In triangle WXY, what is the length of side XY? (1) a = 45 (2) a – b

Question

https://gmatclub.com/forum/download/file.php?id=43813 In triangle WXY, what is the length of side XY? (1) a = 45 (2) a – b = 0 image009.gif

EgmatQuantExpert · Answer

Solution 
  To find:  
 • The length of side XY, in triangle WXY

Analysing Statement 1  
“a = 45 degrees”

Implies, 
 • ∠XYW = 45 degrees
• ∠XWY = 22.5 degrees
• Thus, ∠YXW = 180 – 45 – 22.5 = 112.5 degrees

This information is not sufficient to find the length of XY

Therefore, Statement 1 is NOT sufficient to arrive at a unique answer

Analysing Statement 2  
“a – b = 0”

• Implies, a = b
• Thus, XY = XZ ………. (1)
• ∠XZW = 180 - b = 180 – a
• In triangle XZW, 
 o  ∠ZXW + 180-a + \frac{a}{2} = 180 
o Implies,  ∠ZXW = \frac{a}{2}  
• Thus, XZ = ZW = 1, since ∠ZXW = ∠XWZ

Therefore, the length of XY = 1 (from (1))

Therefore, Statement 2 is sufficient to arrive at a unique answer

Hence, the correct answer is option B

Answer: B  
  https://e-gmat.com/blogs/wp-content/uploads/2016/12/Geometry-Ability-Quiz-4-e1480581478957.png

vipulshahi · Answer

EgmatQuantExpert  Can you please elaborate in 2nd statement how you arrived that XZ = ZW = 1

EgmatQuantExpert · Answer

From 2nd statement, we know a - b = 0, means a = b As a = b, we can say in triangle XYZ, angle XYZ = angle XZY = a Now, we can also say angle XZY + angle XZW = 180 Or, a + angle XZW = 180 Or, angle XZW = 180 - a Considering triangle XZW, angle XZW + angle ZXW + angle ZWX = 180 Or, (180 - a) + angle ZXW + a/2 = 180 Or, angle ZXW = a/2 As angle ZXW = angle ZWX = a/2, we can say side ZX = side ZW = 1. Hope this helps

vipulshahi · Answer

EgmatQuantExpert  Now i got it, thank you Mam for your explanation.

thefibonacci · Answer

1) a = 45*
clearly insuff.

2) a-b = 0
or a=b
in other triangle angles are a/2, 180-(a/2), and a/2
this makes common side as 1
and since a=b so XY = 1 as well
so B alone is suff.

In triangle WXY, what is the length of side XY? (1) a = 45 (2) a – b

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In triangle WXY, what is the length of side XY? (1) a = 45 (2) a – b

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