GMAT Ninja Quant Ep 6: Ratios

[@santoshinimahadev]

sir, your teaching methods are extremely clear.

[@rodamaster]

Great video! For Q8 I used pure logic and intuition: Statement 1: ..."is greater for the whole university than for the men"-> lesser for men -> greater for women, so the ratio is greater for women. Statement 2: "fewer than half are men"-> +1/2 are women and "more than half are men" -> less than a half is women -> we divide and the ratio is greater for women.

[@parvindernogi6264]

I can’t have a third of swimmer, it will be weird floating around the swimming pool 😂😂😂

[@thebaratheon]

last question - the number of women can be 0 (there was NO restriction indicating that there must be at least 1 person of each gender in French or Spanish). in a hypothetical case of 75 total students in French and 25 total students in Spanish, the ratio of F:S for men can be 40:25, and F:S for women can be 10:0. If this is the case, how can this be compared at all if the ratio for women is undefined? The answer should be E based on the lack of limitations given in the question stem.

[@harryduthie]

Hi Baratheon, Good spot! You're right: this question is missing a restriction and has a problem with it as it is written. Given the chance to rewrite this question, I'd find a way of including the restriction that there is at least one male and at least one female major in both languages. This is another example of how difficult it is to write good GMAT questions. The real questions go through much, much more testing than we could manage with the questions for these videos, so you shouldn't run into a problem like this on the real GMAT exam. Thanks for commenting!

[@jamesbridgetteray2759]

I am very confused with question 8. You began crossing out A, B, C, and E what are those in reference to? I am really struggling to understand the w

[@lakhangupta1828]

I know its too late to reply to your question but here is my best shot to explain it to you: The ratio of french to spanish for university as a whole means the average of ratio of french to spanish for women and ratio of french to spanish for men. If the average ratio is greater than the ratio for men, then the ratio for women has to be greater than the average ratio. I hope this helps.

[@lucianopavarotti-yq3pf]

You are awesome

[@CareerGroovesWithOleg]

Thank you for the video, very helpful! Just have concern about Q6. It has a very bad wording choice - it unclear what the calculated ratio of 5:2:20 means. Is it the ratio just for the afternoon or is it the ratio for the whole business day? Ofc if it is just for the afternoon, then the question is obvious, but it is not explicitly stated. In fact, wording choice in this question means (at least for me) that this calculated ratio of 5:2:20 represents the ratio of orders for the whole day, that is for the morning plus afternoon (initial ratio after morning orders became 5:2:20). And in this case the answer would be 10. Yes, no such answer is provided, so we can understand that something else is meant, but why do I need to guess what was meant in the question?

[@saksrocks1]

Hi - Interesting observation in Question 8. If a/b>c/d ; then (a+c)/b+d lies between a/b and c/d. While I was not initially able to decipher it by intuition, I think we can arrive at the result by assuming a/b>c/d and then adding cd and ab separately to both sides. then c/d

[@tarynharalson1181]

Question about #8 -- When you pushed the question, you ended up coming to Fw/Sw > Fm/Sm. Then by the end of statement 1, you ended up with Fw/Sw > Fm/Sm, which matches the question. How is statement 1 alone not sufficient?

[@GMATNinjaTutoring]

Hi there! Statement 1 is sufficient, that's why we crossed out BCE and were left with A and D as possible answer choices. Since statement 2 was also sufficient by itself, we crossed out A and chose D as the answer to this question. I hope that helps!

[@ngoichoixoinuoc2743]

Q3, I did differently but somehow still comes to the correct answer. c/h = 1/5 => c= h/5 we have d/c = 4/3 => d/ (h/5) =4/3 => d/h = 20/3

[@bonasusan]

Hi @gmatclub in Q 5 they said guards to swimmers ratio must be atleast 3:10, so shouldnt the inequality sign be greater than or equal to?

[@GMATNinjaTutoring]

Yes, you're right. That was a slip-up in the notation there. Instead of saying L/S > 3/10, we should have said L/S >= 3/10. It doesn't make a difference to the final answer, but it's important to be accurate with these things. Thank you for pointing it out!

[@pranavagarwal5605]

Awesome explanation to each question! I have a doubt in question 5. Isn't at least translated into inequality as 'greater than or equal to' instead of 'greater than'?

[@harryduthie]

Hi Pranav, You're right! That's totally my fault for being a little sloppy with my notation in the solution. It doesn't change the answer, but I should have used the 'greater than or equal to' sign in that question. Thank you for pointing it out!

[@ArshdeepSingh-ek6su]

hello, just a query in question 5. Supposedly, on solving the value comes out to be 23.8888. Then what are we supposed to choose in that case? 23 or 24?

[@harryduthie]

Hi Arshdeep, This is explained in the video starting at 30:50. Please let me know if you have any questions after you've watched that section and I'd be happy to help!

