We like giving you a challenge at the end of these videos! That one is indeed tough -- fair game on the GRE, but not something you need to get right unless your goal is a super-elite quant score. For most applicants, that nasty final question is very much optional. :) Have fun studying!
I actually visualized the circles in a way they would fit in the circle if they were cut in 2 so we'd have 4 smaller parts and how we would fit them within the circle, then i just guessed it would be 1/2 no way I can calculate this with 90sec time for a question
@@martynadydyk9714 yeah i did it the same way, but it's risky since it could be deceptive too. But anyways it's better than wasting 3 minutes behind a question that you eventually might get wrong.
The base of the equilateral triangle Alex drew on the board at about 28:20 is 8. When he splits that triangle with the dashed line at about 28:35, then we have two triangles that each have a base of 4. We want to find the area of the original equilateral triangle Alex drew at about 28:20. This means the base of the triangle is 8, and Alex demonstrated that the height of the triangle is 4sqrt(3), meaning that the area of this triangle is 0.5*8*4sqrt(3). I hope that helps!
For question 3 just imagine it in 3d and see that D is 0,0,0 and A is 0,2,0 and point E is 0,2,11 and lastly point C is 10,0,0. Now use distance formula on C and E and you'll get 15
Hi @@JennyLiang-oi9zc, This is based on a property of isosceles triangles. We can draw a line that bisects angle AOB and that reaches the side AB. Since AOB is an isosceles triangle, we know that the angle between the line we've drawn and AB will be 90 degrees. You can find a proof of this property through the following link: www.nagwa.com/en/explainers/973164576417/#:~:text=Corollary%20of%20the%20Isosceles%20Triangle%20Theorems,and%20is%20perpendicular%20to%20the%20base. I hope that helps!
I tried to write out an answer to your question, but it's really hard to explain something like this without a diagram. Instead, I filmed a quick video: ruclips.net/video/dIzacjZ8W5g/видео.html I hope this helps! Here's a link to the proof I mentioned in the video that the perpendicular bisector of a chord passes through the center of a circle: www.nagwa.com/en/explainers/567105213104/
@@GRENinjaTutoring Brilliant! It answers my question. And words can't express how grateful I am to you for answering it this quick. Incredibly kind of you to make a video about it. Thanks a ton! Will always remember this generosity🙏
In somae problemes with circles you should ifnd tigonometry relations between the r of the different circles, like a right isoscele triangle with 90 45 45, withe the hypotoneuse R1 AND THE OTHER SIDE R2
Question two is wrong, there are no solutions for the two equations l^2 + w^2 = 81 and l*w = 20, a rectangle with diagonal 9 and area 20 simply does not exist.
There definitely aren't any integer solutions to these equations, but we can find a solution. If the length of the rectangle is 8.70156 and the width is 2.29844 then we get l^2 + w^2 = 81, l*w = 20, and l + w = 11. I hope that helps!
@@GRENinjaTutoring i stand corrected should've plugged those numbers in mathway before i comment but oh well. Thanks for the videos really appreciate them.
@@visheshgupta9663 yeah, I plotted the functions in desmos to find the solutions. There's no way I'd expect to have to find these values in a GRE question. Thank you for commenting, and please let us know if you have doubts about any other questions. We're the first to admit we're not perfect and have made mistakes in other questions. Good luck in your studies!
Yup, that's what the GRE feels like sometimes! Part of what makes these tests challenging is that the wrong answers sometimes look right, and the right answers sometimes look wrong. That's often the case on both verbal and quant on the GRE. So yes, sometimes the answers don't feel intuitive or correct. But everything in this video is indeed correct, for better or worse. :) I hope that helps a bit, and have fun studying!
Could you please assist us in our learning process by identifying any questions you believe to be incorrect? You know, the ultimate goal is learning. I have personally found this site to be engaging and informative. Therefore, rather than simply raising doubts, it would be greatly beneficial if you could pinpoint specific questions you feel may have incorrect answers or explanations, and provide reasoning for why you believe they are incorrect.
@@hagoskalu7293 Q.4 31:42 he states he uses the formula A=1/2 *b*h which after he plugs in his values it would be (1/2 )*8* 4 sqrt(3) . That assumes the base is 8. I think the base should be 4 bc 8cos(60) = 4 (base) and 8sin(60) = 4sqrt(3) (height) . If you want me to further break down why I believe he is wrong, I can.
@@seabasschukwu6988 I understand the point you're making, and I see where the confusion lies. It seems he's calculating the area of one of the six equilateral triangles, each with sides of length 6. He's decomposed one of these triangles into two 30-60-90 triangles to find the height, and indeed, these triangles have a base of 4. If you wish to compute the area for this triangle, you can proceed, but ultimately, you'll need to multiply the entire area by 12, not 6, since there are a total of 12 30-60-90 triangles. Personally, though, I find this to be a bit of a time-consuming process. But I still insist he made no mistake in this regard, with due respect.
Last question killed me lmao
We like giving you a challenge at the end of these videos! That one is indeed tough -- fair game on the GRE, but not something you need to get right unless your goal is a super-elite quant score. For most applicants, that nasty final question is very much optional. :)
Have fun studying!
I actually visualized the circles in a way they would fit in the circle if they were cut in 2 so we'd have 4 smaller parts and how we would fit them within the circle, then i just guessed it would be 1/2 no way I can calculate this with 90sec time for a question
@@martynadydyk9714 yeah i did it the same way, but it's risky since it could be deceptive too. But anyways it's better than wasting 3 minutes behind a question that you eventually might get wrong.
