GMAT Question of the Day - Data Sufficiency - Geometry/Triangles

GMAT Question of the Day Data Sufficiency Geometry Triangles Question Diagram

If the length of side AC is equal to the length of side BC and the length of segment AD is equal to the length of segment BD is the length of segment CD less than half the value of the length of side AB?

1) The measure of angle ACB is not less than 90

2) The area of triangle ABC is 20

Answer Show

GMAT Question of the Day Solution

This question of the day is tricky but not tough if you stay organized. From the diagram and the given information we know that this is an isosceles triangle. Is it a right isosceles triangle? We don't know. However, if it is a right isosceles triangle then we can certainly calculate the values for all of the sides and determine the relationship between AB and CD. So one of the ways of answering this question comes down to determining whether triangle ABC is in fact a 45-45-90 triangle.

Statement 1) Not less than 90 means greater than or equal to 90. That means that we could have a right isosceles triangle. If we do have a right isosceles we can calculate the values for all of the sides based on the ratio 1:1:√2. That would make side CD exactly half of the value of AB. Meaning that we could answer NO to the question. Can we answer YES? Well, if the angle ABC is greater than 90 the hypotenuse will get longer while CD gets shorter. Hence CD will be less than half of AB (you can see this clearly in the diagram). So the answer would be YES. Both YES and NO means Insufficient.

GMAT Question of the Day Data Sufficiency Geometry Triangles Solution Diagram

2) It would have been great to have calculated the 45-45-90 scenario in advance. We shouldn't have assumed that this was a 45-45-90 but because it is an easy scenario to calculate it is worth doing. This is something that I always try to encourage in my GMAT tutoring students: to take simple steps to create more useful information.

This area proves that the triangle is in fact a right isosceles so we can determine the values for all of the sides. Sufficient.

GMAT Question of the Day - Problem Solving - Geometry/Coordinate Plane

In the XY plan, line J has a positive slope and an x-intercept of 6. If the area of the triangle formed by line J and the two axis is 18, what is the y-intercept of line J?

A. -6

B. -3

C. 3

D. 6

E. 9

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GMAT Question of the Day Solution

For most Geometry questions it is critical to make a diagram. Be careful: double check that you are making a diagram that reflects the information that you are given. A lot of GMAT success is about the proper interpretation of the information that you are given in the question. Take your time setting up the question. I see a lot of GMAT students who feel that there is so much time pressure that they need to speed up. But trying to move faster can create mistakes that slow you down. Improving your speed is about applying the right process and controlling mistakes rather than actually speeding up how you do things. During tutoring sessions I often find myself encouraging students to slow down.

In this question of the day it's important to note that line J has a positive slope. This means that the triangle will be in quadrant IV. I've seen many people take this question and draw a negative slope with the triangle in quadrant I. Once you've drawn the appropriate triangle you can set up the area formula and solve for the height of the triangle. Then realize that the answer must be negative since the triangle is in quadrant IV.

GMAT Question of the Day Geometry Coordinate Plan Solution Diagram

GMAT Question of the Day - Problem Solving - Geometry

The perimeter of a right isosceles triangle is 8x + 4x√2. In terms of x what is the area of the triangle?

A. 4x

B. 8x^2

C. 16x^2

D. 24x

E. 32x^2

Answer Show

GMAT Question of the Day Solution:

Start by defining what you are looking for - in this case the area of an isosceles right triangle or s^2. You have been given the perimeter so go ahead and set the given perimeter to the standard perimeter of an isosceles right triangle. Simplify and solve for s. Now square that result because you are looking for the area.

GMAT Question of the Day Geometry Solution Diagram 3

 

GMAT Question of the Day - Data Sufficiency - Geometry

GMAT Question of the Day Geometry Diagram

In the figure above ABCD is a rectangle and point K is the center of ABCD. What is the value of x?

(1) KB is equal to MB

(2) M is the midpoint of LC

Answer Show

GMAT Question of the Day Solution

One way to find the measure of angle x is to find the measures of its adjacent angles MBC and KBA. Because ABCD is a rectangle all three of those angles must sum to 90 degrees. Also notice that KB is half of the diagonal of the rectangle but don't assume that this means that angle KBA is 45 degrees. In fact, there is no way to tell how the 90 degrees is divided between the 3 angles. You can prove this to yourself by distorting the shape. Another thing to think about: in GMAT Geometry questions with mixed shapes consider how you can add lines to create new connections.  Notice that we can add a line at point K to create another right triangle.

GMAT Question of the Day Geometry Diagram 2

You can also add the other diagonal KC.

GMAT Question of the Day Geometry Diagram 3

Statement (1) Our shape can still change. Angle x will vary depending on the proportions of the rectangle. Try drawing different variations of the shape to prove this to yourself. You will see that as the rectangle gets short angle x must get more acute regardless of whether BK = BM. Insufficient.

Statement (2) This statement is also insufficient. This can be proven with trigonometry which is not necessary on the GMAT or by distorting the shape. When you change the proportions you can see x change.

GMAT Question of the Day Geometry Solution 5 Diagram

Put Statement (1) and Statement (2) together and half of the rectangle becomes a square. Once you have square, symmetry is forced on all of the angles.

 

 

 

GMAT Question of the Day - Data Sufficiency - Geometry

GMAT Question of the Day Data Sufficiency Geometry 4 Diagram

 Is the perimeter of parallelogram ABCD greater than 10?

(1)  Sides AB and BC are in a ratio greater than 7 to 1
(2)  The distance from A to C is 5

Answer Show

GMAT Question of the Day Solution:

(1) The sides being in a certain ratio doesn't tell us anything about the perimeter. AD could be 1000 and AB could be 7000 or AD could be .1 and AB could be .7. Insufficient.

(2) The diagonal is 5. Whenever there is a perimeter question dealing with triangles always think of the third side rule: The third side of a triangle must be greater than the difference and less than the sum of the other two sides. In this case AD + AB must be greater than 5. Same thing for DC + BC. So the perimeter must be greater than 10. Sufficient.

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