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# The vertices of triangle Q are located

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Intern
Joined: 21 Feb 2018
Posts: 23
The vertices of triangle Q are located  [#permalink]

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20 Jul 2018, 07:47
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Difficulty:

55% (hard)

Question Stats:

66% (02:00) correct 34% (01:29) wrong based on 76 sessions

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The vertices of triangle Q are located at the origin and at the x- and y- intercepts of line q, respectively. If live q is described by the equation y=Ax+B, then which of the following values of A and B will result in the greatest area of triangle Q?

a. A=1, B=5
b. A=2, B=3
c. A=0.2, B=1
d. A=-5, B=-1
e. A=.01, B=-10
Manager
Joined: 22 Jun 2017
Posts: 71
Location: Brazil
GMAT 1: 600 Q48 V25
GPA: 3.5
WE: Engineering (Energy and Utilities)
Re: The vertices of triangle Q are located  [#permalink]

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20 Jul 2018, 08:54
2
Option E

y=Ax+B

- x- and y- intercepts:

x=0 > y=B

y = 0 > x = -B/A

- area of triangle Q = (1/2)*(|x- * y- intercepts|) = |- (B^2)/2A|

Therefore, Option E.
Intern
Joined: 21 Feb 2018
Posts: 23
Re: The vertices of triangle Q are located  [#permalink]

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20 Jul 2018, 09:48
HI FillFM how did you get y = 0 > x = -B/A?

Thanks!
Manager
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Location: Brazil
GMAT 1: 600 Q48 V25
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Re: The vertices of triangle Q are located  [#permalink]

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20 Jul 2018, 09:58
1
franteraoka wrote:
HI FillFM how did you get y = 0 > x = -B/A?

Thanks!

x intercept, so y = 0.

y = Ax + B. So, if y = 0, Ax + B = 0 ...... Ax = -B .... and x = -B/A
Intern
Joined: 21 Feb 2018
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The vertices of triangle Q are located  [#permalink]

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20 Jul 2018, 10:00
FillFM makes sense! Thank you so much!
Intern
Joined: 21 Feb 2018
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Re: The vertices of triangle Q are located  [#permalink]

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20 Jul 2018, 10:32
@fillfim sorry one more question, why is it |x- * y- intercepts| and not just x-*y-intercepts? Thanks again!
Manager
Joined: 22 Jun 2017
Posts: 71
Location: Brazil
GMAT 1: 600 Q48 V25
GPA: 3.5
WE: Engineering (Energy and Utilities)
Re: The vertices of triangle Q are located  [#permalink]

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20 Jul 2018, 10:43
1
franteraoka wrote:
@fillfim sorry one more question, why is it |x- * y- intercepts| and not just x-*y-intercepts? Thanks again!

sorry franteraoka !

is the modulus of (x intercept)*(y intercept)

= |-(B/A)*B |
Intern
Joined: 21 Feb 2018
Posts: 23
Re: The vertices of triangle Q are located  [#permalink]

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20 Jul 2018, 13:03
FillFM makes sense, thank you very much!
Intern
Joined: 10 Feb 2018
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Location: United States (TX)
Schools: McCombs '21 (I)
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Re: The vertices of triangle Q are located  [#permalink]

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23 Jul 2018, 19:10
1
franteraoka wrote:
The vertices of triangle Q are located at the origin and at the x- and y- intercepts of line q, respectively. If live q is described by the equation y=Ax+B, then which of the following values of A and B will result in the greatest area of triangle Q?

a. A=1, B=5
b. A=2, B=3
c. A=0.2, B=1
d. A=-5, B=-1
e. A=.01, B=-10

Just look at the orders of magnitude between A and B to get the E.

If the vertices at are X-intercept, Y-intercept and origin, that means the height of the triangle is 10 (0 --> -10) and when y=0, X will = 100 (0=.1x - 10)
Intern
Joined: 22 Apr 2018
Posts: 13
Re: The vertices of triangle Q are located  [#permalink]

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26 Jul 2018, 04:20
FillFM
Can you please explain it by drawing a diagram?
I'm not able to visualise it
Manager
Joined: 22 Jun 2017
Posts: 71
Location: Brazil
GMAT 1: 600 Q48 V25
GPA: 3.5
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Re: The vertices of triangle Q are located  [#permalink]

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26 Jul 2018, 04:40
1
rraman wrote:
FillFM
Can you please explain it by drawing a diagram?
I'm not able to visualise it

rraman you just need to substitute x=0 (in y = Ax+B) to find the value of y-intercept.
and then substitute y=0 (in y = Ax+B) to find the value of x-intercept.

and then put this values in the formula of the area of the triangle.

Hope it helps.
Intern
Joined: 09 Jul 2018
Posts: 1
Re: The vertices of triangle Q are located  [#permalink]

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03 Aug 2018, 00:09
franteraoka wrote:
The vertices of triangle Q are located at the origin and at the x- and y- intercepts of line q, respectively. If live q is described by the equation y=Ax+B, then which of the following values of A and B will result in the greatest area of triangle Q?

a. A=1, B=5
b. A=2, B=3
c. A=0.2, B=1
d. A=-5, B=-1
e. A=.01, B=-10

I can understand the solution but why can't we just use the theory that isosceles right triangle has the biggest area?
Senior Manager
Joined: 22 Feb 2018
Posts: 414
The vertices of triangle Q are located  [#permalink]

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03 Aug 2018, 09:09
1
rraman wrote:
FillFM
Can you please explain it by drawing a diagram?
I'm not able to visualise it

OA:E
Using Intercept form of line,The equation of a straight line whose x and y intercepts are a and b, respectively can be represented as
$$\frac{x}{a}+\frac{y}{b}=1$$
Attachment:

ab.PNG [ 30.46 KiB | Viewed 329 times ]

Then area of triangle thus formed is given $$\frac{1}{2}|a|*|b|$$,as third vertice is at origin.
Mode of x and y intercept is required as length of sides of triangle is always positive.
In the question stem , equation of line is given as $$y=Ax+B$$
In intercept form, it can be written as

$$\frac{x}{\frac{-B}{A}}+\frac{y}{B}=1$$

$$a. A=1, B=5$$
$$\frac{x}{\frac{-5}{1}}+\frac{y}{5}=1$$
Area $$=\frac{1}{2}*|\frac{-5}{1}|*|5| = \frac{25}{2}$$

$$b. A=2, B=3$$
$$\frac{x}{\frac{-3}{2}}+\frac{y}{3}=1$$
Area $$=\frac{1}{2}*|\frac{-3}{2}|*|3| = \frac{9}{4}$$

$$c. A=0.2, B=1$$
$$\frac{x}{\frac{-1}{0.2}}+\frac{y}{1}=1$$
Area $$=\frac{1}{2}*|\frac{-1}{0.2}|*|1| = \frac{5}{2}$$

$$d. A=-5, B=-1$$
$$\frac{x}{\frac{+1}{-5}}+\frac{y}{-1}=1$$
Area $$=\frac{1}{2}*|\frac{-1}{5}|*|-1| = \frac{1}{10}$$

$$e. A=.01, B=-10$$
$$\frac{x}{\frac{+10}{0.01}}+\frac{y}{-10}=1$$
Area $$=\frac{1}{2}*|1000|*|-10| = 5000$$
Clearly E gives largest area.
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The vertices of triangle Q are located &nbs [#permalink] 03 Aug 2018, 09:09
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