[@AkritiKhetawat]

Hi team, in Q7, since it says the cost rose by p%, doesn't it mean p already includes p/100 and we don't have to include it again? This is where I went wrong in that question but I'm not sure why we divide by 100 again.

[@GMATNinjaTutoring]

The percent symbol (%) represents a percentage, which is a number or ratio expressed as a fraction of 100. This means that 50% is the same as 50/100, and p% means p/100. Whenever you see something expressed with a percentage symbol, the symbol means you should divide that by 100 when you use it in algebra. I hope that helps!

[@tudorsafta3742]

Quick query for Q4- in the final formula we have (5x-2)/(2x+8) = 3/2 ; my question is why is it equal to 3/2 as if we definitively know there are 3 cars and 2 trucks left? My understanding is the formula should equal 3x/2x. Where am I misunderstanding?

[@GMATNinjaTutoring]

The (5x - 2) on the left hand side represents the actual number of cars after the changes described in the question, and the (2x + 8) represents the actual number of trucks. If we knew the value of x, we'd be able to find the numbers of cars and trucks. If we could then simplify this fraction, we'd have the ratio of the cars to trucks. This was given in the question as 3/2 so we can make the two sides of this equation equal each other. I hope that helps!

[@tudorsafta3742]

@@GMATNinjaTutoring That makes sense, the 3/2 is the final ratio, not necessarily the final ‘count’. Thanks for explaining and a sincere thank you for the free tutoring you provide!

[@randyorton9863]

Hey guys, why'd question 4 suddenly change answer choices around 21:20?

[@nehashashidhar462]

woahh great observation. I feel they had given wrong choices so they changed

[@ashshettyvlogs3220]

Loved the 8th question. I have a doubt 'in Q5, isnt "atleast" be L/S >= 3/10 instead ?'

[@GMATNinjaTutoring]

Yes! You got me, it should be L/S >= 3/10. Thankfully, it doesn't make a difference to the outcome of this question, but I should have been more careful with my notation in this solution. Thank you for the comment!

[@АртурТайжанов-щ2с]

I wish I had such teacher at school

[@GMATNinjaTutoring]

Thank you for the kind words! I'm so pleased you found the video helpful. Best of luck with your GMAT studies and please let us know how you get on.

[@TamirKalderon-v6o]

Question 7 is very hard... Also its very annoying i cant see i can cancel R/B... IT took Me 3 more steos

[@preyanshisingh1476]

great video.. i had a doubt although in question 8. hypothetically, what if we could say a definitive yes with statement 1 and a definitive no if we went with statement 2. in this case what would be the correct option? A or E?

[@harryduthie]

Hi Preyanshi! Thank you for the kind words! In Data Sufficiency, you're always trying to work out if you have enough information to answer the question. It doesn't matter whether the answer is yes or no. We're trying to see if the information provided is sufficient to reach an answer. If you can use one statement to definitively say yes, that statement is sufficient. Similarly, if you can use one statement to definitively say no, that statement is sufficient. However, in a real GMAT DS question, the situation will be consistent across both statements. The hypothetical you presented wouldn't happen as there wouldn't be a question in which we could definitively say yes using statement 1 and definitively say no using statement 2. One statement may or may not provide sufficient information to answer the question, but it won't provide information that contradicts the information presented in the other statement. I hope that helps!

[@preyanshisingh1476]

@@harryduthie thankyou so much for taking time in writing such descriptive explanation.. it helped a lot❤️

[@Xoustus]

Hello Harry, For Q1, why did you divide by 14 and how did you get that answer?

[@GMATNinjaTutoring]

Hi Xavier, this is explained in the solution in the video between around 5:40 and 8:20. It would be more difficult to explain the answer to your question here than it would be for you to watch this part of the video. Check that out and please let me know if you have any other questions!

[@Xoustus]

@@GMATNinjaTutoring thanks for your response. I have never seen the numerator divided for in a ratio.

[@justzzzzletgo]

Thank you for the insightful video, I have a question for the 7th problem. Since they had asked for % change, can't I write the eqn directly as [((100+p)-(100-q))/(100+q)]*100? Please let me know why this isnt ok if I made a conceptual error. Thank you.

[@GMATNinjaTutoring]

Algebraically, that's going to get you the correct answer and it's going to get you there very quickly. My question would be: what do you mean when you say to write the equation directly? I'd love to know how you knew this was the correct equation. Thank you!

[@justzzzzletgo]

@@GMATNinjaTutoring Hi Harry., there's probably been a slight misunderstanding of the problem from my side. I directly substituted the p and q in the formula -> new -old/old where new = 100+p and old = (100+q) since i took into consideration only the change in percentage part.

