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Math Expert V
Joined: 02 Sep 2009
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A triangle is formed by the x-axis, the y-axis, and Line M. Is the are  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 58% (01:47) correct 42% (01:49) wrong based on 371 sessions

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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.

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GMAT 1: 630 Q44 V32 GMAT 2: 680 Q47 V35 Re: A triangle is formed by the x-axis, the y-axis, and Line M. Is the are  [#permalink]

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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

Please correct me if i have gone wrong anywhere.
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One Kudos for an everlasting piece of knowledge is not a bad deal at all... ------------------------------------------------------------------------------------------------------------------------
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Manager  Joined: 11 Sep 2013
Posts: 105
Re: A triangle is formed by the x-axis, the y-axis, and Line M. Is the are  [#permalink]

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Bunuel wrote:
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.

(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
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Re: A triangle is formed by the x-axis, the y-axis, and Line M. Is the are  [#permalink]

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[quote="arhumsid"]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

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.
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Re: A triangle is formed by the x-axis, the y-axis, and Line M. Is the are  [#permalink]

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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

Manager  B
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Joined: 04 May 2014
Posts: 229
Location: India
Concentration: Marketing, Social Entrepreneurship
GMAT 1: 630 Q44 V32 GMAT 2: 680 Q47 V35 Re: A triangle is formed by the x-axis, the y-axis, and Line M. Is the are  [#permalink]

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goldfinchmonster wrote:
arhumsid wrote:
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

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.

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 In this case, it should indeed be E.

Thanks for pointing out goldfinchmonster!
_________________
One Kudos for an everlasting piece of knowledge is not a bad deal at all... ------------------------------------------------------------------------------------------------------------------------
Twenty years from now you will be more disappointed by the things you didn't do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover.
-Mark Twain
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Re: A triangle is formed by the x-axis, the y-axis, and Line M. Is the are  [#permalink]

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Bunuel wrote:
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.

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.

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Intern  Joined: 02 Oct 2015
Posts: 11
Re: A triangle is formed by the x-axis, the y-axis, and Line M. Is the are  [#permalink]

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2
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
Math Expert V
Joined: 02 Sep 2009
Posts: 58435
Re: A triangle is formed by the x-axis, the y-axis, and Line M. Is the are  [#permalink]

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Bunuel wrote:
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.

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.
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Joined: 12 Feb 2015
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Re: A triangle is formed by the x-axis, the y-axis, and Line M. Is the are  [#permalink]

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Bunuel wrote:
Bunuel wrote:
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.

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.

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
Intern  Joined: 26 Sep 2017
Posts: 1
Re: A triangle is formed by the x-axis, the y-axis, and Line M. Is the are  [#permalink]

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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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Re: A triangle is formed by the x-axis, the y-axis, and Line M. Is the are  [#permalink]

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