A triangle is formed by the x-axis, the y-axis, and Line M. Is the are

Question

A triangle is formed by the x-axis, the y-axis, and Line M. Is the area of this triangle greater than 5?

(1) Line M has a slope of −4/3.

(2) The x-intercept of Line M is 25% less than the y-intercept.

Kudos for a correct  solution .

arhumsid · Answer

I think it should be A.

Since 2 sides of the triangle are the two axes, it has to be a right angled triangle with one of the two axes as base and the other as altitude. The line M is the hypotenuse.
As we are concerned with the area, the quadrant in which the triangle lies wont bother us. Assuming the triangle lies in 1st quadrant. 
Line M will intersect X axis at point (x,0) and Y axis at point (0,y). 
=> x = height of the triangle and y = base 
=> Area =  \frac{xy}{2} 
We need to show if  \frac{xy}{2} > 5

S1- Slope of M =  \frac{-4}{3} 
 =>  \frac{y-0}{0-x} = \frac{-4}{3} 
 =>  \frac{-y}{x} = \frac{-4}{3} 
 =>  y=4; x=3 
hence, area =  \frac{4*3}{2}  = 6 >5.  Sufficient

S2- x is 25% less than y
 =>  .75y = x 
here, we can have any pair values that would not necessarily satisfy  \frac{xy}{2} > 5 
eg,  y=1; x=.75  =>  \frac{xy}{2} < 5 
and  y=4; x=3  =>  \frac{xy}{2} > 5 
hence  Not sufficient

Answer: A

Please correct me if i have gone wrong anywhere.

camlan1990 · Answer

(1) Line M has a slope of −4/3

There are many parallel lines having a slope of -4/3 => Cannot make sure formed triangle having the area greater than 5
=> INSUFFICIENT
(2) The x-intercept of Line M is 25% less than the y-intercept.
=> Know slope => The same (1)
=> INSUFFICIENT

Ans: E

goldfinchmonster · Answer

I think it should be A.

Since 2 sides of the triangle are the two axes, it has to be a right angled triangle with one of the two axes as base and the other as altitude. The line M is the hypotenuse.
As we are concerned with the area, the quadrant in which the triangle lies wont bother us. Assuming the triangle lies in 1st quadrant. 
Line M will intersect X axis at point (x,0) and Y axis at point (0,y). 
=> x = height of the triangle and y = base 
=> Area =  \frac{xy}{2} 
We need to show if  \frac{xy}{2} > 5

S1- Slope of M =  \frac{-4}{3} 
 =>  \frac{y-0}{0-x} = \frac{-4}{3} 
 =>  \frac{-y}{x} = \frac{-4}{3} 
 =>    y=4; x=3   
hence, area =  \frac{4*3}{2}  = 6 >5.  Sufficient

S2- x is 25% less than y
 =>  .75y = x 
here, we can have any pair values that would not necessarily satisfy  \frac{xy}{2} > 5 
eg,  y=1; x=.75  =>  \frac{xy}{2} < 5 
and  y=4; x=3  =>  \frac{xy}{2} > 5 
hence  Not sufficient

Answer: A

Hi arhumsid,

I wanted to know whether  x/y = 4/3 indicates that x=4 and y=3  or  x & y are in a ratio of 4 : 3 ...?

If they are in ratio ( That is what i understand ) then A would't be a sufficient solution similar to B.

Answer should be E.

peachfuzz · Answer

A triangle is formed by the x-axis, the y-axis, and Line M. Is the area of this triangle greater than 5?

(1) Line M has a slope of −4/3.
We know nothing of the x and y intercept.
insufficient.

(2) The x-intercept of Line M is 25% less than the y-intercept.
This is a ratio, we do not know of the slope of line m or the exact coordinates of the intercepts.
insufficient

combined, we still only know the slope and a ratio of the intercepts. area could be greater or less than 5.
Insufficient

Answer: E

arhumsid · Answer

oops! 100%, I cant agree with you more. x/y is a ratio and it wont give precise values.. My bad.. that's a blunder :cry:

In this case, it should indeed be E. Thanks for pointing out goldfinchmonster !

thembaseeker · Answer

Statement 1:

Equation of line can be written as y =-(4/3)x+c =>4x+3y=3c.....Infinite number of such lines possibles.

Hence the Area of triangle formed by 3 lines cannot be determined.

Insufficient

Statement 2: Equation of line can be written as
x/0.75a +y/a=1 => 4x+3y=3a

Infinite number of such lines possibles.

Hence the Area of triangle formed by 3 lines cannot be determined.

Insufficient

Statement 1 and 2 represents same set of lines, together they are insufficient.

Answer : E

ramajha · Answer

Both the statements are similar..m=y/x=-4/3 from first statement
from second y/x=1.25 so Both alone or together are insufficient
So E is the answer

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

On this problem, statements 1 and 2 each give you the same information. The slope of −4/3 tells you that the line goes down 4 places for every 3 it moves to the right. And statement 2 tells you the same thing (the intercepts could be y = 4 and x = 3 or y = 8 and x = 6, for example - each of which has an area greater than 5). But note that you're never actually given a point on Line M, so the intercepts could also be y = 4/3 and x = 1 (with an area much less than 5).  Therefore, the answer is E.

himanshukamra2711 · Answer

Is this the right approach?

triangle formed n any of the 4 quadrant will have an area of 3c^2/8(1/2*3c/4*c....y=-4/3x+c,finding x and y intercept),but since we do not know the value of c we cannot say anything,and by B also we are getting the same thing that x=3c/4 so the answer is E

pulkitmehdiratta2 · Answer

Arhamsid you are wrong cause you are assuming the ratio as 4 and 3, where it can be 8 or 6, or even 2 and 1.5. So that's why satement 1 alone doesn't satisfy the condition.

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Basshead · Answer

Notice that both statements give the same information. In this case, the answer MUST be either D or E.

In each statement, we're only given ratios. We are not able to determine an area based off of ratios.

Answer is E.

bumpbot · Answer

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A triangle is formed by the x-axis, the y-axis, and Line M. Is the are

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