One small thing about question 6, yes its fair to just look at the top part and figure out what equals 0. However, you must check your answer to be sure that your solution for x does not make the denominator 0 as well. For instance, if (x-1) were in the denominator you could not say x = 1 is a valid solution. Of course the answer is still A but its something to be weary of.
The last question if you substitute the letter P with quadratic numbers you'd solve (4, 9 , 16 , 25) them with ease , it would save more time! , thanks :) and if after you calculate it you dont get quadratic numbers than its wrong.
Having tutired quite a number of high school students during my bachelor's for some extra money has finally come in handy😅 and also your way of approach to these problems is very nice indeed, thanks for these videos ❤
Question 1 answer doesn't make sense to me, where did you lose that additional x? (x+4)(x-3)=0 if you actually try to do this equation, it comes as x2 -3x + 4x - 12 = 0 So as you can see, it is going to be x2 + x -12 = 0 so where did you lose the x in the middle?? Question 7, how is it not answer choice A? I did it through the cross multiplication and I got 28.8? Also if there are 36 days of fuel for 20 trucks, then if you divide 36 days by the number of trucks, so 36:20=1.8 this means one truck = 1.8 days worth of fuel. So we have 16 trucks now, so 16x1.8d = 28.8. I'm not trying to argue, I'm here because I'm bad at math but however I tackle this question, it gives me 28.8 answer.
I'm sorry, I don't know what you mean by losing the additional x in question 1. If we start with x^2 + x - 12 = 0 and factor the left-hand side, we'd get (x + 4)(x - 3) = 0. If you're not sure how to perform that process, it might help to check out the factoring quadratics section in the Khan Academy link at the bottom of this message. In Question 7, we can't equate 20 trucks with 36 days and we can't equate 16 trucks with y days. However, we can use the units of each quantity to try to simplify the question a little. At the start, the company has enough fuel to run 20 trucks for 36 days, so instead of saying 20 = 36, we can multiply these numbers to get 720 truck-days of fuel. Here, we're saying that the total amount of fuel the company has in its stock is equal to the number of trucks multiplied by the number of days the company can keep that truck running. To represent this figure, we can use the made-up unit of a truck-day, where one truck-day represents the amount of fuel one truck uses per day. This means we can divide the number of truck-days of fuel we have available by the number of trucks we want to run. If we think of the units as variables, we'd be doing truck-days / trucks and we could cancel the trucks on the top and bottom of this fraction to leave us with the number of days. Doing this with the numbers involved in the question means we'd do 720 truck-days / 16 trucks to get 45 days of fuel available. I hope this helps! Link to quadratic factoring lessons: www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring
In this question, the number of trucks available to the company changed because 4 of the trucks failed a maintenance test. We know the company has enough fuel to keep its 20 trucks running for 36 days. This means the company has 20*36 = 720 truck-days worth of fuel. A stock of 720 truck-days means at one extreme the company could keep 1 truck running for 720 days. At the other extreme, the company could keep 720 trucks running for 1 day. Between those extremes, there is a range of values the number of trucks and the number of days could take. In this question, we're trying to find out how many days the company could keep 16 trucks running, so we can do 720/16 = 45 to find the answer to this question. I hope that helps!
@@MuhammadAbdullah-qk2dq NO bro if 20T =36days then 16T=____days so 36/4=9days 4T=9days so 16T=36+9 =45 days with decrease in trucks will automatically increase fuel days
@@MuhammadAbdullah-qk2dq if company have 20 trucks it can run for 36 days If company have only 1 truck then company can have it running for 36*20 days=720 days According to question, if 4 trucks fails means 16 trucks left,16 trucks can run for?? 1 truck =720 days 16 truck =720/16 =45 days
@@GRENinjaTutoring the correct answer is 28.8 if 20 trucks runs for 36 days 16 trucks would run for _ days we would cross multiply, let 16 truck run for x days (20*x)=(36*16) x=28.8 Reply
Those equations were made up to demonstrate how to use elimination when dealing with systems of linear equations. There was no development of those equations from any part of the question. They were more of a side note before we worked on the solution of the given question. I hope that helps!
