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# If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what

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If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what [#permalink]

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22 Jun 2011, 07:47
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Question Stats:

62% (01:54) correct 38% (00:57) wrong based on 85 sessions

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If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what is its area?

Statement 1: If , y is 10 but x could be -10 or 10. The area is same for x=10 and X= -10 . This is sufficient to answer the question.

Statement 2: If , x=10 but y could be 10 or -10 but different value of y does not affect the area of the triangle. This statement is also sufficient to answer the question.
[Reveal] Spoiler: OA

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Re: If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what [#permalink]

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22 Jun 2011, 08:18
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joana0 wrote:
hi:
this is what i got from diagnosis test - but i think its wrong!

If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what is its area?

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient
Statement 1: If , y is 10 but x could be -10 or 10. The area is same for x=10 and X= -10 . This is sufficient to answer the question.

Statement 2: If , x=10 but y could be 10 or -10 but different value of y does not affect the area of the triangle. This statement is also sufficient to answer the question.

Formula for triangle
|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|

A (5, 0), B (x, y) and C (25, 0),
St 1: Y = 10 X can be -10 or +10
lets try both
A (5, 0), B (10, 10) and C (25, 0),
| 5(10-0)+ 10(0-0) + 25(0-10)|
|50 +0-250|= 200

no lets try X as -10
A (5, 0), B (-10, 10) and C (25, 0),

| 5(10-0)-10(0-0) +25(0-10)| = 200

same with St 2:

hence D
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Re: If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what [#permalink]

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22 Jun 2011, 19:18
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Area = 1/2 * base *height = 1/2*20*h

where h is the length of the perpendicular from (x,y) to x axis.

1. Sufficient

x>=0
=> x=y=10 => (x,y) = (10,10)
x<0
=> -x =y=10 =>(x,y) = (-10,10)

both of the above points result in the height of 10

2. Sufficient

y>=0

x=y=10 => (x,y) = (10,10)

y<0
x=-y=10 => (x,y) = (10,-10)

both of the above points result in the height of 10

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Re: If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what [#permalink]

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07 Feb 2015, 07:33
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Re: If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what [#permalink]

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07 Feb 2015, 07:47
Dear Math experts, I need to understand by drawing how statement 1 is suff

I used this formula X1(Y2-Y3)+X2(Y3-Y1)+X3(Y1-Y2)/2 to find the triangle area and the answer was D but i really confused

when i tried to draw statement 1 especially in the case x,y=(-10, 10) i do not know how to get the height equal to 10
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Re: If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what [#permalink]

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07 Feb 2015, 07:59
23a2012 wrote:
Dear Math experts, I need to understand by drawing how statement 1 is suff

I used this formula X1(Y2-Y3)+X2(Y3-Y1)+X3(Y1-Y2)/2 to find the triangle area and the answer was D but i really confused

when i tried to draw statement 1 especially in the case x,y=(-10, 10) i do not know how to get the height equal to 10

Discussed here: d01-183495.html and here: gmat-diagnostic-test-question-79365.html
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Re: If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what   [#permalink] 07 Feb 2015, 07:59
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