DS Is equation of a straight line y = Root 3 x - 5 root 3?

Question

DS Is equation of a straight line y = Root 3 x - 5 root 3?
(1) The straight line cuts equal intercepts on the axes.
(2) The straight line cuts x-axis at distance 5 and makes an angle 60 degree with the x- axis.

Vithal · Answer

E

y = mx+c

slope = m = tan(60) = Root 3 or it could be -Root(3)

and y = 0 at x = 5 (or at x = -5)

0 = -5*Root(3) + c => c = 5*Root(3)

0 = 5*Root(3) + c => c = 5*Root(3) (this is when the line cuts the X axis in the first quadrant and y in the fourth quadrant)

therefore the answer cannot be uniquely determined

Karthik · Answer

this is not clear....can anybody explain?..again is this GMAT Stuff??

mba · Answer

I think the answer should be (A), if line makes equal intercepts on both the axis, the the distance from origin for both x and y should be same,

Now put x=0 in the equation ---> y = -5sqrt(3)
Put y=0 in the equation ----> x= 5.

The intercepts are not equal, hence it cannot be the equation of the line. So (1) is sufficient.

Choice (2) is not sufficient because slope can be -sqrt(3) or sqrt(3), as explained by Vithal

mallelac · Answer

Yes..she is right. Even I picked up E. But the question is whether the given eq represents the lines stated in (1) or (2). The answer is No in case (1) or case (2). Thus, it is D.

Bingo..very good query. Though we know the entire stuff about coordinate geometry, answering is limited to the guys with common sense 8-)

boksana

The answer is D!

ian7777 · Answer

Why?

Statement 2 can be interpreted as two possible lines:

y = (root3)x - 5(root3)
or
y = -(root3)x + 5(root3)

The first one is exactly what's asked about. The points of interception are (0,-5root3) and (5,0). But since it doesn't tell us which one to go for, the answer is a maybe. Am I reading it wrong?

But here's my question: If statement one refers to a line that's at equal points on the respective axes, and statement two refers to a line that's at different points on their respective axes, how then can they both be referring to the same line in the question stem?

mallelac · Answer

Hi Ian,

I agree with you. The question is ambigious. It cannot be D if it is 'Yes or No type'.

As far as my understanding goes, we cannot take 60degrees(the angle be) as +60degrees and -60 degrees and arrive at the equations of two lines. It is clealy stated in (2) that "The straight line cuts x-axis at distance 5 and makes an angle 60 degree with the x- axis.". I believe that it has to be +60degrees as the reference axis is x-axis because when we say 60, we always mean +60. Also, -60degrees means 300degrees.

Thus, you can take only y = Root 3 x - 5 root 3, which is given in the question stem. Do correct me if I am wrong.

You are repeatedly getting us cleal-bowled over and over. I think I need to pick up the nitty-gritty way of thinking as soon as possible to do well on GMAT maths.

ian7777 · Answer

It's an interesting question. But to me, 60 degrees can be interpreted as 60 degrees from any direction. Nothing says anything about the direction of this line. I think both of the following scenarios match the statement:
 https://www.integratedlearning.net/gmatclub/60degreeangle.gif

boksana · Answer

60 is always clockwise from x. So it's cannot be two scenario.
My explanations:

y=xsrt3-5sqrt3, => (0,-5sqrt3), (5,0) => distances are not equal! so 
From 1) we can definitely say NO, therefore 1 is sufficient 

slope of the line = sqrt 3 unambiguously! From 2 slope =tan 60=sqrt 3 
WE can definitely say YES. 2 is sufficient 

THUS, each is sufficient. D.

ian7777 · Answer

not sure I agree. but then, boksana and I seem to like to disagree.

but how can one statement be no and the other be yes? Aren't they supposed to be talking about the same line?

mallelac · Answer

I think +ve angle is defined anti-clockwise from X-axis. Not clock-wise.
Then only you get the answer "slope of the line = sqrt 3 unambiguously!".

Just to assure yourself, look at the number of quadrants(I,II,III,IV) in xy plane of co-ordinate geometry. Do let me know if I am wrong.

Ian does have a point here. If (1) is saying No and (2) is saying yes, as per the definition of D, we can say D is the answer. However, it also answers E where statements (1) & (2) together are NOT sufficient. Thus, both D & E are correct. That is why such questions donot appear in GMAT.

This fundamentally boils down to the fact, if you get 'yes' for (1) (i.e., individually sufficient), then you get 'yes' for (2) also (i.e., individually sufficient) to enable you to go for the answer D.

Alternately, if you get 'no' for (1) (i.e., individually sufficient), then you get 'no' for (2) also (i.e., individually sufficient) to enable you to go for the answer D.

But, never do you get 'yes'(or 'no') for (1) and 'no'(or 'yes') for (2) to enable you to go for the answer D in GMAT. Take my bet for it. 100$ is tough for me as I am from India. But, 100 rupees is definitely what I can afford 8-)

boksana

60 is always clockwise from x. So it's cannot be two scenario.
My explanations:

y=xsrt3-5sqrt3, => (0,-5sqrt3), (5,0) => distances are not equal! so
From 1) we can definitely say NO, therefore 1 is sufficient

slope of the line = sqrt 3 unambiguously! From 2 slope =tan 60=sqrt 3
WE can definitely say YES. 2 is sufficient

THUS, each is sufficient. D.

ywilfred · Answer

y = root3x - 5root3
gradient, m = root3
y intercept -5root3

Statement1
Line cuts equal intercepts on the axes
The slope in this case would be -1

So 1 is sufficient to answer that y != root3x - 5root3

Statement2
Can have two cases here. One would give a gradient -root3
and another gives a gradient root3
Without further information, 2 is not sufficient to say
if y = root3x - 5root3

So (A) should be the answer, since we just need to say
if y=root3x-5root3 given the conditions in (1) and (2)

DS Is equation of a straight line y = Root 3 x - 5 root 3?

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