Thanks teacher BUT I got 28.8days. Here is how I got my answer . Let ''y'' be the number of days the company's fuel supply will last. 20truscks =36days 16 trucks = y days (since we don't know the numbers of days for 16 trucks) Crossed multiply :) 20 y =16*36days y=16*36days /20 y= 28.8days
Unfortunately, we can't equate 20 trucks with 36 days and we can't equate 16 trucks with y days. However, we can use the units of each quantity to try to simplify the question a little. At the start, the company has enough fuel to run 20 trucks for 36 days, so instead of saying 20 = 36, we can multiply these numbers to get 720 truck-days of fuel. Here, we're saying that the total amount of fuel the company has in its stock is equal to the number of trucks multiplied by the number of days the company can keep that truck running. To represent this figure, we can use the made-up unit of a truck-day, where one truck-day represents the amount of fuel one truck uses per day. This means we can divide the number of truck-days of fuel we have available by the number of trucks we want to run. If we think of the units as variables, we'd be doing truck-days / trucks and we could cancel the trucks on the top and bottom of this fraction to leave us with the number of days. Doing this with the numbers involved in the question means we'd do 720 truck-days / 16 trucks to get 45 days of fuel available. I hope this helps!
That's a viable method, thank you for sharing it. However, we need to be a little more strict with the range of values that x can take or we'd end up selecting (D), which is not one of the correct answers, as one of our answer choices. While x can be -2, -1, or 1, x cannot be 2 because then (x - 2)(x + 3) = (0)(5) = 0 and this is not less than zero. Similarly, x cannot be between 2 and 3 because then (x - 2)(x + 3) will be positive and we want (x - 2)(x + 3) to be less than zero. By using either your method or the one shown in the video, we can say that x is between -3 and 2. This is why (B) and (C) are the answers to this question. I hope that helps!
I'm not 100% sure which inequality you're referring to. I'm going to assume you mean the inequality written in blue text on the right-hand side of the board that was written at about 42:00, but please tell me if you're asking about a different inequality. In this question, we want to know which values of x would make (x - 2)(x + 3) < 0. At that point of the solution, we'd established that x = -3 and x = 2 would make (x - 2)(x + 3) equal zero. The next step is to look at either side of these points to see whether (x - 2)(x + 3) is greater than or less than zero. This means we should examine what happens when x < -3, when -3 < x < 2, and when 2 < x. When we looked at the area where 2 < x, we found that this would mean (x - 2) would be greater than zero and (x + 3) would be greater than zero. This means that (x - 2)(x + 3) would be greater than zero when 2 < x, so 2 < x does not satisfy the inequality in the question. I hope that helps a bit, but please let me know if you have any further questions!
Yes, you can and that's essentially what Harry did in the solution. He said 20*36 = 720, so we want 16*(some variable) = 720. This is basically the same as saying 20*36 = 16*(some variable) and solving for the variable. I hope that helps!
Are you looking for practice material? If so, the official GRE guides are the best place to start: amzn.to/4g6bs8K. You can also access up to five official practice exams (two free, three paid) at ets.org/gre. I hope that helps a bit!
If x is less than -3, then x - 2 < 0 and x + 3 < 0. This means that for (x - 2)(x + 3), we would multiply two negative numbers together, giving us a positive number. This wouldn't satisfy (x - 2)(x + 3) < 0, so (A) is not one of the answers to this question. I hope that helps!
Things to rememeber: Can be true vs have to be true Truck days or jour homme, i can operate 20 trucks for 36 days or 1 truck for 20*36 or16 ttruck for 20*36/16
Hi Professor, would you mind explaining why in the trucks question we multiply 20 by 36? I don’t understand how that gives us the number of days only1 truck can run. Why are we multiplying and not dividing to see what a truck makes on one day
It might be easier to think about this question in terms of the units of each quantity. At the start, the company has enough fuel to run 20 trucks for 36 days, so instead of dividing 36 by 20, we can multiply these numbers to get 720 truck-days of fuel. Here, we're saying that the total amount of fuel the company has in its stock is equal to the number of trucks multiplied by the number of days the company can keep that truck running. To represent this figure, we can use the made-up unit of a truck-day, where one truck-day represents the amount of fuel one truck uses per day. This means we can divide the number of truck-days of fuel we have available by the number of trucks we want to run. If we think of the units as variables, we'd be doing truck-days / trucks and we could cancel the trucks on the top and bottom of this fraction to leave us with the number of days. Doing this with the numbers involved in the question means we'd do 720 truck-days / 16 trucks to get 45 days of fuel available. I hope this helps!
