Lesson: Lines and Angles

Comment on Lines and Angles

the Improvement Charts are really great, thanks a lot =)

do you also have those for 2017 and for the Quantitative Review ? =)
gmat-admin's picture

No, we haven't created similar resources for the quant-only books.

no problem.

But found it for 2017

thank you! very helpful :)

would you recommend the Manhattan Quant Books ?

Ive got 1 month+ left (already went over official guide + math only + verbal only + 1729 videos on khan (73% wom mission), all magoosh videos, and soon all your videos :)

But still have serious doubts to get 700+
gmat-admin's picture

The Manhattan books are great. However, I’d like to point out that HOW you study is just as important as WHAT you study. In my opinion, many students don’t dig deep enough while learning the concepts tested on the GMAT.

Many students spend a lot of their time answering random/unrelated practice questions (a geometry question then a statistics question, algebra question, geometry question, probability question, etc.).

This strategy doesn’t allow you to fully explore the intricacies of each concept, and this is very limiting, because the test-makers can take ANY concept (no matter how simple) and create dozens of wildly different questions, each requiring a different approach. So, to achieve great score, you must answer tons of practice questions that are specifically-related to each individual concept tested on the GMAT.

Please note that, when I say “concept,” I’m not referring to broad topics like Statistics or Geometry; I’m referring to the *individual concepts* that comprise those topics. For example, the concepts that fall under the umbrella of “Geometry” include the properties of parallel lines, triangles, right triangles, special right triangles, quadrilaterals, circles, etc. For each of these, you need to understand/anticipate all of the various ways the test-makers can evaluate your knowledge.


Grasping and effectively applying the concepts is what concerns me the most. I have started the 60 day study plan, but I feel a bit rushed. If I can carve out an average of 4 hours a day during the week and about 6 hrs Sat & Sun, do you think it's reasonable to go from a 490 (practice) to between 600-650 on test day within 60 days?
gmat-admin's picture

Hi Paul,

An increase from 490 to 600+ is possible, but it will take a lot of time and energy.

If you're following the 60-Day Study Guide (https://www.beatthegmat.com/mba/gmat-guide), then on Day 22, you'll take another practice test. This will give you a good idea of your score trajectory and the time it will take to reach 600+.


sir i m having doubt in this question

Hi, even after going through the solutions mentioned for: http://gmatclub.com/forum/if-in-the-figure-above-l1-and-l2-are-parallel-what-is-x-224812.html

I am unable to understand the concept. Could you please tell me how i should approach this question and solve it?

gmat-admin's picture

Hi aanchal890,

I'm happy to help.

I provide a step-by-step solution here: https://gmatclub.com/forum/if-in-the-figure-above-l1-and-l2-are-parallel...

If you tell me which step(s) you'd like me to go over, I can help.


Hi Brent,

In questions like in the below link, should we never assume the lines to be parallel even though they are named as L1 and L2; L3 and L4?

gmat-admin's picture

Question link: https://gmatclub.com/forum/what-is-the-value-of-x-187602.html

That's correct; we can't assume that any lines are parallel unless we're told so (either directly or indirectly)


On a DS question, what are some of the terms used to typically indicate that the lines are parallel and intersect?

You mention that parallel lines on their own are not that interesting. What do you mean by this? Does that mean that we can't derive any useful information just from this fact?
gmat-admin's picture

The most common way is to just specify that two lines are parallel.

However, there are times when you're indirectly told two lines are parallel.
For example in the diagram here https://imgur.com/a/vbsEXdV, the fact that those two angles are both equal to x°, then we can be certain that line k || line j

All I meant by that comment is that 2 parallel lines on their own (without any transversals) are kind of boring.



If both the lines were parallel in this question, would that be sufficient to derive x? If so, does that mean that when two lines are parallel they have the same properties - creating the same angles and bisecting the lines equally?
gmat-admin's picture

Question link: https://gmatclub.com/forum/what-is-the-value-of-x-187602.html

If line 1 and 2 were parallel AND lines 3 and 4 were parallel, we'd still need one angle measurement to determine the value of x.

