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livio04
Joined: 21 Nov 2014
Last visit: 25 Nov 2016
Posts: 21
Given Kudos: 5
Location: United States
Concentration: Marketing, Social Entrepreneurship
Schools: HEC '18 (A) INSEAD Jan '17 Bocconi '17 IE
GPA: 3.55
WE:Brand Management (Consumer Packaged Goods)
02 Apr 2016, 12:43
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
74% (01:30) correct
26%
(01:29)
wrong
based on 1203
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Which side of triangle PQR is the longest?
(1) PQ is longer than QR.
(2) The measure of angle PQR is 70 degrees.
(1) PQ is longer than QR.
(2) The measure of angle PQR is 70 degrees.
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02 Apr 2016, 19:51
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livio04
Hi,
RULE - the longest side of a triangle has the largest angle opposite to it..
lets see the statements
(1) PQ is longer than QR.
we know QR is not the answer..
But we do not know about the third side PR
Insuff
(2) The measure of angle PQR is 70 degrees
we know from this that the other two angles combined are 180-70=110..
largest side has the largest angle against it..
It is possible that both angles are less than 70 : 60 and 50
Also it is possible that one angle is more than 70 : 75 and 35
Insuff
Combined
we still cannot say if PQ is longest or PR
Insuff
E
04 Apr 2016, 05:59
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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.
Which side of triangle PQR is the longest?
(1) PQ is longer than QR.
(2) The measure of angle PQR is 70 degrees.
In the original condition, for a triangle, there are 3 variables, which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer as 1 more equation is needed.
When 1) & 2), you cannot figure out which angle is the biggest and which side is the longest, which is not sufficient.
Thus, the answer is E.
For cases where we need 3 more equations, such as original conditions with “3 variables”, or“4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
Which side of triangle PQR is the longest?
(1) PQ is longer than QR.
(2) The measure of angle PQR is 70 degrees.
In the original condition, for a triangle, there are 3 variables, which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer as 1 more equation is needed.
When 1) & 2), you cannot figure out which angle is the biggest and which side is the longest, which is not sufficient.
Thus, the answer is E.
For cases where we need 3 more equations, such as original conditions with “3 variables”, or“4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
