Which of the following lists the number of points at which a circle can intersect a triangle?

(A) 2 and 6 only

(B) 2, 4 and 6 only

(C) 1, 2, 3 and 6 only

(D) 1, 2, 3, 4 and 6 only

(E) 1, 2, 3, 4, 5 and 6 only

I'm often asked: "What's the most important thing to work on in order to succeed on the GMAT". Not a simple question. Of course you need all of the quant and verbal fundamentals. And you're going to need to learn GMAT specific strategy. Above all that though is what I think is the most important quality: organized curiosity. You have to be willing to explore a bit. Not randomly though. In an organized way. Conducting mini experiments to feel out a question. This geometry question from the GMAT prep tests is a good example of the type of GMAT puzzle that rewards those willing to try a few things. Most often students stare at this one and refuse to play a little bit drawing out scenarios. Time pressure gets the best of them and then it's over. You have to ignore the clock a bit so you can let some ideas flow. GMAT time pressure is real. In that it's a timed exam and for most people that adds a formidable constraint. Still, if you're going to spend precious time working on a question better make that quality time leaving yourself open to the type of thinking that tends to lead to success. Developing the habit of organized curiosity requires taking the risk of ignoring the clock. Hopefully you'll find that by opening things up a bit you think more flexibility and creatively and give yourself the time to organize things properly so that you actually are not only more effective but more efficient. This isn't a skill that you just turn on. It needs to be practiced. And while you're practicing you're probably going to fail a whole bunch. But remember to keep practicing how you actually want to perform. It's true that in the short term you might be able to get away with lower quality thinking and make some gains refining that but if you're looking to fundamentally change your GMAT performance you likely need to not only work on GMAT content by your general approach to problem solving. Diagram below with the solution and here's a video explanation: Which of the following lists the number of points at which a circle can intersect a triangle

Which of the following lists the number of points at which a circle can intersect a triangle

GMAT Question of the Day - Problem Solving - Geometry

If s is between 0 and 9, how many different equilateral triangles with side s can be formed that have an area which is an integer value?

A. 3

B. 4

C. 5

D. 6

E. 7

Answer Show

GMAT Question of the Day Solution

This GMAT question of the day is tough but not impossible. What makes it tough? You have to consider a few different things while keeping in mind the limitations imposed by the question. First off - what's the area of an equilateral triangle? Now consider what numbers will create an integer value for the area? We have to get rid of the 4 in the denominator and the √3 in the numerator. Let's look at one issue at a time:

1. To cancel the 4 you need to have a at least a 4 in the numerator. It doesn't need to be a 4 but could be an 8 or a 12 or a 16. Anything with at least one 4 as a factor. Keep in mind the limitation that S must be less than 9. So that leaves 2, 4, 6, and 8 each of which when squared will have at least one 4.

2. We also need to either cancel or transform the √3. We can do this by either dividing or multiplying by √3. This means that S must have 3^1/4 in the numerator or the denominator.

Putting both together you have these options for S:

2(3^1/4), 4(3^1/4), 6(3^1/4)

2/(3^1/4), 4/(3^1/4), 6/(3^1/4), 8/(3^1/4)

Note that 8(3^1/4) will not work because it is greater than 9. That leaves seven different triangles.

GMAT Question of the Day Geometry Solution

 

 

 

GMAT Question of the Day - Problem Solving - Geometry

GMAT Question of the Day Geometry Explanation

If DF I| AC and x = 1.5y, what is the ratio of the areas of triangle ABC and triangle DEF?

A. 4/7

B. 3/2

C. 7/4

D. 9/4

E. 16/3

Answer Show

GMAT Question of the Day Solution

The rules governing similar triangles are relatively basic. So what's challenging about GMAT similar triangles questions?

1. Spotting that the question is in fact testing similar triangles

2. Organizing the information so that it is clear which angles and sides are corresponding.

How can you make GMAT similar triangles questions easier? First thing, whenever you see triangles that share sides or triangles within triangles consider that the triangles may be similar. Remember that you only need two angles to be the same in order to prove similarity. One thing that can help to keep things organized is to label the angles. You don't need to know that actual values. Just giving the angles variables will help illustrate which angles are in fact the same and which sides correspond with one another.

In this case the two triangles must be similar because two of the angles are the same. You can infer this information by the fact that DF and AC are parallel (parallel lines cut by a transversal). Now you can substitute x for y and find the ratio of the sides. Here's a GMAT shortcut: the square of the ratio of sides is equal to the ratio of the areas.

 

GMAT Question of the Day - Data Sufficiency - Geometry

A hardware store sells paint in two different containers. Container A is a cube with an edge of k. Container B is a right cylinder with a height of 5k. Assuming that each container is filled to capacity which container will cost less per unit of volume?

(1) Container A costs 1/3 as much as Container B

 

(2) Container B has an inside diameter which is less than 2k

Answer Show

GMAT Question of the Day Solution

GMAT Question of the Day - Problem Solving - Geometry/Puzzle

The measurements obtained for the sides of a certain triangle are 18 centimeters by 18 centimeters by 18 centimeters. If each of the sides has a measurement error of at most 2 centimeters, which of the following is equal to the maximum possible difference between the actual area of the triangle and the area calculated using these measurements?

A. 17√3

B. (35/2)√3

C. 18√3

D. (39/2)√3

E. 19√3

Answer Show

GMAT Question of the Day Solution

Although this GMAT question involves geometry it is also a bit of a puzzle because of the measurement error portion. If you're not sure how the measurement error will affect the area you might want to try some small numbers to get a feel for the question. Try a triangle with sides measuring one versus a triangle with sides measuring three. Let's remember that we want the maximum difference so you should make the measurement error a plus not a minus. Why a plus? Because the bigger the numbers the more the difference of two will make. The difference between 1000*1000 and 1002*10002 is much greater than the difference between 3*3 and 5*5. So we want the numbers to be as big as possible.

The other thing that will help in this question of the day is: the formula for the area of an equilateral triangle. For my GMAT tutoring students I try to keep the esoteric formulas to a minimum (no memorizing standard deviation here!) but this formula is useful. Side^2 * (√3/4)

Once you set up the expression you should notice that you can factor out √3/4. Once you've done that you'll see a difference of squares. Go for it! Using this special quadratic will make the simplifying easier.

GMAT Question of the Day Problem Solving Geometry Puzzle Solution Diagram

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