For us to be certain that any of these options MUST be a square number, we need to be able to rewrite them as (an integer)^2. For example, we can rewrite (A) as (12k)^2, so we know for certain that (A) is a square number. We cannot rewrite (D) as (an integer)^2, no matter how we twist of turn the algebra. Alternatively, we could look at some examples. Consider the cases in which p = 36, 49, 64, 81, or 100. , then p - 25 = 11, 24, 39, 56, or 75. In none of these cases is p - 25 equal to the square of an integer, so we cannot say that (D) MUST be the square of an integer. This is enough justification for us to say (D) is not an answer to this question. I hope that helps!
hi, in the fourth question, it was stated that x and y are two-digit integers and x is less than 35, so doesn't that exclude 1 to 9 as they are single digit numbers.
Our full GRE quant video course covers all of the key quant concepts that you'll need for the exam. The GRE can -- and sometimes does -- get creative about how it tests these quant concepts, so even if you practice every single official question out there, it's possible that a few questions will feel unusual on test day. But everything you'll see on the GRE quant section is built on the quant concepts that are covered in this series. I hope that helps a bit, and have fun studying!
There are two ways of looking at this. The first (and probably the best way of thinking about this problem) is that Harry didn't multiply this equation by a variable because he didn't multiply the equation by anything at all. He said that if you have a fraction that equals zero, then the numerator of that fraction must equal zero. That's what the first line of algebra says: Harry isolated the numerator of the fraction and said that equals zero. The second way of looking at it is to say that the eventual solution to the question is x = 1 or x = 2. If we substitute either of these options into the denominator of the original fraction then neither set of parentheses will equal zero. This means that Harry could have multiplied the equation by (x + 1)(x - 3)^2 and there wouldn't have been any problems. It's not a rule that says you can't multiply both sides of an equation by a variable. However, it's something to be very, very careful about because you don't know whether the variable equals zero. It's usually safer to avoid doing it at all but there are situations, like this one, where you can do it. I hope that helps!
for the truck queston can't we take this method 20 trucks for 36 days so 1 truck makes it run of 36/30 = 1.8 days so 16 trucks will make it run for 16 x 1.8 = 28.8 days??
Hi @VapTex, as @claschodes0855 says, the problem with the method you suggest is that reducing the number of trucks the company runs should increase the number of days its store of fuel lasts. It might be easier to think about this question in terms of the units of each quantity. At the start, the company has enough fuel to run 20 trucks for 36 days, so instead of dividing 36 by 20, we can multiply these numbers to get 720 truck-days of fuel. Here, we're saying that the total amount of fuel the company has in its stock is equal to the number of trucks multiplied by the number of days the company can keep that truck running. To represent this figure, we can use the made-up unit of a truck-day, where one truck-day represents the amount of fuel one truck uses per day. This means we can divide the number of truck-days of fuel we have available by the number of trucks we want to run. If we think of the units as variables, we'd be doing truck-days / trucks and we could cancel the trucks on the top and bottom of this fraction to leave us with the number of days. Doing this with the numbers involved in the question means we'd do 720 truck-days / 16 trucks to get 45 days of fuel available. I hope this helps!
If x < -3, then x - 2 < 0 and x + 3 < 0. This means that if we were to multiply (x - 2) and (x + 3), we'd be multiplying two negative numbers together which would give us a positive number. This positive number wouldn't satsify (x - 2)(x + 3) < 0, so (A) is not one of the correct answers to this question. I hope that helps!
Hi @@vishwasravikumar, While (D) is in the a^2 - b^2 form, the result doesn't have to be a perfect square number. If p was 169, then p - 25 = 144 and (sqrt(p) - 5)(sqrt(p) + 5) would be a perfect square. However, if p was any other number (1, 4, 9, 16, 25, 36....), then p - 25 would not be a square number. This means option (D) doesn't have to be a square number, so it is not an answer to this question. I hope that helps!
