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What is the value of z in the triangle above? (1) x+y=139 (

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Source: — Data Sufficiency |
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What is the value of z in the triangle above?

by fskilnik@GMATH » Mon Jan 21, 2019 4:17 am
BTGmoderatorDC wrote:Image

What is the value of z in the triangle above?

(1) x+y=139
(2) y +z= 108
Source: Official Guide
All angles are measured in degrees.
$$? = z$$
$$\left( 1 \right)\,\,\,x + y = 139\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,z = 180 - 139\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{\rm{SUFF}}.\,$$
$$\left( 2 \right)\,\,\,y + z = 108\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {x,y,z} \right) = \left( {72,60,48} \right)\,\,\,\, \Rightarrow \,\,\,{\rm{? = 48}} \hfill \cr
\,{\rm{Take}}\,\,\left( {x,y,z} \right) = \left( {72,48,60} \right)\,\,\,\, \Rightarrow \,\,\,{\rm{? = 60}}\, \hfill \cr} \right.$$

The correct answer is therefore (A).


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

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by Brent@GMATPrepNow » Mon Jan 21, 2019 6:31 am
BTGmoderatorDC wrote:Image
What is the value of z in the triangle above?

(1) x + y = 139
(2) y + z = 108
Target question: What is the value of z in the triangle above?
IMPORTANT: Since angles in a triangle must add to 180 degrees, we can write: x + y + z = 180

Statement 1: x + y = 139
Take: x + y + z = 180 and replace (x + y) with 139 to get: 139 + z = 180
Solve equation for z to get: z = 41
So, the answer to the target question is z = 41
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: y + z = 108
Take: x + y + z = 180 and replace (y + z) with 108 to get: x + 108 = 180
Solve equation for x to get: x = 72
Hmmm, we know the value of x, but we have no way to find the value of z.
So, statement 2 is NOT SUFFICIENT

If you're not convinced, consider the following scenarios that satisfy statement 2:
Case a: x = 72, y = 50 and z = 58. In this case, the answer to the target question is z = 58
Case b: x = 72, y = 60 and z = 48. In this case, the answer to the target question is z = 48
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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