Your question: Does that mean that when two lines are parallel they have the same properties - creating the same angles and bisecting the lines equally?
I think I agree with that (other than the bisecting part. What is getting bisected?)
That said, rather than try to create a universal rule regarding the intersections of two pairs of parallel lines, it's probably easier to just treat each intersection as a transversal passing through parallel lines.


So if all lines were parallel and if given the value of y=70 in this case, then statement 2 would be sufficient?
gmat-admin's picture

Yes, that's correct.


How do we know when opposite angles are equal to each other? In this diagram, it doesn't look like we could infer that the angle opposite the 40 degrees is 40 degrees or that the angle x+y = to its sum. It doesn't work given the properties of a straight line and that x+y would equal 100 degrees.
gmat-admin's picture

Question link: https://gmatclub.com/forum/what-is-the-value-of-x-in-the-figure-above-1-...

Opposite angles are always equal to each other.
Whenever you have two lines intersecting each other, there will have two pairs of opposite angles, and those opposite angles will be equal.

I believe you are wondering how we know for sure that the lines are actually straight.
On the GMAT, all lines that appear to be straight can be assumed to be straight.

For more on this, watch: https://www.gmatprepnow.com/module/gmat-geometry/video/863


Hi Brent,

What kind of approach you would apply to solve this?

Thanks a lot


gmat-admin's picture


Approach plz
gmat-admin's picture

Hi Brent,


Lot of debate on this question, i think answer should be A, but OA says E.

Help !

gmat-admin's picture

Question link: https://gmatclub.com/forum/in-the-xy-plane-is-the-slope-of-line-k-equal-...

Great question!! I don't recall ever seeing it.

TARGET QUESTION: In the xy-plane is the slope of line k equal to 0?
STATEMENT 1: The x-intercept of k is 0.

PROPERTY #1: If the x-intercept is 0, then the line passes through the origin (0,0)

PROPERTY #2: If a line lies on the x-axis, then that line has INFINITELY-MANY x-intercepts, because the line passes through (1,0), (2,0), (3,0), (4,0), etc.

PROPERTY #3: If line k passes through the origin AND has a slope of 0, then line k would be on top of the x-axis (it would be the same as the x-axis)

Statement 1 says "The x-intercept of k IS 0"
In other words, there is EXACTLY ONE x-intercept, and it's 0
This means line k CANNOT be on top of the x-axis, which means its slope cannot be 0.
The answer to the target question is "NO, the slope of line k is not 0"

So, Statement 1 is sufficient

Hi Brent,
Can you please explain this question
All the dots in the array are 2 units apart vertically and horizontally. What is the length of the longest line segment that can be drawn joining any two points in the array without passing through any other point ? (3*3 matrix).
gmat-admin's picture

I'm happy to help.
Here's my full solution (with diagrams): https://gmatclub.com/forum/all-the-dots-in-the-array-are-2-units-apart-v...

In the future, please provide either a link to the question or provide all of the answer choices. In many cases, we can use the answer choices to quickly identify the correct answer.


Thank you so much Brent.From next time will provide the link to the problem.

Hey Brent, I think I'm having a brain fart.
I cross simplified prior to multiplying --> x/(180) = 3/8 to get x/60=1/8. Is that only applicable with the multiplication sign? Because when I do it here I dont get the correct answer.
gmat-admin's picture

That's right; cross simplification applies only when you're multiplying fractions.
So in the case of the equation x/180 = 3/8, we can't cross simplify.

Instead we must cross multiply to get: 8x = (3)(180).....etc

Thank you! I knew I was going crazy.

Hi Brent, at video 6:53, x+y = 180. To clarify will x above line L1 and y under Line y2 add to 180 also? Similarily with y under Line L1 and x under L2? Thanks Brent
gmat-admin's picture

In that diagram, all x-values are equal, and all y-values are equal.
So, if we add any x-value and any y-value, the sum will be 180 degrees.

Brilliant thanks Brent for confirmation.

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