Lesson: Tackling Data Sufficiency Questions

Comment on Tackling Data Sufficiency Questions

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.

Hi Brent,

If we are able to lock in a Geometric figure then can we say that the figure is essentially a diagram drawn to scale? Is this the reason why you have said that "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."

Thanks & Regards,
Abhirup
gmat-admin's picture

Hey Abhirup,

I think you're saying two different things. I agree with one part but not the other part.

I agree that, if we're able to LOCK IN the measurements/angles of a geometric figure, then we can just recreate a super accurate representation of the figure (using a compass, ruler, protractor, etc), and then measure the line with a ruler.

I don't think agree with: If we are able to lock in a Geometric figure then can we say that THE FIGURE IS essentially a DIAGRAM DRAWN TO SCALE.
Perhaps I'm reading this wrong, but in a DS geometry question, the accompanying diagram may or may not be drawn to scale.

For example, let's say a diagram features a triangle that LOOKS LIKE an equilateral triangle, and the target question asks "What is the area of ∆ABC?
If statement 1 reads "The lengths of the three sides are 3, 4 and 5" then we know that ∆ABC is a right triangle with hypotenuse 5, and the legs have length 3 and 4.
This information definitely LOCKS IN the shape of the triangle, HOWEVER this does NOT mean that the accompanying figure (the one that LOOKS LIKE an equilateral triangle) is drawn to scale.

Does that help?

Cheers,
Brent

Thanks Brent for your response. If I understand correctly, if we're able to LOCK IN a diagram then we can recreate a super accurate representation of the figure and this RECREATED REPRESENTATION (NOT the diagram accompanying the question stem) will be a figure DRAWN TO SCALE i.e. we may accurately measure the lengths of sides in the diagram using a ruler. Since this is the case we don't actually need to calculate the CONCRETE VALUE of the side to determine data sufficiency of the provided statements.

Please correct me if there is a flaw in this reasoning.
gmat-admin's picture

All of that is perfectly correct.

Cheers,
Brent

Thanks Brent!!

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

Hey Brent,

I've always thought that when they show a line separating the little box in the angle of the triangle (90 degree angle) that means that it's split in half to make two 45 degree angles. I think it does that for lots of other problems. Why not the one from the video?

Thanks
gmat-admin's picture

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

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