Lesson: Tackling Data Sufficiency Questions

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Why shouldn't we estimate lengths and angles when most figures on the gmat are drawn to scale? Actually, it's a great idea to estimate lengths and angles if you cannot answer the question using traditional methods. Most books on the gmat tell you to do this.
gmat-admin's picture

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.

Hi Brent,

I get your point on the statements together forcing the line to have only one length. But why should we not check till the point of at least formulating an equation that will find the length?

How can we be sure that the data will give us a length?

Additionally, I'm also curious as to how you use this data to find the length in this specific problem.

Thanks!
gmat-admin's picture

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.

Brent,
I am having a hard time understanding the solution to this question.
https://gmatclub.com/forum/if-in-the-figure-above-ad-db-and-de-2-what-is-the-length-of-line-se-224874.html

From your excellent 'lock-in' method, I found the length of AC can take more than one value and this value seems to be dependent on the angle x. However, the question asks if we can find the value of AC. Using statement 2, dont we get more than one value? Shouldnt the answer be C because we are looking for one value of AC? Please clarify.
gmat-admin's picture

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

gmat-admin's picture

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

Hi Brent,

How is AD= DB? It's AE = AC. Also i didn't got DE || AC.
gmat-admin's picture

Brent, I think your excellent diagraming skills are in order... seems to be lots of different answers to this problem.

For sure! Thanks for the quick response Brent.

HI Brent

I think this one needs some clarification on all the points mentioned previous with some of your great diagram work.

https://gmatclub.com/forum/if-in-the-figure-above-ad-db-and-de-2-what-is-the-length-of-line-se-224874.html

Thanke
gmat-admin's picture

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: https://gmatclub.com/forum/the-hypotenuse-of-a-right-triangle-is-10-cm-what-is-the-93911.html

How is the result D? How will A do any good?

Does the perimeter work out to be 20?
Coz a^2 +b^2=100
So a+b=10 and a+b+hypotenuse=10+10?
I am confused, please help.
gmat-admin's picture

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

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