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14 Feb 2016, 04:16
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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:
35%
(medium)
Question Stats:
60% (00:44) correct
40%
(00:54)
wrong
based on 82
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If a triangle has one side of 3 cm and another side of 4 cm, how long is the third side?
(1) The triangle is a right triangle.
(2) The third side is the longest side.
(1) The triangle is a right triangle.
(2) The third side is the longest side.
14 Feb 2016, 05:21
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Bunuel
Hi,
its easy to error, if we move with pre concieved thoughts...
we have read so many times about 3-4-x triangle, that the Q becomes difficult over say 6-7-x..
lets see the Q ..
two sides are 3 and 4..
so third side is>1 and <7..the moment we right this down, the chances of getting trapped into 3-4-5 triangle goes down
lets see the choices
(1) The triangle is a right triangle.
again there can be various combinations of right triangle with two sides 3 and 4..
Insuff
(2) The third side is the longest side.
third side is the longest , so it can be anything between 4 and 7..
insuff..
combined...
only possibility is of 3-4-5, as its a right triangle with two sides other than hyp as 3 and 4..
C
15 Feb 2016, 00:08
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
If a triangle has one side of 3 cm and another side of 4 cm, how long is the third side?
(1) The triangle is a right triangle.
(2) The third side is the longest side.
Modify the original condition and the question. Suppose the length of the third side as x, it becomes 4-3<x<4+3, 1<x<7. Then, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), you cannot certain that x is the longest side. So, 3^2+4^2=x^2 or 3^2+x^2=4^2, which is not unique and not sufficient.
For 2), even if it is the longest side, you cannot figure out the side in a unique way, which is not sufficient.
When 1) & 2), x=5, which is unique and sufficient.
Therefore, the answer is C.
For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
If a triangle has one side of 3 cm and another side of 4 cm, how long is the third side?
(1) The triangle is a right triangle.
(2) The third side is the longest side.
Modify the original condition and the question. Suppose the length of the third side as x, it becomes 4-3<x<4+3, 1<x<7. Then, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), you cannot certain that x is the longest side. So, 3^2+4^2=x^2 or 3^2+x^2=4^2, which is not unique and not sufficient.
For 2), even if it is the longest side, you cannot figure out the side in a unique way, which is not sufficient.
When 1) & 2), x=5, which is unique and sufficient.
Therefore, the answer is C.
For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
