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Re: If the two horizontal lines in the figure provided are parallel, what
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11 Sep 2015, 03:13
2
1
Answer: (B) (2) alone is sufficient.
Let's consider these one-by-one:
(1) a+f = 180
This does not provide any information we don't already have. If the lines are parallel, the following equalities hold - a = d (opposite angles) a = e (corresponding angles) b + d = 180 a + b = 180 e + f = 180 d + f = 180 b = f and so on.
So, we already know that a + f = 180.
This is not helpful in finding (a + f + d) – (e + h), as we don't know any of these values.
(2) a - f = 60
This is SUFFICIENT:
a + f = 180 (because a = d and d+f = 180, which is because d + b = 180 and b = f) a - f = 60
So, 2a = 240
or a = 120
Also, a = d so d = 120; f = 180 - a = 60 ; e = a = 120 ; h = e = 120
So, we can evaluate (a + f + d) – (e + h).
Hence sufficient.
Answer: (B) _________________
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Given : From Parallel Line case, a = d = e = h b = c = f = g
Question : what is (a + f + d) – (e + h) = (a+f+a) - (a+a) = f = ?
Statement 1: a + f = 180 a is Unknown Hence f can't be calculated Also, a+f=180 is a Universal Truth (Supplementary angles) and no extra information so this can't be used to answer the question because we are expected to know about this information NOT SUFFICIENT
Statement 2: a - f = 60 Also, We know a+f=180 (Supplementary angles) i.e. a = 120 and f = 60 SUFFICIENT
Answer: option B
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This question solely relies on our knowledge of angle measures and parallel lines. Angles a and b are complementary (add up to 180, a straight line), and angles b and f are congruent, so we already know that a + f = 180 without Statement (1) telling us. (a + f + d) – (e + h) = a + f + d – e – h = 180 – h. Since we do not know the exact value of h (the difference between the obtuse and acute angles), Statement (1) is not sufficient. Statement (2) gives us the difference between the obtuse and acute angle, and so it is sufficient. _________________
Re: If the two horizontal lines in the figure provided are parallel, what
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15 Sep 2015, 09:32
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 the two horizontal lines in the figure provided are parallel, what is (a + f + d) – (e + h)?
(1) a + f = 180
(2) a – f = 60
Transforming the original condition and the question, we have a=d=e=h thus (a + f + d) – (e + h)?--> f=?. a+f=180 we have 2 variables (a,f), and 1 equation (a+f=180) therefore we need 1 more equation. Therefore there is high probability that D is the answer
In case of 1), a+f=180 is the repetition of the original condition. Therefore the condition is not sufficient. In case of 2), a-f=60 and a+f=180 gives us 2f=120, f=60. Therefore the condition is sufficient, and the answer is B.
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60% (01:25) correct 
