Line l lies in the xy-plane and does not pass through the origin. What

Question

Line  \ell  lies in the xy-plane and does not pass through the origin. What is the slope of line  \ell  ?

(1) The x-intercept of line  \ell  is twice the y-intercept of line  \ell 
(2) The x-and y-intercepts of line  \ell  are both positive

BrentGMATPrepNow · Accepted Answer

Target question :    What is the slope of line l?

Statement 1 : The x-intercept of line  \ell  is twice the y-intercept of line l   
Let k = the y-intercept of line l
This means 2k = the x-intercept of line l
If the y-intercept is k, then line l passes through the y-axis at the point  (0, k) 
If the x-intercept is 2k, then line l passes through the x-axis at the point  (2k, 0) 
Since  (0, k)  and  (2k, 0)  are both points on line l, we can apply the slope formula to these points to find the slope of line l. 
We get: slope = (k - 0)/(0 - 2k) = k/(-2k) = -1/2
So,  the slope of line l = -1/2 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : The x-and y-intercepts of line l are both positive  
If we're able to imagine different lines (with DIFFERENT SLOPES) that satisfy this condition, we'll quickly see that statement 2 is not sufficient. However, if we don't automatically see this, we can take the following approach...
There are many different cases that satisfy statement 2 yet yield different answers to the target question. Here are two: 
Case a: the x-intercept is 1 and the y-intercept is 1, which means line l passes through (1, 0) and (0, 1). Applying the slope formula, we get:  slope = (0 - 1)/(1 - 0) = -1 
Case b: the x-intercept is 2 and the y-intercept is 1, which means line l passes through (2, 0) and (0, 1). Applying the slope formula, we get:  slope = (0 - 1)/(2 - 0) = -1/2 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Answer: A

ccooley · Answer

When I see something like this, I just start drawing. For me, it's easier to look at the slopes and compare them, versus trying to understand the slopes based on numbers and equations.

For statement 1, draw a couple of lines that have an x-intercept twice the y-intercept. Don't forget negatives (for instance, x-intercept of -2 and y-intercept of -1). You should notice that all of the slopes of these lines are equal.

https://i.imgur.com/OUO1NWf.png

Note that this is an example of a DS problem with a 'nice but not necessary' statement. Be very careful to analyze the statements each on their own before putting them together. It's  nice  to know that the slopes are both positive (statement 2), because it gives you a clearer picture of what's going on. But critically, it's not  necessary  to know that. You can answer the question even without it.

ScottTargetTestPrep · Answer

We need to determine the slope of line ℓ, given that it doesn’t pass through the origin.

Statement One Alone:

The x-intercept of line ℓ is twice the y-intercept of line ℓ.

We can let b = the y-intercept of line ℓ; thus, 2b = the x-intercept of line ℓ. Thus, the two points through which line ℓ passes are (2b, 0) and (0, b). With two points known, we can calculate the slope of line ℓ:

(b - 0)/(0 - 2b) = b/(-2b) = -½

Statement one alone is sufficient to answer the question.

Statement Two Alone:

The x- and y-intercepts of line ℓ are both positive.

Knowing that both the x- and y-intercepts of a line are positive does not allow us to determine the slope of the line. For example, the slope of the line with x-intercept = 1 and y-intercept = 2 will be different from the slope of the line with x-intercept = 1 and y-intercept = 3. Statement two alone is not sufficient to answer the question.

Answer: A

GMATinsight · Answer

Answer: Option A

Video solution by  GMATinsight

https://www.youtube.com/watch?v=jtLkbjiWrTA

Mo2men · Answer

Dear  ccooley  and Brent,

I have a question. You both consider the slop is negative., while it could be positive too. For example, the line could intersect the 'y' in point (0,1) and 'x' in point (-2,0). This line satisfies the condition too. What did not you take it into consideration?

Thanks

BrentGMATPrepNow · Answer

In your example, the x-intercept is -2 and the y-intercept is 1

However, statement 1 says that the x-intercept twice the y-intercept. 
-2 is not twice 1

Cheers,
Brent

Mo2men · Answer

Thanks Brent. What I understand from Fact 1 is the that 'twice' means x-intercept 'double' the y-intercept regardless of any sign. It treated the intercept as distance from zero to the intercept regardless the sign. Where is the problem in my understanding?

Thanks in advance

Thanks in advance

BrentGMATPrepNow · Answer

I think you  might  be confusing the x- and y-intercepts with the DISTANCE from the origin. 
An x-intercept of -2 is 2 units away from the origin (0,0) and a y-intercept of 1 is 1 units away from the origin.

Cheers,
Brent

thangvietname · Answer

y=ax+ b
x intercept mean y=0
x= -b/a
y intercept mean x=0
y =b
I have no
-b/a=2b

we can infer a, which is slope

dont draw anything.

Leo8 · Answer

Line ℓ lies in the xy-plane and does not pass through the origin. What is the slope of line ℓ ?

(1) The x-intercept of line ℓ is twice the y-intercept of line ℓ

(2) The x-and y-intercepts of line ℓ are both positive.

Guys - Are we not talking about absolute values of the x & y intercept? How can we infer that even the signs have to be same for the intercepts.

X intercept = -4 & y intercept = 2 - this will make the statement 1 insufficient.

the statement as such does refer to the magnitude only and not the signs .

@experts - please help.

chetan2u · Answer

hi...
when we talk of intercept and say y-intercept is 2, it means 2 and not -2..
the intercepts are never the absolute values but exact value..

we always say y- intercept or x- intercept is -2 and so on

Raihanuddin · Answer

Line L is in the form of Y= mx + b (Here, m is the slope)

St 1: Y-intercept = b so, x-intercept = 2b

In general, We know from the equation of any line
 Y-intercept = b (when x=0)
 x-intercept = -b/m (when y=0)

Now replace the value x=2b, we get 2b = -b/m or m = - 1/2 Sufficient

St 2: No specific value or no relation is given. Insufficient.

Ans A

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=DJDfJlHHY7I

bhanu29 · Answer

Let slope intercept form of equation of a line y = mx +b, where m is the slope and b is the y intercept.

Now rearranging this, we'll get x intercept by equation x = y/m - b/m => x-intercept = -b/m

Statement 1:

Given x intercept is twice y intercept
=> -b/m = 2*b => m = -1/2 
Sufficient

AD/ BCE

Statement 2:
-b/m >0, b>0 this can tell us that m<0, but we can't determine slope
Insufficient
A D / BCE

Correct Answer:  A

Line l lies in the xy-plane and does not pass through the origin. What

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GMAT Data Sufficiency (DS) Questions

Line l lies in the xy-plane and does not pass through the origin. What

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