If the two horizontal lines in the figure provided are parallel, what

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

answer (B)
(a + f + d) – (e + h)?
a=e & d=h ( corresponding angles)

so a+f+d-a-d=f
To find f, we need two equations but we know that a+f=180
So we only need a-f=60

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

(a + f + d) – (e + h) = a + f + d - d -a = f on applying alternate angle theory --- as e =d and a =h
so f =?

st 1. a+f =180
hence 1 not sufficient


st 2. a -f =60
and f =b ( corresponding angle )

so a-b =60 ----- a
and a+b = 180 ---- b(angle on a straight line equal 180 )

solving a and b we get a = 240/2= 120
and therefore f = 60

B sufficient

Ans

The question stem says the horizontal lines are parallel.

Using this information we can deduce,
a = d -------------------(1) (opposite angles)

a= e ------------------(2) (corresponding angles)

e= h ------------------(3) (opposite angles) , therefore a = h

d + f = 180
from (1)
a + f = 180 ----------- (4)

using this info in the equation (a + f + d) – (e + h)

180 + a - 2a => 180 - a --------------- (5)

Statement 1:

a + f = 180 => same as eq. (4) . No new info. Cannot get the value - Insufficient

statement 2

a – f = 60 ------------- (6)
from (4) and (6) can find the value of a
substitute in (5) we can find the value of (a + f + d) – (e + h)

Ans B => Statement 2 sufficient

answer is B.

f=c (parallel lines having same interception)
hence, a+c or a+f=180
B gives that a-f=60

solving for both we get the vales for a and f.

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

GROCKIT OFFICIAL SOLUTION:

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.

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.

This is what you call a trick question.... How I fell for it... C trap question ...

A + B = 180
B = F
A + F = 180
Therefore you should skip this option first of all

Solution:
I solved this one without actually doing any calculations(may be little bit)

so we know opposite angle are equal, so we know that a=d and c=b, also if the two lines are parallel then a=e=h,

so basically the question is asking what is the value of a because all else simply cancels out.

1.a+f=180. we know that already by the virtue of the rules of parallel lines.

no help because we cant find the value of a.

2. a-f=60,
we know that a+f=180(not from option 1 but from the property itself.)

so we get 2a=240 so a=120.

thats the solution of the question. so Option B is correct.

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