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10 Apr 2020, 03:55
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Difficulty:
5%
(low)
Question Stats:
85% (01:06) correct
15%
(01:26)
wrong
based on 67
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ABC.PNG [ 8.38 KiB | Viewed 3388 times ]
What is the length of side AC of triangle ABC?
(1) AB = 13 and BC = 5
(2) \(x + y = 90\)
12 Apr 2020, 09:10
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Beware of the traps involved in this question. Firstly, the diagram gives you an impression that it’s a right-angled triangle – not necessarily, the diagram is not to be trusted.
From statement I alone, AB = 13 and BC = 5. Now, you have this stronger feeling that this HAS to be a right- angled triangle. Not really.
AC can be any value between 8 and 18. Note that the sum of any two sides is greater than the third side, while the difference of any two sides is lesser than the third side.
Statement I alone is insufficient to find a unique value for AC. Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone, angle x + angle y = 90 degrees. Therefore, angle ACB = 90 degrees. This is insufficient to find the length of AC.
A common trap that is easy to fall for is to sub-consciously use the first statement’s data and conclude that AC has to be 12. That’s against the rules of DS.
Answer option B can be eliminated. Possible answer options are C or E.
Combining statements I and II, we have the following:
From statement II, triangle ACB is a right angled triangle. From statement I, the hypotenuse AB = 13 and one of the perpendicular sides, BC = 5. Therefore, the other perpendicular side AC = 12 since 5, 12, 13 is a Pythagorean triplet.
The combination of statements is sufficient. Answer option E can be eliminated.
The correct answer option is C.
Hope that helps!
From statement I alone, AB = 13 and BC = 5. Now, you have this stronger feeling that this HAS to be a right- angled triangle. Not really.
AC can be any value between 8 and 18. Note that the sum of any two sides is greater than the third side, while the difference of any two sides is lesser than the third side.
Statement I alone is insufficient to find a unique value for AC. Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone, angle x + angle y = 90 degrees. Therefore, angle ACB = 90 degrees. This is insufficient to find the length of AC.
A common trap that is easy to fall for is to sub-consciously use the first statement’s data and conclude that AC has to be 12. That’s against the rules of DS.
Answer option B can be eliminated. Possible answer options are C or E.
Combining statements I and II, we have the following:
From statement II, triangle ACB is a right angled triangle. From statement I, the hypotenuse AB = 13 and one of the perpendicular sides, BC = 5. Therefore, the other perpendicular side AC = 12 since 5, 12, 13 is a Pythagorean triplet.
The combination of statements is sufficient. Answer option E can be eliminated.
The correct answer option is C.
Hope that helps!
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