I am just starting to watch your videos and I don't even want to sleep any more, I am confident that I will pass my GRE
Haha, thank you! Make sure that you get some sleep, too -- it helps your GRE performance. :)
@@GRENinjaTutoring sir please tell the answer of 9th question its option A or B
@@LioPaul-qp7ks both
@peelolyetunembenge311 When will you be appearing for gre?
When will you be appearing for gre?
You are amazing and a life saver ❤ thanks alot for uploading this playlist.
One small thing about question 6, yes its fair to just look at the top part and figure out what equals 0. However, you must check your answer to be sure that your solution for x does not make the denominator 0 as well. For instance, if (x-1) were in the denominator you could not say x = 1 is a valid solution. Of course the answer is still A but its something to be weary of.
Thanks professor
Thank you so much for watching, Vaidehi!
@@GRENinjaTutoring sir please tell the answer of 8th question its option B or C
"Pause the video, go away..." nice
Then there's me,.... got the last one (apparently the trickiest one) correct, messed up all the easy ones🙃
loved the last question
Haha, thank you! I'm glad that you're enjoying this stuff. :)
Sir, your videos are amazing! Like your content.
Thank you, Bharat!
Great explanation. Thanks
Thank you!
thank you so much sir for such a beautiful, Lucid and coherent way of explaining algebra and arithmetic. :)
Thank you so much for the kind words, Aditya! Have fun studying.
Weldone...
The last question if you substitute the letter P with quadratic numbers you'd solve (4, 9 , 16 , 25) them with ease , it would save more time! , thanks :) and if after you calculate it you dont get quadratic numbers than its wrong.
Having tutired quite a number of high school students during my bachelor's for some extra money has finally come in handy😅 and also your way of approach to these problems is very nice indeed, thanks for these videos ❤
Thank you so much! ❤️❤️
What are the other things that would help if I have them memorized?
Excellent video btw
Question 1 answer doesn't make sense to me, where did you lose that additional x? (x+4)(x-3)=0 if you actually try to do this equation, it comes as x2 -3x + 4x - 12 = 0 So as you can see, it is going to be x2 + x -12 = 0 so where did you lose the x in the middle?? Question 7, how is it not answer choice A? I did it through the cross multiplication and I got 28.8? Also if there are 36 days of fuel for 20 trucks, then if you divide 36 days by the number of trucks, so 36:20=1.8 this means one truck = 1.8 days worth of fuel. So we have 16 trucks now, so 16x1.8d = 28.8. I'm not trying to argue, I'm here because I'm bad at math but however I tackle this question, it gives me 28.8 answer.
I'm sorry, I don't know what you mean by losing the additional x in question 1. If we start with x^2 + x - 12 = 0 and factor the left-hand side, we'd get (x + 4)(x - 3) = 0. If you're not sure how to perform that process, it might help to check out the factoring quadratics section in the Khan Academy link at the bottom of this message.
In Question 7, we can't equate 20 trucks with 36 days and we can't equate 16 trucks with y days. However, we can use the units of each quantity to try to simplify the question a little.
At the start, the company has enough fuel to run 20 trucks for 36 days, so instead of saying 20 = 36, we can multiply these numbers to get 720 truck-days of fuel. Here, we're saying that the total amount of fuel the company has in its stock is equal to the number of trucks multiplied by the number of days the company can keep that truck running. To represent this figure, we can use the made-up unit of a truck-day, where one truck-day represents the amount of fuel one truck uses per day.
This means we can divide the number of truck-days of fuel we have available by the number of trucks we want to run. If we think of the units as variables, we'd be doing truck-days / trucks and we could cancel the trucks on the top and bottom of this fraction to leave us with the number of days. Doing this with the numbers involved in the question means we'd do 720 truck-days / 16 trucks to get 45 days of fuel available.
I hope this helps!
