to find the remainder. The remainder in a particular division problem can contain multiple digits

[@harryduthie]

Hi S, In general, I completely agree: the remainder in a division problem can contain multiple digits. It just depends on what you're dividing by. However, if you think about what happens when you look for the remainder after dividing a number by 10, you're just looking for the units digit of the number you started with. For example: The remainder when 12 is divided by 10 is 2. The remainder when 2,973 is divided by 10 is 3. The remainder when 24,862,915 is divided by 10 is 5. This is a special case: the remainder and the units digit are only interchangeable when you're dividing by 10. I probably didn't make that clear enough in my explanation in the video, so thank you for your question! I hope that helps!

[@boogerbuttnose]

How did you go from 1/(5^6) to 2^6/10^6. How did the ^6 get on top.

[@harryduthie]

Hi Shelby! If you think of 1/(5^6) as (1/5)^6, then you could change the (1/5) within the parentheses to (2/10) as they're equivalent fractions. Then you'd have (2/10)^6 and you could apply the exponent to both the top and bottom of the fraction, giving (2^6)/(10^6). I hope that helps!

[@teslaecotech7076]

Please ignore my stupidity but in question 3 , I divided 7785/45 = 173. Later divided 173 / 8 = 5 is left as remainder and 21 complete circles hence added 5 steps to 5 quadrant which is 6,7,8,1 and 2 is fifth so 2nd quadrant is answer. Please explain how is this approach incorrect so that I can learn.

[@teslaecotech7076]

@harryduthie , loved each second of your video. It helps a lot of people like us who are otherwise unable to have quality education due to resources. I am grateful for your videos here.

[@harryduthie]

Hi @@teslaecotech7076! Your approach got you to the right answer and looks good to me! The method I used in the video isn't the only one you can use to reach the answer, and it looks like you found another good way to solve this question. I hope that helps, and I'm pleased you found the video helpful! I hope you enjoy the rest of the series just as much.

[@socialcommentator21]

also for the first question why are we just finding out the units digits of 3^37….? Arent we supposed to find the remainder of 3^37 when it is divided by 10? am i missing a step? thanks

[@harryduthie]

Hi S, The remainder when a number is divided by 10 and the units digit of that number are the same thing. The remainder when 53 is divided by 10 is 3, the remainder when 247 is divided by 10 is 7, and the remainder when 2,476,389 is divided by 10 is 9. You're correct in your other comment below when you say a remainder *can* contain multiple digits, but it depends on what you're dividing by. In this case, because we're dividing by 10, the remainder and the units digit of the original number are the same. I hope that helps!

[@socialcommentator21]

@@harryduthie Thanks for the reply! So Im assuming that is a general rule we should keep in mind…is there any other rules like these that we should strive to keep in mind for the GMAT…? . I think making a separate video on rules to absolutely keep in mind so that we can solve GMaT quant questions faster will really help.

[@purin586]

Difficulty ramps up from here... me not getting a single question so far XD. I can just hope I don't get these questions on the exam XD

[@shahrhave]

Probably a stupid doubt but in Q7 say (m+6)/2 where m is 2 is 4 an even number but where m is say 4, the answer is 5, that's odd. So could be even could be odd. How am I seeing it incorrectly?

[@harryduthie]

Hi Shah, Your algebra is totally correct once you've started substituting numbers into (m+6)/2. However, m can't just be any even number, m can only be a multiple of 4. So, m could be 4, 8, 12, 16.... but it can't be 2, 6, 10, 14, 18.....Therefore, the problem with your explanation is that one of your scenarios involves m = 2 and that's not possible. For an explanation of why take another look at the video from about 42:30 until 44:30. In this section, I look at what we can tell from the information provided in the question and explain why m must be a multiple of 4. Please let me know if you still have any problems after watching that section again. I hope that helps!

[@shahrhave]

@@harryduthie thanks Harry, this helps. You're doing a wonderful job and your lectures are a godsend

[@harryduthie]

@@shahrhave Great! I'm pleased that sorted things. And thank you for the kind words, it really means a lot. Good luck with the rest of your GMAT studies!

