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Difficulty:
75%
(hard)
Question Stats:
36% (01:50) correct
64%
(01:45)
wrong
based on 74
sessions
History
Date
Time
Result
Not Attempted Yet
In the figure, is the line AB perpendicular to the line CD?
(1) x + y =180
(2) AOC is an isosceles triangle
Attachment:
2019-09-06_2106.png [ 32.3 KiB | Viewed 4003 times ]
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
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firas92
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Since AB and CD are intersecting lines, x=y
We need to find whether x=y=90
(1) x + y =180
2y=180
y=90
1 is sufficient
(2) AOC is an isosceles triangle
If AO=AC
y+y+y/2=180
y=72
If AO=CO
y+y/2+y/2=180
y=90
2 is insufficient
Answer is (A)
Posted from my mobile device
_________________
We need to find whether x=y=90
(1) x + y =180
2y=180
y=90
1 is sufficient
(2) AOC is an isosceles triangle
If AO=AC
y+y+y/2=180
y=72
If AO=CO
y+y/2+y/2=180
y=90
2 is insufficient
Answer is (A)
Posted from my mobile device
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imants12
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Joined: 19 Jul 2019
Last visit: 16 Sep 2025
Posts: 15
Location: India
Schools: ISB '23 (A$)
GMAT 1: 710 Q47 V41
GPA: 3.84
If AB & CD are intersecting lines, then x is equal to y.
Only then we can make out from stat1 that x+y=180, therefore 2y=180 making y equal to 90.
In the stat 2, it says that triangle AOC is Isoc,meaning AO & OC are equal sides since angle AOC is y°, and one other angle is given to be y°/2. Hence, again 2y=180, therefore AB is perpendicular to CD.
Correct answer is D, please amend the OA.
Posted from my mobile device
Only then we can make out from stat1 that x+y=180, therefore 2y=180 making y equal to 90.
In the stat 2, it says that triangle AOC is Isoc,meaning AO & OC are equal sides since angle AOC is y°, and one other angle is given to be y°/2. Hence, again 2y=180, therefore AB is perpendicular to CD.
Correct answer is D, please amend the OA.
Posted from my mobile device
GMAT 1: 760 Q51 V42
Posts: 10,057
Bunuel
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.
We have \(x = y\), since \(x°\) and \(y°\) are vertical each other
Since we have 2 variables (\(x\) and \(y\)) and 1 equation, D is most likely to be the answer. So, we should consider each condition on its own first.
Condition 1)
Since \(x = y\) and \(x + y = 180\), we have \(x = y = 90\).
Thus, \(AB\) and \(CD\) are perpendicular each other and the answer is 'yes'.
Since condition 1) yield a unique answer, it is sufficient.
Condition 2)
If \(AO=OC\), then we have the angle \(<ACO = y/2\) and \(x+y = 180\) or \(x = y = 90\), \(AB\) and \(CD\) are perpendicular each other and the answer is 'yes'.
If \(AO=AC\), then we have the angle \(<ACO = x\) and \(2x+y/2 = 180\) or \(x = y = 72\), \(AB\) and \(CD\) are not perpendicular each other and the answer is 'no'.
Since condition 2) does not yield a unique answer, it is not sufficient.
Therefore, A is the answer.
If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
Kinshook
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Schools: HBS '28 CBS '26 Wharton '26
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Bunuel
Asked: In the figure, is the line AB perpendicular to the line CD?
Q. Is x = 90?
x = y
(1) x + y =180
Since x = y ; x = 90
SUFFICIENT
(2) AOC is an isosceles triangle
Case 1:
x + y/2 + y/2 = 180
x +y = 180
2x = 180
x = 90
Case 2:
2x + y/2 = 180
5x/2 = 180
x = 72
line AB may or may not be perpendicular to the line CD
NOT SUFFICIENT
IMO A
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