M16, #15

ritula · **Posted:** Mon Mar 30, 2009 3:20 am

Vertices of a triangle have coordinates (-1,0), (4,0) and (0,A). Is the area of the triangle bigger than 15 ?

(1) A<3
(2) The triangle is right

[Reveal] Spoiler: OA

B

Source: GMAT Club Tests - hardest GMAT questions

I cldnt understand the explanation given for second statement. Can anyone explain?

Bunuel · **Posted:** Mon Jan 18, 2010 12:02 pm

bmillan01 wrote:

I hate to be too demanding, but what are the steps to find find the coordinates of (0, A)?

Knowing that the triangle is right means that the right angle must be at the point D(0,A), see the picture attached by dzyubam.

Next, we know that line segment AD is perpendicular to the line segment BD, hence the slopes of these line segments must be negative reciprocals of each other.

Slope AD=\frac{A-0}{0-(-1)}=A;
Slope BD=\frac{A-0}{0-4}=\frac{A}{-4}.

As they must be negative reciprocals, then: A=-\frac{-4}{A} --> A^2=4 --> A=2 or -2.

Hope it's clear.

silasaaa2 · **Posted:** Wed Mar 03, 2010 5:33 am

Vertices of a triangle have coordinates , and . Is the area of the triangle bigger than 15?
1. A<3
2. The triangle is right

stmt 1: we know that 1 side length will be 5 and other side will be less than 3 so the third side can be as big as 7.999 and as small as 2.1 so it is not sufficient

stmt 2: if the given triangle is right angle then one side which forms the hypotenuse is 5 so the other two sides will be less than 4. so definitely area of triangle has to be less than 15

so ans is B

ExecMBA2010 · **Posted:** Wed Mar 03, 2010 8:37 am

ritula wrote:

Vertices of a triangle have coordinates (-1,0), (4,0) and (0,A). Is the area of the triangle bigger than 15 ?

(1) A<3
(2) The triangle is right

[Reveal] Spoiler: OA

B

Source: GMAT Club Tests - hardest GMAT questions

I cldnt understand the explanation given for second statement. Can anyone explain?

Someone pl explain why A cannot be the answer? If we map the triangle on a coordinate plane we have the base on X-axis and apex on Y-axis. Going by formula: Area = 1/2 (base x height) we have the base as 5 units and in order to have the area bigger than 15 we need the height to be >6 units. S1 says A<3, so height of triangle is <3 too hence area is less than 15. S1 SUFFICIENT

From S2 we know the triangle is right hence if the side on X-axes is 5 units the other 2 sides will be 3 & 4 units. Again, area <15. S2 SUFFICIENT
If above are correct then answer is D. Comments welcome.

Igor010 · **Posted:** Wed Mar 03, 2010 9:14 am

ExecMBA2010 wrote:

Someone pl explain why A cannot be the answer? If we map the triangle on a coordinate plane we have the base on X-axis and apex on Y-axis. Going by formula: Area = 1/2 (base x height) we have the base as 5 units and in order to have the area bigger than 15 we need the height to be >6 units. S1 says A<3, so height of triangle is <3 too hence area is less than 15. S1 SUFFICIENT - consider A=-10, what is the area then?

From S2 we know the triangle is right hence if the side on X-axes is 5 units the other 2 sides will be 3 & 4 units. Again, area <15. S2 SUFFICIENT
If above are correct then answer is D. Comments welcome.

Hope that helps! :-D

PTK · **Posted:** Fri Nov 12, 2010 1:04 pm

The easiest approach to solve this problem is to realise that there is only one single point in each positive and negative y-axis. or |A|, either A or -A.

If there is one measure (I mean |A|) we can definitively say YES or NO, so 2) is suffiicient.

dzyubam · **Posted:** Mon Mar 30, 2009 4:19 am

What explanation for S2 is trying to say is that if we know that the triangle is right then we can find the coordinates of the point (0,A). Thus, we'll have enough info to answer the question. There are only two possible triangles with S2. See the image below. Do you think we need to change the wording of the OE for S2? If yes, please tell us what exactly was confusing.

Hope this helps.

Greenberg · **Posted:** Fri Jul 10, 2009 5:40 am

Adding this drawing to the OE will greatly help.

dzyubam · **Posted:** Fri Jul 10, 2009 7:28 am

Added the image there.

bmillan01 · **Posted:** Mon Jan 18, 2010 11:36 am

I hate to be too demanding, but what are the steps to find find the coordinates of (0, A)?

saqibbaig · **Posted:** Wed Mar 03, 2010 9:01 am

"A" could be -ve as well

ExecMBA2010 · **Posted:** Wed Mar 03, 2010 10:22 am

Thanks Igor010....silly me, should have realised seeing the figure drawn above!

nvgroshar · **Posted:** Wed Mar 03, 2010 11:22 am

To get the value of A apply twice Pythagorean Theorem:
1^2+A^2+4^2+A^2=5^2, A=\pm2, area=5<15. Certainly, B.

dmetla · **Posted:** Wed Mar 03, 2010 2:10 pm

1 is sufficient as well i think answer is D

rongali · **Posted:** Tue Mar 08, 2011 8:37 am

+1 for B

rajeshaaidu · **Posted:** Tue Mar 08, 2011 7:55 pm

ExecMBA2010 wrote:

ritula wrote:

Vertices of a triangle have coordinates (-1,0), (4,0) and (0,A). Is the area of the triangle bigger than 15 ?

(1) A<3
(2) The triangle is right

[Reveal] Spoiler: OA

B

Source: GMAT Club Tests - hardest GMAT questions

I cldnt understand the explanation given for second statement. Can anyone explain?

Someone pl explain why A cannot be the answer? If we map the triangle on a coordinate plane we have the base on X-axis and apex on Y-axis. Going by formula: Area = 1/2 (base x height) we have the base as 5 units and in order to have the area bigger than 15 we need the height to be >6 units. S1 says A<3, so height of triangle is <3 too hence area is less than 15. S1 SUFFICIENT

From S2 we know the triangle is right hence if the side on X-axes is 5 units the other 2 sides will be 3 & 4 units. Again, area <15. S2 SUFFICIENT
If above are correct then answer is D. Comments welcome.

A) can't be the answer because when it is given <3. For positive value statement is true, but we can go in negative direction till infinite and while calculating area of the triangle we will take the magnitude of the height of the triangle. You are just thinking about positive value of the cordinate, just draw your triangle taking -20 or -30 which is also less than 3. Is first statement is true???

rajeshaaidu · **Posted:** Tue Mar 08, 2011 7:56 pm

Bunuel wrote:

bmillan01 wrote:

I hate to be too demanding, but what are the steps to find find the coordinates of (0, A)?

Knowing that the triangle is right means that the right angle must be at the point D(0,A), see the picture attached by dzyubam.

Next, we know that line segment AD is perpendicular to the line segment BD, hence the slopes of these line segments must be negative reciprocals of each other.

Slope AD=\frac{A-0}{0-(-1)}=A;
Slope BD=\frac{A-0}{0-4}=\frac{A}{-4}.

As they must be negative reciprocals, then: A=-\frac{-4}{A} --> A^2=4 --> A=2 or -2.

Hope it's clear.

Bunnel as usual you are great!!! +1.

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