If l and k are lines in the xy-plane, is the product of the slopes of

Question

If l and k are lines in the xy-plane, is the product of the slopes of l and k equal to -1 ?

(1) Line l passes through the origin and the point (1,2).
(2) Line k has x-intercept 4 and y-intercept 2.

Bunuel · Accepted Answer

We don't need to calculate anything to answer this question.

If L and K are lines in xy- plane, is the product of the slope of l and k equal to -1?

The product of two lines equal to -1 if these lines are perpendicular to each other. So, the question basically asks whether L and K are perpendicular to each other.

Now, if we knew the equations of each line we would be able to answer the question. What do we need to find equation of a line? Since a line is defined by two points, then if we knew any two points of a line then we could get its equatiom

(1) Line L passes through the origin and the point (1,2). We have two points of line L: (0, 0) and (1, 2). So, we can get the equation of line L, though we know nothing about line K. Not sufficient.

(2) Line K has x-intercept 4 and y-intercept 2. We have two points of line K: (4, 0) and (0, 2). So, we can get the equation of line K, though we know nothing about line L. Not sufficient.

(1)+(2) We know both equation, hence we can answer whether the lines are perpendicular to each other. Sufficient.

Answer: C.

venmic

Can anyone give a better explanation on this one please

Hovv does K have a slope of -1/2 out of novvhere at all

Please any expert

Given two points \((x_1,y_1)\) and \((x_2,y_2)\) on a line, the slope \(m\) of the line is:

\(m=\frac{y_2-y_1}{x_2-x_1}\).

Since x-intercept of line K is 4, then it passes through point (4, 0) and since y-intercept of line K is 2, the it passes through point (0, 2). Hence it's slope is \(m=\frac{2-0}{0-4}=-\frac{1}{2}\).

For more on Coordinate Geometry check: math-coordinate-geometry-87652.html

Hope it helps.

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BrentGMATPrepNow · Answer

IMPORTANT : For geometry and coordinate plane Data Sufficiency questions, we are often checking to see whether the statements  "LOCK"  a particular line, angle, length, or shape into having just one possible position or measurement. This concept is discussed in much greater detail in the video below.

Target question :    Is the product of the slopes of l and k equal to -1?

IMPORTANT: The product of the slopes will equal -1 if the lines are perpendicular to each other (unless the two lines are horizontal and vertical, in which case the product will equal zero). This allows us to REPHRASE the target question as...

REPHRASED target question :    Are the two lines perpendicular to each other?

Statement 1 : Line l passes through the origin and the point (1, 2)   
NOTICE that statement 1 LOCKS line l into ONE AND ONLY ONE line. 
That said, we have no information about line k, so  we cannot determine whether the two lines are perpendicular to each other .
Since we cannot answer the  REPHRASED target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : Line k has x-intercept 4 and y-intercept 2.  
NOTICE that statement 1 LOCKS line k into ONE AND ONLY ONE line. 
That said, we have no information about line l, so  we cannot determine whether the two lines are perpendicular to each other .
Since we cannot answer the  REPHRASED target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
Statement 1 LOCKS in the shape of line l
Statement 2 LOCKS in the shape of line k
So,  we COULD very well determine whether or not the two lines are perpendicular to each other 
Since we can answer the  REPHRASED target question  with certainty, the combined statements are SUFFICIENT

Answer: C

RELATED VIDEO
 https://www.youtube.com/watch?v=wetqSGMdY7Y

GMATBLACKBELT · Answer

C

1: we dont know anything about the other line but we can find the slope of line l = 2

2: again we dont know the other line's slope but k's is -1/2

Together 2*-1/2= -1

But you could just realize that 1 and 2 are suff together b/c we know the slopes we are going to get a YES OR A NO NOT BOTH. so u could save some time.

GMATBLACKBELT · Answer

(4,0) and (0,2) --> (0-2)/(4-0) --> -2/4 --> -1/2

Formula for slope is (y1-y2)/(x1-x2)

neelesh · Answer

>> Line K has x-intercept 4 and y-intercept 2.

Its not clear if the x-intercept is going to be a (4,0). All it said is that x-intercept is 4 and y-intercept is 2. Even a coordinate of (-4,0) equals an x-intercept of 4.

So the x coordinates can be (4,0) or (-4,0) and y coordinates can be (0,2) or (0,-2)

So there are two possible lines that are perpendicular and the other 2 are not.

So in my opinion E.

What is the OA ?

neelesh · Answer

my mistake if 1) is true then 2) will have a specific set of coordinates. C is correct... :wall

Need to be more cautious.

blog · Answer

what do u mean by 2 has to have a specific set of cordinates .. form what i see i agree to your earlier assumption ...when u say line k has 4 as x cordinate and 2 as y cordinate u can very well say that it is a cordinate of the same point (4,2) then u cannot say anything about K's slope as it just passes through one point .. please explain as i still feel it should be E

lclausen0108 · Answer

read 2) carefully - line K has an x-intercept of 4 (meaning it hits the x axis at 4--- so the point would therefore be 4,0) and y-intercept of 2 (meaning it hits the y axis at 2---so the point would therefore be 0,2). So we now have (4,0) and (0,2) as our two points for line K and we can plug it into our slope formula of y2 - y1/x2 - x1 --> y2 = 2 y1 = 0 x2 - 0 y1 = 4 --> 2-0/0-4 ---> 2/-4 = -1/2.

