GRE Quant Ep 3: Coordinate Geometry

[@artfulandtricky]

Thank you so much. Compared to the GMAT questions, the difficult level seems considerably easier. It would be great if you do a video covering: mixture, distance, and work word problems. Thanks!

[@owenburns5698]

What videos would you recommend if I'm aiming for a 170?

[@jesuslover2714]

I want to ask a question regarding the last question; if -b0. Thank you. Your videos are really helpful.

[@GRENinjaTutoring]

There are two ways of thinking about this: If we have -b < 0, we could add b to both sides to get 0 < b. Alternatively, if we have -b < 0, we can multiply both sides by -1. If we do this, we have to remember to flip the inequality sign because we're multiplying both sides by a negative number. This means we'd go from -b < 0 to b > 0. I hope that helps!

[@HarshPatel-bv9rz]

Another great video Harry! Great algebraic solution for Question 8. I did a graphical solution for each choice in my head and found it to be more efficient. Is this a good way to handle problems of this magnitude or can it result in errors?

[@GRENinjaTutoring]

Graphical solutions can be a great way to handle coordinate geometry problems. However, there are things you might miss in a graphical solution that are captured in an algebraic one. It's impossible to say for certain whether a graphical solution will be a good way to handle any problem without seeing the problem -- that's part of the challenge of the GRE. What we can say is that if you can use both graphical and algebraic solutions, and you can choose the best option for each question as it's presented to you, then you're in great shape to do well in the quant section of the GRE! I hope that helps!

[@dariushsayson7959]

Amazing video. Question for you. On question #8, the line does not pass through the origin which is (0,0). If it did pass through (0,0), then x=0 would be the x-intercept of the line. Therefore, on answer choice C, because it says that the product of the slope of line m and its x-intercept is negative, this means that the x-intercept is either a positive number if the slope is negative, or a negative number if the slope is positive. Therefore, this would make answer choice C correct without doing any math because if the x-intercept passed through the origin, the product of the slope and the x-intercept would simply be 0. Did I interpret this correctly without having to do any algebra?

[@GRENinjaTutoring]

If the x-intercept of the line was zero, then the product of the x-intercept and the slope would also be zero. We wouldn't then be able to say that the product of the slope of line m and its x-intercept is negative because this wouldn't be possible -- we've already said it is zero. The GRE will ask difficult questions, but it will never provide a scenario with contradictions or one that isn't possible. For this reason, if line m passed through the origin then option (C) would not be an answer choice. I hope that helps!

[@dariushsayson7959]

Exactly, so because the product is negative this means that answer C is clearly yes because if it had crossed over (0,0) then the product would have been zero. We didn’t have to do any algebra at all, all we had to do was recognize that the product is negative, meaning the slope is negative and the x-int is positive or vice versa.

[@GRENinjaTutoring]

I'm sorry to say it doesn't work like that. You say at the end of your post that "the product is negative", but the product cannot be negative if the x-intercept is zero. There is a contradiction in the question you're trying to construct that means this whole scenario would never occur. The GRE will not ask you a question with a contraction like this. If the question had stated that the line passed through the origin, then answer choice (C) would not be asked. I hope that helps!

[@Th3Crazy4rg0n1an]

This is how I arrived to the answer, but without considering passing through the origin. In order to get a negative product, either the slope or the x-intercept must be negative. I drew a couple of lines that fit these criteria to find that in either case, the y-intercept would be positive. Either the line advances upwards in a forward direction from the x-axis or a backwards direction, but the both result in a positive y-intercept. Does this help shed any light on the question?

[@leahtowery3144]

Thank you for these videos!! For question 4, wouldn't you want to double check that the point of intersection between the two lines corresponds with the graph? For example an answer choice that had a point of intersection with a positive x value would not work even if the slopes and intercepts aligned (in this case both B and D still work). Is this something we should look out for or is there a way to confirm this without doing the additional algebra?

[@GRENinjaTutoring]

Hi Leah, You're welcome! I'm so pleased you like the videos. For question 4, if you know that the slope of line P is greater than the slope of line Q and you know the y-intercept of line P is greater than the y-intercept of line Q, it's not possible for the point of intersection to have a positive x-value. The one other thing you might check is the x-intercept of both lines. From the diagram, we want the x-intercept of line P to be greater (further to the right on the x-axis) than the x-intercept of line Q. If we said the equation of line P was y = ax + b in the same way we did in the video, then we can find the x-intercept by setting y = 0 and solving for x. This gives x = -b/a. If we consider answer choice (B), line P has a slope of 2 and a y-intercept of 6. By plugging these values into x = -b/a we get x = -6/2 = -3. Doing the same thing for line Q, we get an x-intercept of -4. Since the x-intercept of line P is greater than the x-intercept of line Q, combined with the fact we know the slope and y-intercept of line P are greater than those of line Q, we know the intercept must be in the top-left quadrant. You could follow the same process for answer choice (D) to confirm that one is correct too. I hope that helps!

