What is the value of x in the figure above? (1) x 40 (2) x = y

Question

https://gmatclub.com/forum/download/file.php?id=43055 What is the value of x in the figure above? (1) x > 40 (2) x = y image001.gif

PKN · Answer

Question stem:- What is the value of x?

St1:- x > 40
We can say that x+y+40=180 (Angles on a straight line add up to 180)
Or, x+y=140
y is unknown, so x can't be determined.

St2:- x = y

We have, x+y+40=180
Or, x+x=140
Or, 2x=140
Or, x=70.
Sufficient.

Ans. (B)

BrentGMATPrepNow · Answer

IMPORTANT ASIDE:   On GMAT diagrams, all lines that APPEAR straight ARE straight  
I mention this in case some students feel that angles x°, y° and 40° may not be on the straight line. 
So, given all of this, we can say:  x° + y° + 40° = 180°   (since the 3 angles are on the same line)

For more on what can and cannot be assumed on GMAT Geometry questions, see the video below.

Target question :    What is the value of x?

Statement 1 : x > 40  
Let's TEST some values, keeping in mind that it must also be true that  x° + y° + 40° = 180° 
There are several values of x and y that satisfy statement 1. Here are two: 
 Case a : x = 50, y = 90 (this also satisfies the condition that  x° + y° + 40° = 180° ) In this case, the answer to the target question is  x = 50 
 Case b : x = 60, y = 80 (this also satisfies the condition that  x° + y° + 40° = 180° ) In this case, the answer to the target question is  x = 60 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : x = y 
Take our "given" equation  x° + y° + 40° = 180°  and...
..replace y with x to get:  x° + x° + 40° = 180° 
Simplify left side: 2x° + 40° = 180°
Subtract 40° from both sides to get: 2x° = 140°
Solve: x = 70
So, the answer to the target question is  x = 70 
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

RELATED VIDEO FROM OUR COURSE
 https://www.youtube.com/watch?v=MaPuJh3m3Pk

fskilnik · Answer

? = x

Let´s start with (2), because (we believe) it´s (at least at first sight) much easier!

\left( 2 ight)\,\,\left\{ \begin{gathered}
 \,x = y \hfill \
 \,x + y + 40 = 180 \hfill \ 
\end{gathered} ight.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,2x + 40 = 180\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,x\,\,{	ext{unique}}\,\,\,

\left( 1 ight)\,\,\,{	ext{Geometric}}\,\,{	ext{Bifurcation}}\, (below)\,

Obs.: the figure on the left is "visually compatible" to statement (2), in which x is obviously 70 (2x+40=180), therefore the figure on the left (the one presented in the question stem) is viable (70>40). The figure on the right makes x greater, hence also > 40.

Both figures are viable, that is, they are constructible (with straight-edge and compass) AND they satisfy both the question stem pre-statements and the statement considered... the geometric bifurcation is shielded!

(We follow the notations and rationale taught in the GMATH method.)

What is the value of x in the figure above? (1) x > 40 (2) x = y

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