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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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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.

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


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[Reveal] Spoiler: OA

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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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New post 11 Oct 2015, 10:27
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.
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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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New post 11 Oct 2015, 13:28
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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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New post 11 Oct 2015, 18:44
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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

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.

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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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New post 11 Oct 2015, 18:50
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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

Answer: 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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New post 11 Oct 2015, 18:55
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

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.


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!
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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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New post 11 Oct 2015, 21:54
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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.

Answer : 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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New post 12 Oct 2015, 01:09
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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

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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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New post 18 Oct 2015, 12:28
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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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New to the Math Forum?
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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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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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New post 27 Sep 2017, 08:18
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

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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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New post 27 Sep 2017, 14:42
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] 27 Sep 2017, 14:42
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