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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # In triangle WXY, what is the length of side XY? (1) a = 45 (2) a – b

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Math Expert V
Joined: 02 Sep 2009
Posts: 56304
In triangle WXY, what is the length of side XY? (1) a = 45 (2) a – b  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 29% (02:25) correct 71% (02:24) wrong based on 77 sessions

### HideShow timer Statistics  In triangle WXY, what is the length of side XY?

(1) a = 45
(2) a – b = 0

Attachment: image009.gif [ 1.64 KiB | Viewed 752 times ]

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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 2943
Re: In triangle WXY, what is the length of side XY? (1) a = 45 (2) a – b  [#permalink]

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1

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

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Re: In triangle WXY, what is the length of side XY? (1) a = 45 (2) a – b  [#permalink]

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EgmatQuantExpert Can you please elaborate in 2nd statement how you arrived that XZ = ZW = 1
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 2943
Re: In triangle WXY, what is the length of side XY? (1) a = 45 (2) a – b  [#permalink]

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

Quote: 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 _________________
Intern  B
Joined: 24 Sep 2013
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WE: Project Management (Energy and Utilities)
Re: In triangle WXY, what is the length of side XY? (1) a = 45 (2) a – b  [#permalink]

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EgmatQuantExpert Now i got it, thank you Mam for your explanation.
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Re: In triangle WXY, what is the length of side XY? (1) a = 45 (2) a – b  [#permalink]

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Bunuel wrote: In triangle WXY, what is the length of side XY?

(1) a = 45
(2) a – b = 0

Attachment:
image009.gif

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.
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Illegitimi non carborundum. Re: In triangle WXY, what is the length of side XY? (1) a = 45 (2) a – b   [#permalink] 24 Sep 2018, 03:19
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