Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 20 Jul 2019, 17:20

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

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

### Show Tags

18 Sep 2018, 22:13
00:00

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 ]

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

### Show Tags

19 Sep 2018, 05:28
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

_________________
Intern
Joined: 24 Sep 2013
Posts: 23
Location: Saudi Arabia
GPA: 3.8
WE: Project Management (Energy and Utilities)
Re: In triangle WXY, what is the length of side XY? (1) a = 45 (2) a – b  [#permalink]

### Show Tags

21 Sep 2018, 10:40
EgmatQuantExpert Can you please elaborate in 2nd statement how you arrived that XZ = ZW = 1
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2943
Re: In triangle WXY, what is the length of side XY? (1) a = 45 (2) a – b  [#permalink]

### Show Tags

21 Sep 2018, 10:57
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
Joined: 24 Sep 2013
Posts: 23
Location: Saudi Arabia
GPA: 3.8
WE: Project Management (Energy and Utilities)
Re: In triangle WXY, what is the length of side XY? (1) a = 45 (2) a – b  [#permalink]

### Show Tags

21 Sep 2018, 11:05
EgmatQuantExpert Now i got it, thank you Mam for your explanation.
Manager
Joined: 22 Jan 2014
Posts: 172
WE: Project Management (Computer Hardware)
Re: In triangle WXY, what is the length of side XY? (1) a = 45 (2) a – b  [#permalink]

### Show Tags

24 Sep 2018, 03:19
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.
_________________
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
Display posts from previous: Sort by