[@andrewm2000]

The best

[@natashalopez2829]

The answer to the first question is wrong i think. the remainder should be 9.

[@harryduthie]

Hi Natasha, I went back and checked the first question, just to be sure before I responded, and the remainder is definitely 3. I've put another explanation for this question below that I hope clears up any issues you're having. Please let me know if this explanation doesn't help and if you're still having problems with this question, and I'll do what I can to help. We can find the units digit of 3^37 by finding the cycle of units digits for 3^n (where n is a positive integer), and then finding the remainder of 37 divided by the cycle length. As shown in the video, the cycle of units digits for 3^n is 4: 3^1 = 3, 3^2 = 9, 3^3 = 27, 3^4 = 81, and then the cycle repeats as 3^5 =243, 3^6 = 729, 3^7 = 2187, 3^8 = 6561, etc. Since the remainder of 37 divided by 4 is 1, the units digit of 3^37 is the same as the units digit of 3^1, which is 3. I hope that helps!

[@javierromera1997]

nice!

[@srilanka739]

for question 3 can we say it is between 21-22 turns therefore still pointing at 2 ? would need to do at least 22 turns to get to 3? 360*21= 7560 degrees 7785 is between these? 360*22= 7920 degrees So as long as it is below 7920 degrees it will point at 2?

[@harryduthie]

Hi Sri Lanka, You can't say this. If the arrow has made exactly 21 turns (7560 degrees), it will be pointing at the 5. If it has made exactly 22 turns (7920 degrees), it will be pointing at the 5 again. If it has moved some number of degrees between 7560 and 7920, it could be pointing at any number on the dial depending on how far it has turned. For example, if the arrow has turned 7605 degrees (21 full turns plus 45 degrees), we could show it was pointing at the 6 by using a very similar method to the one shown in the video. However, if the arrow has turned 7650 degrees (21 full turns plus 90 degrees), we could show it was now pointing at the 7. I hope that helps!

[@dannymitchell5459]

😝 ᑭᖇOᗰOᔕᗰ

[@milenamatic-g3d]

Hi Harry, Could one argue in Q7 that none of the answers is correct? When we picked (m+6)/2 and split the fraction, we had an even number plus an odd number, which would equal an odd number. However, if m=2 (still even), (m+6)/2 = even. Let me know your thoughts.

[@harryduthie]

Hi, as discussed in the video from between about 42:40 and 44:30, we can show that m must be a multiple of 4 from the information provided in the question. That means that m cannot be 2, it must be one of 4, 8, 12, 16, 20.... If you were to substitute any of those numbers into (m+6)/2, you'd always get an odd number which means (E) is the answer to this question. I hope that helps!

[@Hrushi190]

Ohk... Got it But the question says that m+n AND (m/n) are even no? Then when we cross out the m, n being odd, odd (for m+n), doesn't that imply that m and n are BOTH even? In that case none of the options is the right answer In which case I know I am wrong somewhere but need clarity on above approach Harry can you help please EDIT - Harry already answered this, thanks Harry Even if n is even, n/2 CAN be odd or even

[@Sam66519]

In question 4 did you mean the total (monetary) value for chocolate bar would end in 5 or 0? meaning that the units digit has to end in 5 or 0? [it almost seemed like you meant the total amount of bars bought would end in 5 or 0] anyways, that would force the monetary value of lollipop to also end in 5 or 0 (so that the end result can add up to 235) so essentially since we have to add the equation up to 235 we have to make sure that the respective term’s units digits are either 5 or 0 which would then make the addition possible…. am i correct with that reasoning?

[@harryduthie]

Hi Bob, I think you're correct! Let me clarify the first paragraph of your question, just in case my explanation wasn't clear enough in the video: Since the value of one chocolate bar ends in a 5 ($0.35), it doesn't matter how many chocolate bars we have, the total monetary value of the chocolate bars will end in a 5 or a 0. After that, I totally agree with your reasoning. I hope that helps! Let me know if you have any further questions and I'll do what I can to help.