Lesson: Tackling Data Sufficiency Questions

There are 2 kinds of math questions on the GMAT: Problem Solving questions and Data Sufficiency questions. In a Problem Solving question, the diagram will be drawn to scale unless stated otherwise. In a Data Sufficiency question, the diagrams are not necessarily NOT drawn to scale.

In this video (https://www.gmatprepnow.com/module/gmat-geometry/video/885), we note that (at 0:50) one can use estimation for a Problem Solving question.

In the video above, we deal with strategies pertaining to Data Sufficiency geometry questions. Since the diagrams in Data Sufficiency questions are not necessarily NOT drawn to scale, we advise you to avoid estimation.

Here's why we don't need an equation: if a statement forces a shape into having just one length, then we COULD just recreate a super accurate representation of the figure (using a compass, ruler, protractor, etc), and then measure the line with a ruler.

In the given diagram, we COULD draw an altitude from point A down to side AC. This altitude will divide the triangle into two equal triangles. Both triangles will be 30-60-90 right triangles with a base of length 5. We can then use what we know about 30-60-90 right triangles to calculate the length of side AB.

Keep in mind that we also know that AD = DB.

So, once we know that DE||AC, we have similar triangles (i.e., ∆ABC ~ ∆DBE), which means ∆ABC is TWICE the size ∆DBE (since AB = 2DB)

Since DE = √2, we can be certain that AC = 2√2

Keep in mind that we also know that AD = DB.

So, once we know that DE||AC, we have similar triangles (i.e., ∆ABC ~ ∆DBE), which means ∆ABC is TWICE the size ∆DBE (since AB = 2DB)

Since DE = √2, we can be certain that AC = 2√2

Hey bertyy,

My step-by-step solution is here: https://gmatclub.com/forum/if-in-the-figure-above-ad-db-and-de-2-what-is...

Cheers,
Brent

Question link: https://gmatclub.com/forum/the-hypotenuse-of-a-right-triangle-is-10-cm-w...

Given: The hypotenuse of the triangle has length 10 cm.
If we let x and y represent the lengths of the two legs of the RIGHT triangle, then we can write: x² + y² = 10²
Simplify: x² + y² = 100

Statement 1) The area of the triangle is 25 square cm
Since x and y represent the lengths of the two legs of the RIGHT triangle, the area = xy/2
So, we can write: xy/2 = 25
This means xy = 50
Or, we can write: 2xy = 100

We now have two equations:
x² + y² = 100
2xy = 100

Since both equations are set equal to 100, we can write: x² + y² = 2xy
Rewrite as x² + y² - 2xy = 0
Or write as x² - 2xy + y² = 0
Factor to get: (x - y)(x - y) = 0

So, it must be the case that x - y = 0, which means x = y
Aha!
If x = y, then we can take the equation 2xy = 100 and replace y with x to get: 2x² = 100
Divide both sides by 2 to get: x² = 50
So, x = √50
This means y = √50 too

So, the perimeter = √50 + √50 + 10

Here's my complete solution: https://gmatclub.com/forum/the-hypotenuse-of-a-right-triangle-is-10-cm-w...

Cheers,
Brent

I believe you're referring to the diagram at 1:45 in the above video.

There is no construct in Geometry that says a line dividing a right triangle (where the 90-degree angle is denoted by a box) will divide the right angle into 2 equal angles.

So, we could have any number of scenarios, including the ones shown here: https://imgur.com/VSPYPCc

Cheers,
Brent

Question link: https://gmatclub.com/forum/in-the-figure-above-what-is-the-value-of-z-22...

If the right triangle were a 45-45-90 triangle, then 2 sides would have equal length.
When we combined the two statements, we know that the right triangle has hypotenuse 2, and one leg has side 1.
If we let x = the length of the missing side, we can write x² + 1² = 2²
Simplify: x² + 1 = 4
This means: x² = 3
So, x = √3
So, the triangle has lengths 1, √3 and 2
Since we don't have two equal sides, we don't have a 45-45-90 triangle

I think I agree with you.
The property here is that, if a statement locks in the measurement of a line or angle, then we could simply measure that line or angle.