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If perpendicular lines m and n intersect at (0,b) in the

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If perpendicular lines m and n intersect at (0,b) in the [#permalink]

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If perpendicular lines m and n intersect at (0,b) in the standard (x,y) plane, what is the value of b?

(1) The slope of the line m is -1/2

(2) The point (-1,0) is on the line n
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Oct 2013, 03:56, edited 1 time in total.
Renamed the topic and edited the question.

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Re: If perpendicular lines m and n intersect at [#permalink]

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nave81 wrote:
If perpendicular lines \(m\) and \(n\) intersect at \((0,b)\) in the standard (x,y) plane, what is the value of \(b\)?

1. The slope of the line \(m\) is \(-\frac{1}{2}\)

2. The point \((-1,0)\) is on the line \(n\)


From F.S 1 , all we know is that the slope of the line n is 2. Clearly Insufficient.

From F.S 2, we know a point on the line n, but don't know the slope.Insufficient.

Taking both together, we know that slope of line \(n = \frac{(b-0)}{(0-(-1)}\) = b. And given that the slope is 2. Thus, b=2. Sufficient.

C.
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Re: If perpendicular lines m and n intersect at (0,b) in the [#permalink]

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New post 02 Dec 2014, 18:29
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To find b we need equation of line.
1. gives us equation of line m but we do not know x intercept so not sufficient.
2. we cannot find the equation of line n so not sufficient.

1&2 we know slope of m we can get slope of n (inverse negative) and can find equation of line n. which can give us b.

Answer: C

nave wrote:
If perpendicular lines m and n intersect at (0,b) in the standard (x,y) plane, what is the value of b?

(1) The slope of the line m is -1/2

(2) The point (-1,0) is on the line n

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Re: If perpendicular lines m and n intersect at (0,b) in the [#permalink]

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New post 03 Jan 2016, 09:53
Can someone please explain in detail, how both are insufficient?

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If perpendicular lines m and n intersect at (0,b) in the [#permalink]

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New post 04 Jan 2016, 03:45
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 perpendicular lines m and n intersect at (0,b) in the standard (x,y) plane, what is the value of b?

(1) The slope of the line m is -1/2

(2) The point (-1,0) is on the line n

In the original condition, for the line, there are 2 variables(the slope and the standard y plane). Since there are 2 lines, there should be 4 variables. Also, the two lines perpendicularly meet and multiplication of the slope is -1, which makes 1 equation. In order to match with the number of euqations, you need 3 more equations. For 1) 1 equations, for 2) 1 equation, which is likely to make E the answer. In 1) & 2), the slope if line m is -1/2 and the slope of line n should be 2. So, b=2 is derived from (b-0/0-(-1))=2, which is unique and sufficient. Therefore, the answer is C.


 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.
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Re: If perpendicular lines m and n intersect at (0,b) in the [#permalink]

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New post 12 Jul 2016, 05:49
Could someone explain why st.2 is not sufficient? Wouldn't b = 0 from (-1,0)? I guess this is just for line n.
Mau5 - could you pleas explain why the slope of n would equal b?

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Re: If perpendicular lines m and n intersect at (0,b) in the [#permalink]

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New post 16 Sep 2016, 15:25
nave wrote:
If perpendicular lines m and n intersect at (0,b) in the standard (x,y) plane, what is the value of b?

(1) The slope of the line m is -1/2

(2) The point (-1,0) is on the line n


1) slope of m is -1/2; however, there are infinite number of lines that can have slope of -1/2 and cross the y-axis at x=0. NS

2) (-1,0) is on line n. However, you don't know what is the slope of n; n can slope upwards or downwards to satisfy (0,b) since b can be negative or positive number.

1+2) slope of m is -1/2. Since m and n are perpendicular, that means n has slope of 2. Given n has the point (-1,0) with a slope of 2, you can find out where it crosses the y-axis. C

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Re: If perpendicular lines m and n intersect at (0,b) in the [#permalink]

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New post 02 Oct 2017, 10:38
Hey Bunuel,

In this question, how do we know "b" is positive? if "b" is negative then the value of b = -2

Hence I marked E. Can you explain why we didn't consider the case where "b" is negative

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Re: If perpendicular lines m and n intersect at (0,b) in the [#permalink]

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New post 02 Oct 2017, 10:42
pikolo2510 wrote:
Hey Bunuel,

In this question, how do we know "b" is positive? if "b" is negative then the value of b = -2

Hence I marked E. Can you explain why we didn't consider the case where "b" is negative


How did you get b = -2? Please show your work.
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Re: If perpendicular lines m and n intersect at (0,b) in the [#permalink]

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New post 02 Oct 2017, 10:54
Bunuel wrote:
pikolo2510 wrote:
Hey Bunuel,

In this question, how do we know "b" is positive? if "b" is negative then the value of b = -2

Hence I marked E. Can you explain why we didn't consider the case where "b" is negative


How did you get b = -2? Please show your work.


Sure Bunuel :-)

Each statement is insufficient, so I am considering the case when we look at the both the statement together

Case 1: -
Equation of line M
y = (-1/2)*x + b

Equation of line N
y = 2*x + b

As (-1,0) lies on line N, it should satisfy Equation of line N and hence value of b comes to b=2

Case 2 : -
Equation of line M
y = (-1/2)*x - b

Equation of line N
y = 2*x - b

As (-1,0) lies on line N, it should satisfy Equation of line N and hence value of b comes to b=- 2

The question says the two lines intersect at (0, b) , I don't know if b is positive or negative, hence I considered two cases of b and got two values of b i.e. -2 and 2. Let me know your thoughts

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Re: If perpendicular lines m and n intersect at (0,b) in the [#permalink]

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pikolo2510 wrote:
Bunuel wrote:
pikolo2510 wrote:
Hey Bunuel,

In this question, how do we know "b" is positive? if "b" is negative then the value of b = -2

Hence I marked E. Can you explain why we didn't consider the case where "b" is negative


How did you get b = -2? Please show your work.


Sure Bunuel :-)

Each statement is insufficient, so I am considering the case when we look at the both the statement together

Case 1: -
Equation of line M
y = (-1/2)*x + b

Equation of line N
y = 2*x + b

As (-1,0) lies on line N, it should satisfy Equation of line N and hence value of b comes to b=2

Case 2 : -
Equation of line M
y = (-1/2)*x - b

Equation of line N
y = 2*x - b

As (-1,0) lies on line N, it should satisfy Equation of line N and hence value of b comes to b=- 2

The question says the two lines intersect at (0, b) , I don't know if b is positive or negative, hence I considered two cases of b and got two values of b i.e. -2 and 2. Let me know your thoughts


It's not y = mx - b. It's always \(y=mx+b\), where: \(m\) is the slope of the line and \(b\) is the y-intercept of the line.
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Re: If perpendicular lines m and n intersect at (0,b) in the [#permalink]

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New post 04 Oct 2017, 01:27
Got my mistake, thanks Bunuel

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Re: If perpendicular lines m and n intersect at (0,b) in the   [#permalink] 04 Oct 2017, 01:27
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