Geometry DS Question

sanaa.rizwan wrote:In the figure above, what is the value of x + y
1.x = 70
2.∆ABC and ∆ADC are both isosceles triangles

In this case, to determine the value of (x + y), we need to know the value of x and y. Hence, we need to know, fixed positions of the points which makes the angles x and y.

Now, neither of the statements tells us anything about the position of point D, which makes angle y. We can satisfy both statements by placing D as low or as high we can inside the triangle, thus making the value of y smaller or larger.

Hence, both statements together is also not sufficient

The correct answer is E.

sanaa.rizwan wrote:OG13 DS 149



In the figure above, what is the value of x + y
1.x = 70
2.∆ABC and ∆ADC are both isosceles triangles

Important point: For geometry DS questions, we are typically checking to see whether the statements "lock" a particular angle or length into having just one value.

This concept is discussed in much greater detail in our free video: https://www.gmatprepnow.com/module/gmat- ... cy?id=1103

Statement 1 locks angle x by forcing it to have just one value (however it does not lock angle y).

Statement 2 forces the two triangles to be isosceles but the statement does not force the angles to have any particular values.

When we combine the statements, we should try to mentally grab points and try to move them (and still conform to the rules dictated by the statements). In this question, we can "grab" point D and pull it up or down, while still maintaining a 70-degree angle for x AND keeping the triangles as isosceles triangles. As we move point D up and down, angle y changes. So, there's now way that x+y can have a fixed value.

This means the answer is E

Cheers,
Brent

sanaa.rizwan wrote:OG13 DS 149



In the figure above, what is the value of x + y
1.x = 70
2.∆ABC and ∆ADC are both isosceles triangles

Here are some diagrams to illustrate my comments above:

Target question: What is the value of x + y ?

IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater detail in the video below.

When I use the above strategy, I can see that neither statement LOCKS in the value of y.
Given this, I can jump straight to...

Statements 1 and 2 combined
Statement 1 LOCKS in the value of x
Statement 2 tells us that ∆ABC and ∆ADC are isosceles triangles, but this is not enough to lock in the value of y.
Consider the following two diagrams that satisfy BOTH statements:

DIAGRAM #1



IMPORTANT: Notice that I can mentally take point D and push it down to get...
DIAGRAM #2


Notice that, by mentally pushing point D down, we don't change the fact that x = 70 degrees, AND we don't change the fact that ∆ABC and ∆ADC are isosceles triangles
However, when we mentally push point D down, we CHANGE the value of y

Since the value of y can vary, the value of x+y will also vary.
In other words, we cannot answer answer the target question with certainty.
As such, the combined statements are NOT SUFFICIENT

Answer: E

RELATED VIDEO
https://www.gmatprepnow.com/module/gmat ... /video/884

The technique shown in the above video can save a lot of time.

Here are a few more DS Geometry questions to practice with:
- https://www.beatthegmat.com/good-ds-ques ... 70971.html
- https://www.beatthegmat.com/what-is-the- ... 74620.html
- https://www.beatthegmat.com/what-is-the- ... 77326.html
- https://www.beatthegmat.com/geometry-tri ... 71836.html
- https://www.beatthegmat.com/ds-2-t278892.html
- https://www.beatthegmat.com/coordinate-g ... 77659.html