Link to quadratic factoring lessons:
www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring
For Q7, it says to keep its 20trucks running for 36 days not keep 20trucks EACH for 30days…so i do not understand why we multiplied :(
In this question, the number of trucks available to the company changed because 4 of the trucks failed a maintenance test. We know the company has enough fuel to keep its 20 trucks running for 36 days. This means the company has 20*36 = 720 truck-days worth of fuel.
A stock of 720 truck-days means at one extreme the company could keep 1 truck running for 720 days. At the other extreme, the company could keep 720 trucks running for 1 day. Between those extremes, there is a range of values the number of trucks and the number of days could take. In this question, we're trying to find out how many days the company could keep 16 trucks running, so we can do 720/16 = 45 to find the answer to this question.
I hope that helps!
@@GRENinjaTutoring 28.8 is the answer
@@MuhammadAbdullah-qk2dq NO bro if 20T =36days then 16T=____days so 36/4=9days 4T=9days so 16T=36+9 =45 days with decrease in trucks will automatically increase fuel days
@@MuhammadAbdullah-qk2dq if company have 20 trucks it can run for 36 days
If company have only 1 truck then company can have it running for 36*20 days=720 days
According to question, if 4 trucks fails means 16 trucks left,16 trucks can run for??
1 truck =720 days
16 truck =720/16 =45 days
@@GRENinjaTutoring
the correct answer is 28.8
if 20 trucks runs for 36 days
16 trucks would run for _ days
we would cross multiply, let 16 truck run for x days
(20*x)=(36*16)
x=28.8
Reply
The last question was hardest I have ever seen
For question 3 I'm confused on how you got your starting simplified equations
the 4x+7y=29 and 2x-3y=-5
Those equations were made up to demonstrate how to use elimination when dealing with systems of linear equations. There was no development of those equations from any part of the question. They were more of a side note before we worked on the solution of the given question.
I hope that helps!
Invest in your channel, but some lights so we can see the board
Thanks teacher BUT I got 28.8days. Here is how I got my answer .
Let ''y'' be the number of days the company's fuel supply will last.
20truscks =36days
16 trucks = y days (since we don't know the numbers of days for 16 trucks)
Crossed multiply :) 20 y =16*36days
y=16*36days /20
y= 28.8days
Unfortunately, we can't equate 20 trucks with 36 days and we can't equate 16 trucks with y days. However, we can use the units of each quantity to try to simplify the question a little.
At the start, the company has enough fuel to run 20 trucks for 36 days, so instead of saying 20 = 36, we can multiply these numbers to get 720 truck-days of fuel. Here, we're saying that the total amount of fuel the company has in its stock is equal to the number of trucks multiplied by the number of days the company can keep that truck running. To represent this figure, we can use the made-up unit of a truck-day, where one truck-day represents the amount of fuel one truck uses per day.
This means we can divide the number of truck-days of fuel we have available by the number of trucks we want to run. If we think of the units as variables, we'd be doing truck-days / trucks and we could cancel the trucks on the top and bottom of this fraction to leave us with the number of days. Doing this with the numbers involved in the question means we'd do 720 truck-days / 16 trucks to get 45 days of fuel available.
I hope this helps!
I thought this too but it doesnt make sense logically that less trucks would last less time...
@@melaniestockert3070 The logic is less trucks would leave the company with more fuel thus the increase in number of days
I solved the Q8 in another method: (x-2)(x+3)
That's a viable method, thank you for sharing it. However, we need to be a little more strict with the range of values that x can take or we'd end up selecting (D), which is not one of the correct answers, as one of our answer choices.
While x can be -2, -1, or 1, x cannot be 2 because then (x - 2)(x + 3) = (0)(5) = 0 and this is not less than zero. Similarly, x cannot be between 2 and 3 because then (x - 2)(x + 3) will be positive and we want (x - 2)(x + 3) to be less than zero.
By using either your method or the one shown in the video, we can say that x is between -3 and 2. This is why (B) and (C) are the answers to this question.
I hope that helps!
how did you solve Q3, i didnt get it. could you please provide me with full steps.
I didn't understand the last solution though I tested 4 and got the right answer.
Also, dont get it how is x>2 and not
I'm not 100% sure which inequality you're referring to. I'm going to assume you mean the inequality written in blue text on the right-hand side of the board that was written at about 42:00, but please tell me if you're asking about a different inequality.
