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08 Jul 2023, 05:22
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
61% (02:39) correct
39%
(02:44)
wrong
based on 41
sessions
History
Date
Time
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Line AC is intersected by line XY at point B. Line DF is intersected by line XY at point E. What is the degree measure of angle CBE?
1. The degree measure of angle BEF is three times the degree measure of angle ABE.
2. The degree measure of angle ABX is equal to the degree measure of angle DEY.
1. The degree measure of angle BEF is three times the degree measure of angle ABE.
2. The degree measure of angle ABX is equal to the degree measure of angle DEY.
08 Jul 2023, 08:13
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Look at the following image which shows the problem pictorially.
img.png [ 6.39 KiB | Viewed 1232 times ]
Stmt 1: Let ∠ABE = ?, then ∠BEF = 3?. Since ∠BEF = 3?, ∠DEY = 3?, also as ∠ABE = ?, ∠CBE = 180-?. Since we can not assume line AC and DF to be parallel, we can't proceed from here to find any relation to find ∠CBE. Hence insufficient.
Stmt 2: Let ∠ABX = 180-?, then ∠DEY = 180-? but again we need one more relation which can lock value of ?. This is same condition as in stmt 1 hence insufficient.
Stmt 1 and Stmt 2: As explained above, now ∠ABE = ?, ∠ABX = 180-? and ∠CBE = 180-?. Since ∠BEF = 3?, ∠DEY = 3?. Now as per stmt 2, ∠ABX = ∠DEY = 180-?. So there are two values of ∠DEY, equate them and we can find value of ? and hence ∠CBE = 180-?. Hence sufficient.
Therefore C is the correct answer.
Attachment:
img.png [ 6.39 KiB | Viewed 1232 times ]
Stmt 1: Let ∠ABE = ?, then ∠BEF = 3?. Since ∠BEF = 3?, ∠DEY = 3?, also as ∠ABE = ?, ∠CBE = 180-?. Since we can not assume line AC and DF to be parallel, we can't proceed from here to find any relation to find ∠CBE. Hence insufficient.
Stmt 2: Let ∠ABX = 180-?, then ∠DEY = 180-? but again we need one more relation which can lock value of ?. This is same condition as in stmt 1 hence insufficient.
Stmt 1 and Stmt 2: As explained above, now ∠ABE = ?, ∠ABX = 180-? and ∠CBE = 180-?. Since ∠BEF = 3?, ∠DEY = 3?. Now as per stmt 2, ∠ABX = ∠DEY = 180-?. So there are two values of ∠DEY, equate them and we can find value of ? and hence ∠CBE = 180-?. Hence sufficient.
Therefore C is the correct answer.
rohitgm
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img.png [ 6.39 KiB | Viewed 1330 times ]
11 Jul 2023, 08:52
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IMO C,
Either of the statement is insufficient. I & II combined will give < as 135'
Either of the statement is insufficient. I & II combined will give < as 135'