Goldmine for GRE students like me. My test is on 2nd September and the playlist is really helpful for me to revise the topics.
How much did you score? Just curious😅
THANK YOU VERY MUCH. Que no. 4 and 8 were too awesome. especilally que number 8
Thank you for enjoying them! :)
Q.4 31:42 he states 1/2 8* 4 sqrt(3) is the answer. That assumes the base is 8. I think the base should be 4. Please clarify if im wrong
The base of the equilateral triangle Alex drew on the board at about 28:20 is 8. When he splits that triangle with the dashed line at about 28:35, then we have two triangles that each have a base of 4.
We want to find the area of the original equilateral triangle Alex drew at about 28:20. This means the base of the triangle is 8, and Alex demonstrated that the height of the triangle is 4sqrt(3), meaning that the area of this triangle is 0.5*8*4sqrt(3).
I hope that helps!
Helpful
For question 3 just imagine it in 3d and see that D is 0,0,0 and A is 0,2,0 and point E is 0,2,11 and lastly point C is 10,0,0. Now use distance formula on C and E and you'll get 15
@46:12 How do you know that the pair of triangles are symmetrical when you "cut" them to find the height?
Like, how do you know absolutely for sure that the line AB would be perpendicular to the height?
Hi @@JennyLiang-oi9zc,
This is based on a property of isosceles triangles. We can draw a line that bisects angle AOB and that reaches the side AB. Since AOB is an isosceles triangle, we know that the angle between the line we've drawn and AB will be 90 degrees.
You can find a proof of this property through the following link:
www.nagwa.com/en/explainers/973164576417/#:~:text=Corollary%20of%20the%20Isosceles%20Triangle%20Theorems,and%20is%20perpendicular%20to%20the%20base.
I hope that helps!
okay i need a little intuition for the last question. How can we say for sure that the semicircles touch each other at the centre of the large circle?
I tried to write out an answer to your question, but it's really hard to explain something like this without a diagram. Instead, I filmed a quick video:
ruclips.net/video/dIzacjZ8W5g/видео.html
I hope this helps!
Here's a link to the proof I mentioned in the video that the perpendicular bisector of a chord passes through the center of a circle:
www.nagwa.com/en/explainers/567105213104/
@@GRENinjaTutoring Brilliant! It answers my question. And words can't express how grateful I am to you for answering it this quick. Incredibly kind of you to make a video about it. Thanks a ton! Will always remember this generosity🙏
You're welcome! I'm so pleased it helped.
Good luck with your GRE studies, and please keep us posted on how you get on!
In a triangle: the larger teh angle, the larger the opposite side ( thats why sin is increasing)
Area of a regular hexagon using equilqteral triangles
In equilqterql triangles, the height of the triangle cuts the base in the middle
In somae problemes with circles you should ifnd tigonometry relations between the r of the different circles, like a right isoscele triangle with 90 45 45, withe the hypotoneuse R1 AND THE OTHER SIDE R2
Question two is wrong, there are no solutions for the two equations l^2 + w^2 = 81 and l*w = 20, a rectangle with diagonal 9 and area 20 simply does not exist.
There definitely aren't any integer solutions to these equations, but we can find a solution. If the length of the rectangle is 8.70156 and the width is 2.29844 then we get l^2 + w^2 = 81, l*w = 20, and l + w = 11.
I hope that helps!
@@GRENinjaTutoring i stand corrected should've plugged those numbers in mathway before i comment but oh well. Thanks for the videos really appreciate them.
@@visheshgupta9663 yeah, I plotted the functions in desmos to find the solutions. There's no way I'd expect to have to find these values in a GRE question.
Thank you for commenting, and please let us know if you have doubts about any other questions. We're the first to admit we're not perfect and have made mistakes in other questions. Good luck in your studies!
i honestly think some of these answers are wrong
Yup, that's what the GRE feels like sometimes! Part of what makes these tests challenging is that the wrong answers sometimes look right, and the right answers sometimes look wrong. That's often the case on both verbal and quant on the GRE.
So yes, sometimes the answers don't feel intuitive or correct. But everything in this video is indeed correct, for better or worse. :)
I hope that helps a bit, and have fun studying!
Could you please assist us in our learning process by identifying any questions you believe to be incorrect? You know, the ultimate goal is learning. I have personally found this site to be engaging and informative. Therefore, rather than simply raising doubts, it would be greatly beneficial if you could pinpoint specific questions you feel may have incorrect answers or explanations, and provide reasoning for why you believe they are incorrect.
@@hagoskalu7293 Q.4 31:42 he states he uses the formula A=1/2 *b*h which after he plugs in his values it would be (1/2 )*8* 4 sqrt(3) . That assumes the base is 8. I think the base should be 4 bc 8cos(60) = 4 (base) and 8sin(60) = 4sqrt(3) (height) . If you want me to further break down why I believe he is wrong, I can.
@@seabasschukwu6988 I understand the point you're making, and I see where the confusion lies. It seems he's calculating the area of one of the six equilateral triangles, each with sides of length 6. He's decomposed one of these triangles into two 30-60-90 triangles to find the height, and indeed, these triangles have a base of 4. If you wish to compute the area for this triangle, you can proceed, but ultimately, you'll need to multiply the entire area by 12, not 6, since there are a total of 12 30-60-90 triangles. Personally, though, I find this to be a bit of a time-consuming process.
But I still insist he made no mistake in this regard, with due respect.
@@seabasschukwu6988 He is right. just think properly. You will get your answer.