GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Oct 2018, 20:24

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 08 Dec 2012
Posts: 62
Location: United Kingdom
WE: Engineering (Consulting)
If perpendicular lines m and n intersect at (0,b) in the  [#permalink]

### Show Tags

Updated on: 20 Oct 2013, 04:56
2
35
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:35) correct 25% (01:40) wrong based on 755 sessions

### HideShow timer Statistics

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

Originally posted by nave on 19 Oct 2013, 13:12.
Last edited by Bunuel on 20 Oct 2013, 04:56, edited 1 time in total.
Renamed the topic and edited the question.
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 613
Re: If perpendicular lines m and n intersect at  [#permalink]

### Show Tags

20 Oct 2013, 01:17
13
9
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.
_________________
##### General Discussion
Manager
Status: Please do not forget to give kudos if you like my post
Joined: 19 Sep 2008
Posts: 98
Location: United States (CA)
Re: If perpendicular lines m and n intersect at (0,b) in the  [#permalink]

### Show Tags

02 Dec 2014, 19:29
3
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.

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

_________________

Intern
Joined: 12 Nov 2014
Posts: 19
Re: If perpendicular lines m and n intersect at (0,b) in the  [#permalink]

### Show Tags

03 Jan 2016, 10:53
Can someone please explain in detail, how both are insufficient?
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6399
GMAT 1: 760 Q51 V42
GPA: 3.82
If perpendicular lines m and n intersect at (0,b) in the  [#permalink]

### Show Tags

04 Jan 2016, 04:45
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.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Joined: 18 Jan 2012
Posts: 37
Re: If perpendicular lines m and n intersect at (0,b) in the  [#permalink]

### Show Tags

12 Jul 2016, 06:49
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?
Intern
Joined: 14 Jun 2016
Posts: 19
Location: United States
GMAT 1: 700 Q48 V37
WE: Engineering (Pharmaceuticals and Biotech)
Re: If perpendicular lines m and n intersect at (0,b) in the  [#permalink]

### Show Tags

16 Sep 2016, 16:25
1
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
BSchool Forum Moderator
Joined: 05 Jul 2017
Posts: 489
Location: India
GMAT 1: 700 Q49 V36
GPA: 4
Re: If perpendicular lines m and n intersect at (0,b) in the  [#permalink]

### Show Tags

02 Oct 2017, 11:38
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
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 50042
Re: If perpendicular lines m and n intersect at (0,b) in the  [#permalink]

### Show Tags

02 Oct 2017, 11:42
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

_________________
BSchool Forum Moderator
Joined: 05 Jul 2017
Posts: 489
Location: India
GMAT 1: 700 Q49 V36
GPA: 4
Re: If perpendicular lines m and n intersect at (0,b) in the  [#permalink]

### Show Tags

02 Oct 2017, 11:54
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

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
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 50042
Re: If perpendicular lines m and n intersect at (0,b) in the  [#permalink]

### Show Tags

02 Oct 2017, 12:41
1
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

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.
_________________
BSchool Forum Moderator
Joined: 05 Jul 2017
Posts: 489
Location: India
GMAT 1: 700 Q49 V36
GPA: 4
Re: If perpendicular lines m and n intersect at (0,b) in the  [#permalink]

### Show Tags

04 Oct 2017, 02:27
Intern
Joined: 08 Jul 2017
Posts: 3
Re: If perpendicular lines m and n intersect at (0,b) in the  [#permalink]

### Show Tags

18 Apr 2018, 18:49
Bunuel, can you pls explain how from statement 2 alone you can not assume b= -1? As points in perpendicular lines are opposite
DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1348
Location: India
Re: If perpendicular lines m and n intersect at (0,b) in the  [#permalink]

### Show Tags

18 Apr 2018, 22:06
Simba9 wrote:
Bunuel, can you pls explain how from statement 2 alone you can not assume b= -1? As points in perpendicular lines are opposite

Hello

The lines intersect at point (0,b) while (-1,0) is just a point on line n. That deosnt mean the points (0,b) and (-1,0) will be same.
And also, the two points anyway cannot be same. Because point (0,b) means x coordinate of this point is 0 while for point (-1,0) x coordinate is -1. So there is no point in comparing these two points. (pun not intended)
Re: If perpendicular lines m and n intersect at (0,b) in the &nbs [#permalink] 18 Apr 2018, 22:06
Display posts from previous: Sort by