[@Pradyumna-e8r]

@@GRENinjaTutoring I think he meant depending on which quadrant both lines intercept, x intercepts change. Here in the given graph, they are intersecting in 2nd quadrant, but if there intersect in 3rd quadrant, we'd have no answer among the options.

[@GRENinjaTutoring]

@@Pradyumna-e8r , you're absolutely right that if we were given a different graph that had the two lines intersect in the third quadrant then we'd have no answer among the options. However, the graph provided in the question is the one thing we know to be correct as that's the information that was provided in the question. To know that the two graphs intersect in the second quadrant, it's sufficient to know the slope of P is greater than the slope of Q, the y-intercepts of both P and Q are positive and that of P is greater than that of Q, and the x-intercepts of both P and Q are negative and that of P is greater than that of Q. Since both (B) and (D) satisfy these conditions, we know the lines referred to in these answer choices will intercept in quadrant 2. We could check this to confirm it if we wanted to, but it's not necessary to do this work to get the correct answer to this question. I hope that helps!

[@JimSamonte]

@@GRENinjaTutoring following this logic, choice (C) is also a correct answer, i.e., B C and D are the correct answers. Choice (C) intersects at (-15/11, 2/11) which is in Quadrant 2. Or simply interchanging your lines P and Q, would definitely satisfy by inspection that a>c (slopes) and b>d (y-intercepts). ☺

[@GRENinjaTutoring]

Hi @@JimSamonte! Choice (C) can't be the correct answer because the slope of line Q is greater than the slope of line P, and the y-intercept of line Q is greater than the y-intercept of line P. By looking at the diagram given in the question, we can see we'd need both of these things to be the other way around for (C) to be correct. I hope that helps!

[@imransyed4447]

For question 6, why did you assume that the point of intersection of the two lines is directly above the exact midway point over 3.5 on the x axis? Because the lines you drew are rough estimates, not exact calculations, so what if the point of intersection was not directly above the midway point between the x axis of the two lines?

[@GRENinjaTutoring]

The 3.5 Harry wrote on the board did not indicate a coordinate on the x-axis, instead it represents the length of the base of the triangle. This is shown from about 49:20 to 49:25 in the video as he says the distance between 3 and 6.5 on the x-axis is 3.5. The point of intersection between the two lines is found later in the solution and is (5, 6), so it's not above the midway point between the x-intercepts of the two lines. I hope that helps!

[@Abkuyper]

57:23 'C is less than D' because they both Negative right?

[@GRENinjaTutoring]

It's not just that they're both negative. The point (c, d) is to the left of the line y = x and both coordinates are negative. If we picked a point on the line y = x that has the same y-coordinate as (c, d) then we know that this point is (d, d) because any point on the line y = x will have the same x and y-coordinates. We could then move left until we reach (c, d). By doing this, the y-coordinate of out point remains the same and the x-coordinate becomes more negative. This is how we know that c < d. I hope that helps!

[@Abkuyper]

1:08 , When the line does not go through the origin, it means that it is not Y=X right? thank you

[@GRENinjaTutoring]

Yes, if we know the line does not go through the origin then it cannot be y = x. It could be y = x + 1 or y = x - 3, but the y-intercept of the line cannot be 0. I hope that helps!

[@imransyed4447]

For question 4, why did you assume the first column are the P equations and the second column is the Q equations, the question does not indicate which is which so how can depend for a correct answer on our assumption? What if I did the opposite and labeled the first column Q and the second column P, or what if I said they were all scattered and that each column could have an equation for both P and Q? Please answer I am confused

[@GRENinjaTutoring]

The question says "which of the following could be the equations of P and Q, respectively?" The word "respectively" makes all the difference here because that's the word that tells us that the equations of P are in the first column and the equations of Q are in the second column. For example, if we said "The scores of the students were 85, 90, and 78, for John, Sarah, and Emily, respectively," we'd know that John scored 85, Sarah scored 90, and Emily scored 78. In this context, “respectively” means that the items mentioned in two or more parallel lists correspond to each other in the same order. I hope that helps!

[@yessbenne5924]

straight line with linear equartion y=ax+b doenst cross the x line only if the slope m=0 distance racine((x1-x2)**2+(y1-y2)**2) and midpoint ((x1+x2)/2,(y1+y2)/2) formulat in x,y space

[@yessbenne5924]

at the x intercept y=0 the interecept of a function is where x=0

[@yessbenne5924]

Dont forget to select two anwers if "all that apply" is specified

[@yessbenne5924]

Two lonear graphs are perpondicular if the product of the their slopes =-1 Two linear graphs are paralllel the the two slops are equal

[@yessbenne5924]

You can test points values if you have a qustion about a graph that you vant figure out

[@omkarsawant6046]

Are this question gre level?

[@GRENinjaTutoring]

Hi there, the questions in this video were designed to cover a range of difficulties. The first five questions will probably give you everything you need to answer coordinate geometry questions up to a 160 level. The final three questions were designed to show you the kind of things the GRE could do to make coordinate geometry questions a bit more difficult. These questions would roughly fall into the 160-165 level. I hope that helps!