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22 Nov 2018, 23:38
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B
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95%
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31% (02:01) correct
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Triangle ABC is right angled at B, while triangle ACD is right angled at C. Is the length of CD > length of AB?
(1) Angle BAC = 45 degrees.
(2) Angle ADC = 45 degrees.
(1) Angle BAC = 45 degrees.
(2) Angle ADC = 45 degrees.
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:
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23 Nov 2018, 20:02
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amanvermagmat
So we have a triangle ABC where AC is the hypotenuse and in other triangle AC is a side.
1) angle BAC =45
So triangle BAC is isosceles right angled triangle.
Nothing about D, we could take D to any length
Insufficient
2) angle ADC is 45
So triangle ADC is a right angled triangle with AC=CD
But in other triangle AC is the hypotenuse so it is >the side AB..
Therefore CD is also greater than AB
Sufficient
B
Attachments
PicsArt_11-24-08.27.50.jpg [ 35.33 KiB | Viewed 3566 times ]
29 Nov 2018, 01:10
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Hello,
Since the triangles mentioned in the problem are right-angled triangles, it is natural to think that applying the Pythagoras theorem will help us solve the problem. However, we just need to know the concept that the Hypotenuse is the longest side in a right-angled triangle, to be able to solve this problem.
Using statement 1 alone,
We can say that triangle ABC is an isosceles right-angled triangle and hence, AB = BC. However, this is grossly insufficient to find out a relationship between CD and AB, since we know neither the lengths of the sides of the triangle ACD nor the angles. Hence, statement I alone is insufficient.
Using statement II alone,
We can deduce that triangle ACD is now an isosceles right-angled triangle and hence, CD = AC. Now, in triangle ABC, AC represents the hypotenuse and is, therefore, the longest side in triangle ABC. Hence, it has to be longer than AB; so we can say that CD is definitely longer than AB. Statement II alone is sufficient.
Therefore, the answer option is B.
In such questions, a good thing to do is to draw a diagram and try to put in as many values as possible, before analysing it further. Also, a point to remember about DS questions on Geometry is that any data that gives you a UNIQUE figure/diagram is the data that is going to be sufficient and vice versa.
Hope this helps!
Cheers,
CrackVerbal Academics Team
Since the triangles mentioned in the problem are right-angled triangles, it is natural to think that applying the Pythagoras theorem will help us solve the problem. However, we just need to know the concept that the Hypotenuse is the longest side in a right-angled triangle, to be able to solve this problem.
Using statement 1 alone,
We can say that triangle ABC is an isosceles right-angled triangle and hence, AB = BC. However, this is grossly insufficient to find out a relationship between CD and AB, since we know neither the lengths of the sides of the triangle ACD nor the angles. Hence, statement I alone is insufficient.
Using statement II alone,
We can deduce that triangle ACD is now an isosceles right-angled triangle and hence, CD = AC. Now, in triangle ABC, AC represents the hypotenuse and is, therefore, the longest side in triangle ABC. Hence, it has to be longer than AB; so we can say that CD is definitely longer than AB. Statement II alone is sufficient.
Therefore, the answer option is B.
In such questions, a good thing to do is to draw a diagram and try to put in as many values as possible, before analysing it further. Also, a point to remember about DS questions on Geometry is that any data that gives you a UNIQUE figure/diagram is the data that is going to be sufficient and vice versa.
Hope this helps!
Cheers,
CrackVerbal Academics Team
Attachments
Triangle ABC is right angled at B, while triangle ACD is right angled - 2.jpg [ 63.51 KiB | Viewed 3372 times ]
Triangle ABC is right angled at B, while triangle ACD is right angled - 1.jpg [ 73.46 KiB | Viewed 3351 times ]
kylebecker9
Joined: 05 Oct 2018
Last visit: 22 Apr 2019
Posts: 30
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Given Kudos: 61
Location: United States
Schools: Wharton Exec '21 (M)
GMAT 1: 770 Q49 V47
GPA: 3.95
WE:General Management (Other)
29 Nov 2018, 09:34
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amanvermagmat
Need to draw a picture to answer this question.
S1) Easy to see from the image that point D can be moved anywhere you want, so length of CD can be anything. Insufficient
S2) ACD is a 45:45:90, so CD = AC. AC is hypotenuse of ABC so AC > AB. Therefore CD > AB. Answer definitively is yes. Sufficient
Answer B.
