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18 Jun 2022, 03:30
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A
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Difficulty:
65%
(hard)
Question Stats:
45% (02:21) correct
55%
(02:32)
wrong
based on 29
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In triangle WXZ below, what is the length of side WX ?
(1) Line segment YZ has length 13.
(2) Angle x = 40
Are You Up For the Challenge: 700 Level Questions
PracticePill_1102.png [ 11.26 KiB | Viewed 5345 times ]
(1) Line segment YZ has length 13.
(2) Angle x = 40
Are You Up For the Challenge: 700 Level Questions
Attachment:
PracticePill_1102.png [ 11.26 KiB | Viewed 5345 times ]
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
18 Jun 2022, 04:03
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In △WYX, ∠WYX = ∠WXY = 2x => side WY = WX ......... (i)
In △WYZ, ∠WYZ = 180 - 2x and ∠YWZ = x
∠WYZ + ∠YWZ + ∠YZW = 180
180 - 2x + x + ∠YZW= 180
=> ∠YZW (or ∠WZX) = x
Hence, In △WYZ, ∠YWZ = ∠YZW = x => WY = YZ ......... (ii)
From i and ii, WY = YZ = WX
(1) Line segment YZ has length 13.
Using this statement we can find length of WX. Hence, statement 1 alone is sufficient.
(2) Angle x = 40
=> ∠WXZ = 80 ; ∠WZX = 40 ; and ∠ZWX = 60
We know all the angles for △WXZ, but we know don't know length of any sides with this statement alone.
Hence, the triangle can be very huge with these angle measures or a similar triangle with same angles measures but very small side lengths.
Hence, statement 2 alone is sufficient.
Answer: A
In △WYZ, ∠WYZ = 180 - 2x and ∠YWZ = x
∠WYZ + ∠YWZ + ∠YZW = 180
180 - 2x + x + ∠YZW= 180
=> ∠YZW (or ∠WZX) = x
Hence, In △WYZ, ∠YWZ = ∠YZW = x => WY = YZ ......... (ii)
From i and ii, WY = YZ = WX
(1) Line segment YZ has length 13.
Using this statement we can find length of WX. Hence, statement 1 alone is sufficient.
(2) Angle x = 40
=> ∠WXZ = 80 ; ∠WZX = 40 ; and ∠ZWX = 60
We know all the angles for △WXZ, but we know don't know length of any sides with this statement alone.
Hence, the triangle can be very huge with these angle measures or a similar triangle with same angles measures but very small side lengths.
Hence, statement 2 alone is sufficient.
Answer: A
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