In this question, we want to know which values of x would make (x - 2)(x + 3) < 0. At that point of the solution, we'd established that x = -3 and x = 2 would make (x - 2)(x + 3) equal zero. The next step is to look at either side of these points to see whether (x - 2)(x + 3) is greater than or less than zero. This means we should examine what happens when x < -3, when -3 < x < 2, and when 2 < x.
When we looked at the area where 2 < x, we found that this would mean (x - 2) would be greater than zero and (x + 3) would be greater than zero. This means that (x - 2)(x + 3) would be greater than zero when 2 < x, so 2 < x does not satisfy the inequality in the question.
I hope that helps a bit, but please let me know if you have any further questions!
In the third last question, can we not use the unity method? equating 20 and 36, 16 and the variable?
Yes, you can and that's essentially what Harry did in the solution. He said 20*36 = 720, so we want 16*(some variable) = 720. This is basically the same as saying 20*36 = 16*(some variable) and solving for the variable.
I hope that helps!
What material can I use?
Are you looking for practice material? If so, the official GRE guides are the best place to start: amzn.to/4g6bs8K. You can also access up to five official practice exams (two free, three paid) at ets.org/gre.
I hope that helps a bit!
Hello! I had a quick question: for the second last question, why isn't A the correct answer along with B and C?
If x is less than -3, then x - 2 < 0 and x + 3 < 0. This means that for (x - 2)(x + 3), we would multiply two negative numbers together, giving us a positive number. This wouldn't satisfy (x - 2)(x + 3) < 0, so (A) is not one of the answers to this question.
I hope that helps!
Things to rememeber: Can be true vs have to be true
Truck days or jour homme, i can operate 20 trucks for 36 days or 1 truck for 20*36 or16 ttruck for 20*36/16
Square vs squre root
2 digits integer donc 9
Hi Professor where did you get the formula in Quantity A
I'm sorry, but I'm not sure which question you're asking about. Please let me know and I'll do all I can to help. Thank you!
Hi Professor, would you mind explaining why in the trucks question we multiply 20 by 36? I don’t understand how that gives us the number of days only1 truck can run. Why are we multiplying and not dividing to see what a truck makes on one day
It might be easier to think about this question in terms of the units of each quantity. At the start, the company has enough fuel to run 20 trucks for 36 days, so instead of dividing 36 by 20, we can multiply these numbers to get 720 truck-days of fuel. Here, we're saying that the total amount of fuel the company has in its stock is equal to the number of trucks multiplied by the number of days the company can keep that truck running. To represent this figure, we can use the made-up unit of a truck-day, where one truck-day represents the amount of fuel one truck uses per day.
This means we can divide the number of truck-days of fuel we have available by the number of trucks we want to run. If we think of the units as variables, we'd be doing truck-days / trucks and we could cancel the trucks on the top and bottom of this fraction to leave us with the number of days. Doing this with the numbers involved in the question means we'd do 720 truck-days / 16 trucks to get 45 days of fuel available.
I hope this helps!
Im a bit confused on the last question, can you explain more on why D is not a correct response?
For us to be certain that any of these options MUST be a square number, we need to be able to rewrite them as (an integer)^2. For example, we can rewrite (A) as (12k)^2, so we know for certain that (A) is a square number.
We cannot rewrite (D) as (an integer)^2, no matter how we twist of turn the algebra. Alternatively, we could look at some examples. Consider the cases in which p = 36, 49, 64, 81, or 100. , then p - 25 = 11, 24, 39, 56, or 75. In none of these cases is p - 25 equal to the square of an integer, so we cannot say that (D) MUST be the square of an integer. This is enough justification for us to say (D) is not an answer to this question.
I hope that helps!
hi,
in the fourth question, it was stated that x and y are two-digit integers and x is less than 35, so doesn't that exclude 1 to 9 as they are single digit numbers.
my bad, i did not notice that the-question was to find the maximum value, not the range of all possible vlaues
Sir, will there be any different kind of a problem in gre or all the types are covered in the video?
Our full GRE quant video course covers all of the key quant concepts that you'll need for the exam.
