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# Are lines p (with slope m) and q (with slope n) perpendicular to each

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Are lines p (with slope m) and q (with slope n) perpendicular to each  [#permalink]

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10 Mar 2016, 04:11
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Difficulty:

65% (hard)

Question Stats:

51% (01:39) correct 49% (01:12) wrong based on 143 sessions

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Are lines p (with slope m) and q (with slope n) perpendicular to each other?

(1) m + 2 = n
(2) m + n = 0

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Re: Are lines p (with slope m) and q (with slope n) perpendicular to each  [#permalink]

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10 Mar 2016, 10:02
2 lines are perpendicular if and only if the product of their slopes is −1 .
(1) m + 2 = n
=> m-n = -2 --- equation 1
Not sufficient
(2) m + n = 0 --- equation 2
Not sufficient
Adding 1 and 2 , we get
2m = -2
=> m = -1
n=1
Product of slopes = m*n = -1

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Re: Are lines p (with slope m) and q (with slope n) perpendicular to each  [#permalink]

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12 Mar 2016, 05:57
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.

Are lines p (with slope m) and q (with slope n) perpendicular to each other?

(1) m + 2 = n
(2) m + n = 0

In general, when it comes to lines, there are 2 variables(slope, y-intercept). Since there are 2 lines, there are 4 variables, which should match with the number of equations. So you need 4 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer. When 1) & 2), from n=1, m=-1, mn=-1 is derived, which is yes and sufficient.

 For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% 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 C 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, D or E.
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Re: Are lines p (with slope m) and q (with slope n) perpendicular to each  [#permalink]

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15 Jun 2018, 05:51
Bunuel wrote:
Are lines p (with slope m) and q (with slope n) perpendicular to each other?

(1) m + 2 = n
(2) m + n = 0

For the 2 lines to be perpendicular to each other, we need m*n = -1

Statement 1:
m + 2 = n
m- n = -2
Plug in numbers, m = -1, n = 1, we get m*n = -1...Hence lines are perpendicular
m = 1, n = 3, we get, m*n = 3...Hence lines are not perpendicular

Statement 1 alone is Not Sufficient.

Statement 2:
m + n = 0
m = -n
Plug in numbers, m = -1, n = 1, we get m*n = -1...Hence lines are perpendicular
m = 2, n = -2, we get m*n = -4...Hence lines are not perpendicular

Combining both statements, we get, m = -1 & n = 1, satisfying both the statements.
Hence m*n = -1. the lines are perpendicular.

Thanks,
GyM
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Re: Are lines p (with slope m) and q (with slope n) perpendicular to each  [#permalink]

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15 Jun 2018, 08:13
Given: Line p has slope m and Line q has slope n.
To find: Are lines p and q perpendicular to each other?
For p and q to be perpendicluar m * n = -1

Statement 1:
m + 2 = n.
( m, n ) = ( 0, 2 ), ( 1, 3 ) ( -1 , 1 ) .....
So, statement 1 is insufficient.

Statement 2:
m + n = 0
( m, n ) = ( -2, 2 ), ( -3, 3 ) ( -1 , 1 ) .....
So, statement 2 is insufficient.

From Statement 1 and Statement 2:
Solving equations m - n = -2 and m + n = 0.
m = -1 and n = 1.
m * n = -1.
So, we can conclude that they are perpendicular.
Statement 1 and Statement 2 are sufficient.

Correct choice: C.
Re: Are lines p (with slope m) and q (with slope n) perpendicular to each &nbs [#permalink] 15 Jun 2018, 08:13
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