Walkabout wrote:
Attachment:
Triangles.png
In the figure above, what is the value of x + y ?
(1) x = 70
(2) ABC and ADC are both isosceles triangles
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 (
alone) 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
If we had additional info that could confirm the equal sides according to the diag attached, and also some info like height of ADC is half of ABC, In that case can we find the angle y?