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Statement 1: If |x| = y = 10, 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 = |y| = 10, 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.

Statement 1: If |x| = y = 10, y is 10 but x could be -10 or 10. Area is not same for x = 10 and x = -10. This is not sufficient to answer the question. Statement 2: If x = |y| = 10, 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 sufficient to answer the question.

Therefore the OA is B.

How can a difference in x co-ordinate will change the area. Coz the y co-ordinate will decide the height of the triangle and it is constant. IMHO the answer should be D.

Statement 1: If |x| = y = 10, y is 10 but x could be -10 or 10. Area is not same for x = 10 and x = -10. This is not sufficient to answer the question. Statement 2: If x = |y| = 10, 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 sufficient to answer the question.

Therefore the OA is B.

How can a difference in x co-ordinate will change the area. Coz the y co-ordinate will decide the height of the triangle and it is constant. IMHO the answer should be D.

Agree with kyabe. Even when x = -10, you still can calculate the area of the rectangle (area of 350) and subtract the areas of two other triangles (250 total). That leaves you with 100 for the area of the triangle.

1) B can be two points B1(10, 10) or B2(-10,10) therefore Sabc is not certain

2) B can be B1(10, 10) or B2(10, -10) although AC is certain, but the height from B1 to AC and B2 to AC are not the same. therefore Sabc is not certain

put 1) and 2) together, B can only be (10, 10) Sabc can be calculated.
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1) B can be two points B1(10, 10) or B2(-10,10) therefore Sabc is not certain

2) B can be B1(10, 10) or B2(10, -10) although AC is certain, but the height from B1 to AC and B2 to AC are not the same. therefore Sabc is not certain

put 1) and 2) together, B can only be (10, 10) Sabc can be calculated.

The question does not require that you know exactly where the triangle is or what its shape is... only the area is being discussed here... the area is the same for any of the possible locations for B that were mentioned, so the correct answer is D.

1) B can be two points B1(10, 10) or B2(-10,10) therefore Sabc is not certain

2) B can be B1(10, 10) or B2(10, -10) although AC is certain, but the height from B1 to AC and B2 to AC are not the same. therefore Sabc is not certain

put 1) and 2) together, B can only be (10, 10) Sabc can be calculated.

The question does not require that you know exactly where the triangle is or what its shape is... only the area is being discussed here... the area is the same for any of the possible locations for B that were mentioned, so the correct answer is D.

when B is at different points, the areas are different.

If B is (-10,10), Area=100. If B is (10,10), Area=100. If B is (10,-10), Area=100. 100=100=100. Make sense? If not, I can sketch up a diagram and scan it to prove it.

I agree that the answer is D as well. I spent a lot of time trying to figure this one out.

In short if you assume that two points at (5,0) and (25,0) are the base (which equals 20), you still get the same area regardless of whether the third point is at:

(10,10) (-10,10) (10,-10) (-10,-10)

All that matters is that the height is still 10, because the area of a triange is 1/2*base*height: 1/2*10*20 = 100

doesn't matter what the x coordinate is... as long as your base is fixed, and your height is fixed, area should be the same... but i still have to see it (and drag the coordinates around -- see link above) myself to believe it!!
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Wha? