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It seems to me that you could also do it with a box around the whole thing and just subtract the "missing" triangles. You'd have a total box area of 7 x 4 = 28... Subtract the two 3-4-5 triangles (each with an area of 6) to bring you down to 16, then subtract the top 7 x 1 triangle, so 16-3.5 = 12.5

@manoramasingh2925

Жыл бұрын

X axis is not same. How can you subtract?

Bret, I am an Economist just dusting off some math skills. I thank you for this video, it was extremely clear y clear.

@dominatethegmat

2 жыл бұрын

My pleasure, Javier. As an economist, I'm sure the relevant math skills are still in there somewhere! Stick with it, it'll come back to you. And don't forget that "GMAT math" is different from traditional math in many cases, so be sure to learn some of the non-standard strategies that will help you answer GMAT quant questions more efficiently. Your goal is to get right answers, not to make your high school algebra teacher happy 😀. Good luck and let me know how else I can help!

@JavierBonillaC

2 жыл бұрын

@@dominatethegmat Thank you Brett

By co-ordinate geometry, PQ = 5, PR = 5, QR = 5(2)^0.5 This means, PQ^2 + PR^2 = QR^2 => PQR is right angled triangle. So Area = 0.5 * 5 * 5 = 12.5

It's much quicker and easier to do Area = 28 - A1 - A2 - A3, where A1, A2, A3 are area's of the smaller triangles in a 7x4 box.

I did it this way: 1. Find the length QR, QR=(50)^0.5 2. Find the mid point of QR, say Z, which is (3.5,3.5) 3. Find length PZ (14.75)^0.5 4. Plug PZ, PQ in areas of triangle, PZ is actually >3, but take it as 3 So you’ll end up with 10 as the area, but the value for PZ is a little more than 3, so the area will also be a a little higher than 10 but not higher than 14.

There is a rectangle that contains the triangle, if that makes sense. That would be 7*4 = 28. There are the areas of three triangles to subtract from this rectangle's area. The triangle formed by Q, P and the origin has an area of 1/2*4*3= 6, as does the triangle formed by P,R and (7,0) so we can take those two 6's away from the rectangle and we come up with 16 (eliminating D and E as the answer). We have one more triangle at the top formed by P, Q and (0,4). That area is 3.5, that a rational number (eliminating C as the answer), but is not an integer (eliminating B as the answer), we know A is the answer.

Brilliant thank you!

@dominatethegmat

3 жыл бұрын

You're welcome!

I did calculate the problem correctly and I didn't use any of that extra stuff because that takes time.

The method shown in the video is too conjectural. This might lead you to a wrong answer quite often. The best way to get correct answer is just to subtract the sum of areas of two right triangles from the trapezium. That will give the sure shot answer within 30 seconds.

@AA-pu5qj

6 жыл бұрын

how do you see the trapezium? i cant see the trapezium

In the first illustration when assuming 3 as the height the answer came out to be 10.5. When assuming 4 as the height the answer came out to be 14. So we know that the answer is BW 10.5 and 14. I would like to understand how was option C eliminated as that also lies between 10.5 and 14

@dominatethegmat

9 жыл бұрын

Good point, but.... Answer choice C is 10root2. Remember that we approximate root2 to be 1.4, so we would approximate answer choice C to be 14 as well. So according to what I said in the video, it would still be in the running as you suggested. However, two things: 1) Remember that when answer choices on the GMAT are all numbers like in this question, they're in either ascending or descending order. That's important. That tells you that answer choice C must actually be a little bigger than answer choice B, which in fact it is because root2 is technically 1.4142... so answer choice C is technically 14.142...; 2) 14 was our UPPER approximation anyway, so even if we did approximate answer choice C to be 14, we'd throw it out for the same reason we ultimately threw out B. I hope that makes sense! Let me know if you'd like further clarification.

I really like your other videos but disagree with the guessing. The problem itself is easy enough to calculate.

These types of guess estimation methods should be avoided at best.

How can the height be different? in the beginning the height is drawn through the middle of the trangle, and later the height is the left side of the triangle.

@brettethridge

10 жыл бұрын

Technically the height of a triangle is any altitude (i.e. a line segment creating a perpendicular angle) drawn from one vertex to the opposite base. If you know the triangle is a right triangle, then it's easy -- one of the perpendicular sides is the height, and the other is the base (the third is called the hypotenuse). So in the first illustration, I wasn't assuming the triangle was "right" and therefore I dropped an altitude "through the middle of the triangle" from the base to the opposite vertex. In the second illustration, I did assume the triangle was right (and later proved it to be such) which is why I changed which line segment I used as the height and base. In either case, the area would be the same.

Hey.. how you get the height is 5 in the second method?

@dominatethegmat

5 жыл бұрын

I used the tick-marks on the xy-coordinate plane to literally count the short and long sides of the right triangle, and then I recognized the 3-4-5 Pythagorean Triplet to quickly see that the hypotenuse must be 5. If you didn't recognize that, you could always just use the Pythagorean Theorem. It sounds like you'd benefit from my a-la-carte course on GMAT Triangles: www.dominatethegmat.com/video-purchase/a-la-carte-topics/gmat-triangles/. Enjoy!

I know it's free and I really appreciate it but I really wish you had more than one problem up here. and that would be just to build confidence.

@dominatethegmat

7 жыл бұрын

Yeah, obviously there's a lot more content and strategies in my paid courses, so check those out. But here's another video for you with an example of how logic and common sense can help you get right answers (or at least dramatically improve your guessing odds): kzread.info/dash/bejne/e2eXt5qPj9ecfLQ.html. It's on my GRE channel but the question I go over could realistically appear on the GMAT as well, so it's relevant. Hope it helps!

@samanthamacdoo524

7 жыл бұрын

Dominate the GMAT well thank you for that, are you saying that we shouldn't assume any questions on the GMAT are this simple because then I'd start thinking like: this is too easy because they like to throw tricks at us!

@dominatethegmat

7 жыл бұрын

Part of it is knowing where you are in a given section. If you're early on in the section, there's a chance the questions really are easy, so don't second-guess yourself. If you're later in the section, presumably you've been getting right answers along the way and the questions have gotten more difficult, in which case a question that looks easy may really be difficult...so beware the eye-catchers in that case! Remember that hard questions have hard answers, so take that into consideration, especially if you find yourself in a position where you have to guess.

Poorly explained. It could be simply solved as the area of the rectangle with sides 4,7 minus areas (triangle on the right + triangle on the left + triangle on the top)

@hodagamal

8 жыл бұрын

Wow! I have finally met a cyber bully. I feel sorry for your pitiful life you spend bullying people on the internet. Such a disappointment to humanity you are. Don't eat with that mouth or you might get poisoned. Don't bother reply. You're blocked already.

@riEfs85

3 жыл бұрын

That's exactly correct. I don't get why people over complicate stuff

Subtracting the areas of the two right angles from the area of the trapezium would be the technically accurate way, however in cases like this where the lowest possible value and the highest possible value clearly isolate the solution, it would be a waste of time to do all those calculations. However, in the GMAT official guide they mention " figures are not necessarily drawn to scale". In a more complex geometry question, it would be taking an unnecessary risk to assume the figures are drawn to scale.

@dominatethegmat

4 жыл бұрын

A quick look at the diagram gives you a pretty good indication of whether it's drawn to scale or not. Here, there's nothing in the diagram that violates scale, so you can proceed assuming it's drawn to scale. Moreover, it's the Data Sufficiency section where figures are assumed not to be drawn to scale; you can use that to your advantage when solving DS questions by manipulating figures to show conflicting outcomes, etc.

$300 way expensive course