[@GMATNinjaTutoring]

Hi @@justzzzzletgo, thank you for responding, I can see the misunderstanding now. This question asks us to find the percentage change in "THE RATIO of the cost of renting an apartment to the cost of buying an apartment." This means that the 'old value' in the formula you mentioned will be the ratio before the changes were applied, and the 'new value' will be the ratio after the changes are applied. We could say R is the cost of renting an apartment and B is the cost of buying an apartment since we aren't given values for these costs in the question. This means the 'old ratio' will be R/B. The changes are then applied to these new variables to get the 'new value' in the formula. The cost of renting an apartment has increased by p percent, so the new cost of renting an apartment is R(1 + p/100). Similarly, the new cost of buying an apartment is B(1 + q/100), so the 'new ratio' is [R(1 + p/100)]/[B(1 + q/100)]. The way you approached this question worked on this problem, but I don't think it would work on other similar problems. It's unlikely that only considering the change in percentage part will work in every question of this sort. I hope that helps!

[@justzzzzletgo]

@@GMATNinjaTutoring yup. It does. Thank you!!

[@user-jd5uq6lg6z]

This was great. Thanks sir!

[@GMATNinjaTutoring]

You're welcome! I'm pleased you enjoyed the video. Best of luck with your studies and please keep us posted on how you get on.

[@lenal2092]

Hello ! For question 3 the question says there are 5 times as many cats as hamsters and you wrote C = 5H but wouldn't that translate to H = 5C ?

[@GRENinjaTutoring]

If there are five times as many cats as hamsters, that tells us there are more cats than hamsters. So it makes sense to multiply a small number by five to get a bigger number. Back to the equation -- since H is smaller than C, we'd want to multiply the smaller number by 5 to get the bigger number. That would give 5H = C. You can confirm this logic with some numbers. If there are 5 times as many cats as hamsters, then H could equal 2 and C could equal 10. Since 2 x 5 = 10, this confirms that H x 5 = C. I hope that helps!

[@jettfuku5893]

i didnt understood 7th Question, the new renting after increase of p% how did the equation formed-R(1+p/100)

[@GMATNinjaTutoring]

We could say the new rental cost is the old rental cost (R) plus the increase in the rent. To find the increase, we need to find what p% of the current rental cost (R) is. We do this by multiplying R by p/100, which gives Rp/100. This means the new rental cost is the old rental cost (R) plus the increase in rent (Rp/100). Expressing this algebraically gives R + Rp/100, and we can factor out a common factor of R to give R(1 + p/100) I hope that helps!

[@Sam66519]

hmm in question number 2 why did you use x for both lemons and limes...? shoudnt lemon be x and lime b y since they are probably different amounts?

[@harryduthie]

Hi Bob, The x in this solution doesn't represent the number of lemons or the number of limes, it represents the number of 'groups' of 7 lemons and 5 limes that make up the ratio. There definitely are different amounts of lemons and limes as we know they're in the ratio 7:5. However, even though we know the ratio of lemons to limes, we don't know the actual number of fruit. If x represents the number of 'groups' of 7 lemons and 5 limes, once we know the value of x, we'll know the actual number of lemons and limes in the fruit bowl. If x = 1, then we'll have 7 lemons and 5 limes but if x = 2, then we'll have 14 lemons and 10 limes, and so on. That information is enough to answer this question. I hope that helps!

[@priyankajaiswal8485]

@@harryduthie why option no. 2 will not give the answer as we can take 7*2(lemon)=14 + 5*6(lime)=30 => 44, even two is the possible solution??

[@harryduthie]

Hi @priyankajaiswal8485 ! We can't take a different value for the number of 'groups' of lemons and the number of 'groups' of limes. If we have 2 'groups' of lemons, we must also have 2 'groups' of limes. This would give us 7*2 + 5*2 = 24 pieces of fruit. If we have 6 'groups' of limes, we must also have 6 'groups' of lemons. This would give us 7*6 + 5*6 = 72 pieces of fruit. Since we know we'll have the same number of 'groups' of lemons and limes, we know the total number of fruit must be a multiple of 20 since 7x + 5x = 12x (where x represents the number of 'groups'). Since 42 is not a multiple of 20, option II could not be the number of fruit in the bowl. I hope that helps!

[@audreysfavmelodies]

For question 6 why did you not simplify the ratio for C:W from 5:20 to 1:4? So then minimum # of coffee orders would have been 1 making the answer A?

[@harryduthie]

Hi Audrey, We need to keep in mind the number of tea orders made in the afternoon as well. We found the ratio of coffee to tea orders made in the afternoon is 5 : 2. If you reduce the coffee to water ratio to 1 : 4 and say that only one coffee order was made, the coffee to tea ratio reduces to 1 : 0.4. Since it doesn't make sense to say that 0.4 tea orders were made that afternoon, it can't be true that the minimum number of coffee orders is 1. In order to make the situation make sense, we need to combine the ratios as I did in the video to give the ratio of coffee to tea to water of 5 : 2 : 20. Since this ratio can't be reduced any further, the minimum number of coffee orders that could have been made is 5. I hope that helps!