Hope this helps!

Hope this helps!

thangvietnam · Answer

for this type of question, we do not use algebra until we can not solve the problem by using logic reasoning
from both choice we see that both lines are determined , this mean we know the slope of each lines and can know whether product of the lines are negative.

Kinshook · Answer

Asked: If l and k are lines in the xy-plane, is the product of the slopes of l and k equal to -1 ?

(1) Line l passes through the origin and the point (1,2).
Equation of line l : y = 2x
But line k is unknown
NOT SUFFICIENT

(2) Line k has x-intercept 4 and y-intercept 2.
Equation of line k : x/4 + y/2 = 1
But line l is unknown
NOT SUFFICIENT

(1) + (2) 
(1) Line l passes through the origin and the point (1,2).
Equation of line l : y = 2x
(2) Line k has x-intercept 4 and y-intercept 2.
Equation of line k : x/4 + y/2 = 1 or y = -x/2 + 2
Product of the slopes of l and k = 2* (-1/2) = - 1
SUFFICIENT

IMO C

Kimberly77 · Answer

Hi  BrentGMATPrepNow , regarding line K of (4,0) (0,2), it seems the line can be drawn either vertically or horizontally on point of (4,2). Therefore it doesn't seem line K is perpendicular to line L at the crossing point unless is at the origin point? Have I missed something in the reasoning here?

Also not quite sure with question asked is the product of the slope of L and K equal to -1? Since we got slope = -1/2. Where or how is the product here? Thanks Brent

BrentGMATPrepNow · Answer

Are you referring to the fact that line K has x-intercept 4 and y-intercept 2 (ie, statement 2)?
If so, then statement to is telling us that line K passes through BOTH of the points (4,0) and (0,2), and not just one of them.

Kimberly77 · Answer

Thanks  BrentGMATPrepNow . My bad forgot to mention statement 2. Yes and understand now.
By the way what about the product of the slope of L and K equal to -1? Since we got slope = -1/2. Where or how is the product here? Thanks Brent

BrentGMATPrepNow · Answer

From statement 1, we can conclude that the slope of line L is  2 . 
From statement 2, we can conclude that the slope of line K is  -1/2 .

The target question asks "Is the product of the slope of L and K equal to -1?"
In other words, does ( 2 )( -1/2 ) = -1? 
The answer is YES, which means the combined statements are sufficient.

ScottTargetTestPrep · Answer

Question Stem Analysis:

We need to determine whether the product of the slopes of lines l and k is equal to -1. Remember that if the product of the slopes of two lines is -1, then those two lines are perpendicular.

Statement One Alone:

\Rightarrow  Line l passes through the origin and the point (1,2).

Since we know two points belonging to line l, we can calculate the slope of line l. However, since we know nothing about the slope of line k, this is not sufficient to answer the question.

Eliminate answer choices A and D.

Statement Two Alone:

\Rightarrow  Line k has x-intercept 4 and y-intercept 2.

Since we know two points belonging to line k, we can calculate the slope of line k. However, since we know nothing about the slope of line l, this is not sufficient to answer the question.

Eliminate answer choice B.

Statements One and Two Together:

Using statement one, we can calculate the slope of line l, and using statement two, we can calculate the slope of line k. Since we can calculate the slopes of both lines, we can answer the question of whether the product of the two slopes is equal to -1.

Remember that in DS questions, we don't have to answer the question, we only need to determine whether we have enough information to do so. It would be a huge waste of time to actually calculate the slopes of the two lines in this question when it is clear that neither statement is sufficient on its own, but both statements together are sufficient.

Answer: C

jabhatta2 · Answer

Generic question   Bunuel   KarishmaB   avigutman  : Per my understanding, on the X – Y graph, every line on the X- Y axis has the following template :

Y = mx + constant

But for this line on the graph below , the equation of the line is  x = 5

Question : how to go from  y = mx + constant  to  x =5   ?

Is Y = 0 ? 
Is m = (any number) / 0 ? 
Is Constant = 0 ?

If Yes, then I plug that into the template equation :

Y (=0) = M (any number/0). x + constant (=0)

or

0 = (any number/0) x + 0

I dont see how you get  x = 5  from  y = mx + constant.

I am struggling to go from  y = mx + constant  to  x = 5

KarishmaB · Answer

Think of it in the reverse way. A set of points that satisfy a certain condition is called the locus of the condition. 
The locus of y = mx + c is a straight line where m and c are real numbers. 
The locus on x = a is also a straight line parallel to y axis. 
Since m is not defined (infinity) in this case, we do not represent it in y = mx + c form.

Kimberly77 · Answer

Great explanation BrentGMATPrepNow and crystal clear now. Thanks Brent

avigutman · Answer

See page 220 in my book,  jabhatta2 .

If l and k are lines in the xy-plane, is the product of the slopes of

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