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surupab
Joined: 22 Aug 2014
Last visit: 17 Jan 2017
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Location: United States
Concentration: Human Resources, General Management
Schools: IIMC IIMB KF EMBA"18 Insead Sept '17 XLRI GM"18 NUS '18
GPA: 3.97
WE:Information Technology (Insurance)
D
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If the lengths of two sides of a certain triangle are 5 and 10, what is the length of the third side of the triangle
(1) Perimeter of the triangle is a multiple of 5
(2) The triangle is isoceles
(1) Perimeter of the triangle is a multiple of 5
(2) The triangle is isoceles
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10 Apr 2016, 09:08
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surupab
hi,
let us see the restriction on third side, if two sides are 5 and 10..
let it be x, so 10-5<x<10+15 OR 5<x<15..
now lets see the statements..
(1) Perimeter of the triangle is a multiple of 5
since perimeter is multiple of 5, perimeter will be 15 or 20 or 25..
within the restrictions, ONLY value can be 10 and perimeter 25..
Suff
(2) the triangle is isoceles
there are two triangles possible...
5,5,10... since th third side does not fall in the range 5<x<10 .. not possible
5,10,10.. possible
Suff
D
General Discussion
11 Apr 2016, 02:51
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If the lengths of two sides of a certain triangle are 5 and 10, what is the length of the third side of the triangle
(1) Perimeter of the triangle is a multiple of 5
(2) The triangle is isosceles
We can modify the original condition and the question. If we designate the three sides of the triangle as x, we get 10-5<x<10+5, which is same as 5<x<15. There is 1 variable (x) in the original condition. In order to match the number of variables to the number of equations, we need 1 more equation. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that D is the correct answer choice.
For the condition 1), since x=10, the answer is unique and the condition is sufficient.
For the condition 2), from 5:5:10 and 5:10:10, only 5:10:10 is possible. Hence, the answer is unique and the condition is sufficient. Therefore, the correct answer is D.
l 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.
(1) Perimeter of the triangle is a multiple of 5
(2) The triangle is isosceles
We can modify the original condition and the question. If we designate the three sides of the triangle as x, we get 10-5<x<10+5, which is same as 5<x<15. There is 1 variable (x) in the original condition. In order to match the number of variables to the number of equations, we need 1 more equation. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that D is the correct answer choice.
For the condition 1), since x=10, the answer is unique and the condition is sufficient.
For the condition 2), from 5:5:10 and 5:10:10, only 5:10:10 is possible. Hence, the answer is unique and the condition is sufficient. Therefore, the correct answer is D.
l 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.
