What is the value of q if s = 50? (1) q r (2) t = 80

Question

NJNJJJNJ.jpg What is the value of q if s = 50? (1) q > r (2) t = 80

MahmoudFawzy · Answer

from the given figure, q = s + t = 50 + t

sentence 1 : q>r ; concludes that q is an obtuse angle, but gives no information about its value.

sentence 2 : t = 80 ; q = 50 + 80 = 130, so sufficient

the answer is B

Kinshook · Answer

Asked: What is the value of  q  if  s = 50?

(1)  q > r 
It does not provide the value of q
NOT SUFFICIENT

(2)  t = 80 
q + t + s = 180
q + 80 + 50 = 180
q = 50
SUFFICIENT

IMO B

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary. An exterior angle is a sum of non-adjacent interior angles. Then we have q = s + t and s = 50 from the original condition. Since condition 2) tells t = 80, we have q = 50 + 80 = 130. Since the condition yields a unique solution, it is sufficient. Condition 1) If we have t = 80, then we have q = 130 and r = 50. If we have t = 70, then we have q = 120 and r = 60. Since condition 1) does not yield a unique solution, it is not sufficient. Therefore, B is the answer.

What is the value of q if s = 50? (1) q > r (2) t = 80

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