The GRE can -- and sometimes does -- get creative about how it tests these quant concepts, so even if you practice every single official question out there, it's possible that a few questions will feel unusual on test day. But everything you'll see on the GRE quant section is built on the quant concepts that are covered in this series.
I hope that helps a bit, and have fun studying!
Square vs squre root
for q6, isnt it a rule that you cannot multiply both sides with a variable because you never know whether the variable is zero or not?
There are two ways of looking at this. The first (and probably the best way of thinking about this problem) is that Harry didn't multiply this equation by a variable because he didn't multiply the equation by anything at all. He said that if you have a fraction that equals zero, then the numerator of that fraction must equal zero. That's what the first line of algebra says: Harry isolated the numerator of the fraction and said that equals zero.
The second way of looking at it is to say that the eventual solution to the question is x = 1 or x = 2. If we substitute either of these options into the denominator of the original fraction then neither set of parentheses will equal zero. This means that Harry could have multiplied the equation by (x + 1)(x - 3)^2 and there wouldn't have been any problems.
It's not a rule that says you can't multiply both sides of an equation by a variable. However, it's something to be very, very careful about because you don't know whether the variable equals zero. It's usually safer to avoid doing it at all but there are situations, like this one, where you can do it.
I hope that helps!
for the truck queston can't we take this method
20 trucks for 36 days
so 1 truck makes it run of 36/30 = 1.8 days
so 16 trucks will make it run for 16 x 1.8 = 28.8 days??
I did the same, but think logically, reducing the number of trucks will reduce the fuel consumption and increase days
Hi @VapTex, as @claschodes0855 says, the problem with the method you suggest is that reducing the number of trucks the company runs should increase the number of days its store of fuel lasts.
It might be easier to think about this question in terms of the units of each quantity. At the start, the company has enough fuel to run 20 trucks for 36 days, so instead of dividing 36 by 20, we can multiply these numbers to get 720 truck-days of fuel. Here, we're saying that the total amount of fuel the company has in its stock is equal to the number of trucks multiplied by the number of days the company can keep that truck running. To represent this figure, we can use the made-up unit of a truck-day, where one truck-day represents the amount of fuel one truck uses per day.
This means we can divide the number of truck-days of fuel we have available by the number of trucks we want to run. If we think of the units as variables, we'd be doing truck-days / trucks and we could cancel the trucks on the top and bottom of this fraction to leave us with the number of days. Doing this with the numbers involved in the question means we'd do 720 truck-days / 16 trucks to get 45 days of fuel available.
I hope this helps!
Good job. I hate this question @15:57.
Haha, thank you! And yes: that one isn't the most enjoyable question ever. :)
Have fun studying!
is there any WhatsApp group that we send the questions that we are not able to solve, and others share their info and questions with us?
We haven't set anything like that up, but if other viewers are interested in doing something like that, we'd happily cheer you on!
you sound exactly like Jon Snow
For Question 8, why couldn't a be an answer ?
If x < -3, then x - 2 < 0 and x + 3 < 0. This means that if we were to multiply (x - 2) and (x + 3), we'd be multiplying two negative numbers together which would give us a positive number. This positive number wouldn't satsify (x - 2)(x + 3) < 0, so (A) is not one of the correct answers to this question.
I hope that helps!
sir please tell the answer of last question
The answer to the final question is both (A) and (B). You'd need to select both options to get this question correct.
I hope that helps!
@@GRENinjaTutoring but isnt option d in a2 - b2 form so shouldnt it be marked aswell ?
Hi @@vishwasravikumar,
While (D) is in the a^2 - b^2 form, the result doesn't have to be a perfect square number.
If p was 169, then p - 25 = 144 and (sqrt(p) - 5)(sqrt(p) + 5) would be a perfect square. However, if p was any other number (1, 4, 9, 16, 25, 36....), then p - 25 would not be a square number.
This means option (D) doesn't have to be a square number, so it is not an answer to this question.
I hope that helps!
Seth Rogen after going bankrupt😂
And after doing a whole lot of bench presses, I guess? 😆
Your long pauses are annoying! It's not like a live class where someone watching cannot hit pause!!!
@8:14
@11:46
@20:14