[@audreysfavmelodies]

@@harryduthie Thank you! Just seeing this response. It does!

[@sankalptripathi5787]

It was given in question no.3 that 4 dogs for each 3 cats, so the ratio should be 3/4?

[@harryduthie]

Hi Sanky, If there are four dogs for every three cats, then we could say 3D = 4C. Writing it like this would make both sides of the equation equal if we had four dogs and three cats, or eight dogs and six cats, or twelve dogs and nine cats. From there, we could rearrange the equation to say D/C = 4/3, so the ratio of dogs to cats could be written as 4/3 or as it is in the solution as D:C = 4:3. I hope that helps!

[@sankalptripathi5787]

@@harryduthie Thank you sir

[@pierof6837]

Sorry, but why in ex3 (cats, dogs and hamsters) when you combine the 3 ratios, under the "column" dog, you calculate 3*5=15...while in the ex.6 (coffee,tea and water), under the column "coffee" you put only 5 and not 5*5

[@GMATNinjaTutoring]

When we combine two 2-item ratios to find a single 3-item ratio, we focus on the item that appears in both ratios and find the LCM of the values for that item. In Q3, cats have a value of 3 in the ratio with docus and a value of 5 in the ratio with hamsters. The LCM of 3 and 5 is 15, so that's what appears in the final, 3-item ratio. In Q6, however, when we combine the two ratios at the end, coffee has a value of 5 in the ratio with tea and a value of 5 in the ratio with water. The LCM of 5 and 5 is just 5, so we don't need to multiply anything to get the final value in this column. I hope that helps!

[@pierof6837]

@@GMATNinjaTutoring Thank you!!!

[@jamesbridgetteray2759]

Why did you cross multiply? Could you explain that step?

[@harryduthie]

Hi James & Bridgette! Could you please let me know which question you'd like me to explain further? I'd be happy to help but since I cross multiplied several times in the video, I'll need to know which question you're struggling with.

[@jamesbridgetteray2759]

@@harryduthie I was able to figure this problem out, thank you

[@freen773]

question 3: isn't it pretty obvious it is E? A and B eliminated because dogs > cats > hamsters. c and d cannot be because those are just the ratio between dogs and cats and cats and hamsters respectively so it couldn't possibly be dogs to hamsters? to double check just multiply the ratios together to get to E -> 4*5 and 5*1

[@GMATNinjaTutoring]

Yes - that's a great point! As you suggest, there are sometimes questions where logic alone will help you eliminate wrong answers, even without any calculations. If you're lucky, maybe you'll have only one left, as happens with this problem. Thanks for the comment!

[@freen773]

@@GMATNinjaTutoring tanks for the response! was it just a coincidence that the two ratios multiplied together also came to the correct solution? (assuming each ratio couldn't be simplified further)

[@GMATNinjaTutoring]

Yes, that was just a coincidence from the numbers involved in this question. I wouldn't suggest relying on that method to work in another question.

[@matthijsmelgers960]

@harryduthie First of all, thanks for the video. I have a question about Q7. Could you explain to me why the like terms of R/B cancel out? For some reason my mind can't comprehend it. Thanks in advance.

[@GMATNinjaTutoring]

Trying to write the algebra out in this comment is going to get pretty ugly, but I'll see what I can do to answer your question. There are three terms in the equation at that point. There's [R(1 + p/100)]/[B(1 + q/100)], the R/B on the top line, and the R/B on the bottom line. If we consider the first, more complicated term first, we could rephrase this as (R/B) * [(1+p/100)/(1+q/100)]. This means all three parts of this equation have a common term of R/B, so we can perform the division and cancel out the R/B terms. This process is identical in structure to having (4x + 2)/2. We can divide each of the three terms in that expression by 2, so we could cancel out the 2s and we'd be left with (2x + 1)/1 or just 2x + 1. I hope that helps!

[@honiajamal5056]

please higher quality on the vids

[@s.m.shariqueanwar8730]

video is hazy, texts are not clear.

[@lennyppm]

For Q8, what about non binary students?

[@shivaniherlekar6043]

Hi I’m stuck on following the meaning of “ 5 times as many cats as hamsters “ clearly my logic brain goes to interpreting there are Five multiples of cats for each hamster ( h = 5c)! Please help 🥹

[@harryduthie]

Hi! Your logic is perfect, there are five cats for each hamster! However, the problem is coming when you translate your understanding of what the words say into algebra. If we assume we've got a situation where there is one hamster and five cats, then we would need to multiply the number of hamsters (h = 1) by 5 (5h = 5) to get the number of cats (c = 5). From this, we can say 5h = c. I hope that helps!