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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
33% (02:05) correct
67%
(02:49)
wrong
based on 126
sessions
History
Date
Time
Result
Not Attempted Yet
What is the perimeter of ∆PQS ?
(1) x = 45
(2) w = 15
Because angle w is outside of ∆PQS, it is tempting to think that angle w is not required to construct ∆PQS,
but it is. The second paragraph below shows that w can determine x. Hence, if Statement (1) alone can
answer the question, then Statement (2) can as well.
The minimum details needed to construct a triangle are one side and two angles, or two sides and one
angle, or all the three sides. In ∆PQS, we have ∠PSQ = 30° (from the figure) and the side PS = 1. So, we
are short of knowing one angle or one side to construct ∆PQS. Statement (1) would help with an angle in
the triangle. So, Statement (1) is sufficient.
Construct line PS = 1. Draw an angle making 30 degrees with PS at S and name the line l. Extend the line
PS 2 units further to the right of the point S to locate the point R. Now, draw another line measuring w (=
15) degrees with PR from the point R, and name the line m. So, the point of intersection of l and m is the
point Q. Now, measure ∠PQS to find x.
The answer is (D).
but it is. The second paragraph below shows that w can determine x. Hence, if Statement (1) alone can
answer the question, then Statement (2) can as well.
The minimum details needed to construct a triangle are one side and two angles, or two sides and one
angle, or all the three sides. In ∆PQS, we have ∠PSQ = 30° (from the figure) and the side PS = 1. So, we
are short of knowing one angle or one side to construct ∆PQS. Statement (1) would help with an angle in
the triangle. So, Statement (1) is sufficient.
Construct line PS = 1. Draw an angle making 30 degrees with PS at S and name the line l. Extend the line
PS 2 units further to the right of the point S to locate the point R. Now, draw another line measuring w (=
15) degrees with PR from the point R, and name the line m. So, the point of intersection of l and m is the
point Q. Now, measure ∠PQS to find x.
The answer is (D).
Attachment:
Image.png [ 19.1 KiB | Viewed 4875 times ]
dina98
Joined: 14 Jul 2014
Last visit: 07 Jun 2019
Posts: 121
Own Kudos:
Given Kudos: 110
Location: United States
Schools: Duke '20 (D)
GMAT 1: 720 Q50 V37
GMAT 2: 600 Q48 V27
GPA: 3.2
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28 Sep 2015, 20:24
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is it E? QP cannot be found?
29 Sep 2015, 23:59
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This question is from "Nova's GMAT Data Sufficiency Prep Course" page #54. Fed up with my pathetic performance on DS, i came across this DS-book and its completely different approach to DS problems (i never thought of DS problems the way they take them. No comments of effectiveness though).
As far as this problem is concerned, we dont have to 'find' the perimeter, what we need to know is whether it can be found.
Like every other Quant question, for this question too i am waiting for Bunuel to reply.
Below is the OE by Nova though
As far as this problem is concerned, we dont have to 'find' the perimeter, what we need to know is whether it can be found.
Like every other Quant question, for this question too i am waiting for Bunuel to reply.
Below is the OE by Nova though
Because angle w is outside of ∆PQS, it is tempting to think that angle w is not required to construct ∆PQS,
but it is. The second paragraph below shows that w can determine x. Hence, if Statement (1) alone can
answer the question, then Statement (2) can as well.
The minimum details needed to construct a triangle are one side and two angles, or two sides and one
angle, or all the three sides. In ∆PQS, we have ∠PSQ = 30° (from the figure) and the side PS = 1. So, we
are short of knowing one angle or one side to construct ∆PQS. Statement (1) would help with an angle in
the triangle. So, Statement (1) is sufficient.
Construct line PS = 1. Draw an angle making 30 degrees with PS at S and name the line l. Extend the line
PS 2 units further to the right of the point S to locate the point R. Now, draw another line measuring w (=
15) degrees with PR from the point R, and name the line m. So, the point of intersection of l and m is the
point Q. Now, measure ∠PQS to find x.
The answer is (D).
but it is. The second paragraph below shows that w can determine x. Hence, if Statement (1) alone can
answer the question, then Statement (2) can as well.
The minimum details needed to construct a triangle are one side and two angles, or two sides and one
angle, or all the three sides. In ∆PQS, we have ∠PSQ = 30° (from the figure) and the side PS = 1. So, we
are short of knowing one angle or one side to construct ∆PQS. Statement (1) would help with an angle in
the triangle. So, Statement (1) is sufficient.
Construct line PS = 1. Draw an angle making 30 degrees with PS at S and name the line l. Extend the line
PS 2 units further to the right of the point S to locate the point R. Now, draw another line measuring w (=
15) degrees with PR from the point R, and name the line m. So, the point of intersection of l and m is the
point Q. Now, measure ∠PQS to find x.
The answer is (D).
