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

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

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New post 29 Aug 2018, 00:37
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A
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Re: What is the value of x in the figure above? (1) x > 40 (2) x = y  [#permalink]

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New post 29 Aug 2018, 02:18
Bunuel wrote:
Image
What is the value of x in the figure above?

(1) x > 40
(2) x = y
Attachment:
image001.gif


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)
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Re: What is the value of x in the figure above? (1) x > 40 (2) x = y  [#permalink]

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New post 29 Aug 2018, 06:09
Top Contributor
Bunuel wrote:
Image
What is the value of x in the figure above?

(1) x > 40
(2) x = y

Attachment:
image001.gif


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

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

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New post 29 Aug 2018, 06:41
Bunuel wrote:
Image
What is the value of x in the figure above?

(1) x > 40
(2) x = y
Attachment:
The attachment image001.gif is no longer available



\(? = x\)

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

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

\(\left( 1 \right)\,\,\,{\text{Geometric}}\,\,{\text{Bifurcation}}\, (below)\,\)

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.)
Attachments

File comment: Geometric Bifurcation - GMATH method
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29Ago18_8y.gif [ 6.01 KiB | Viewed 332 times ]


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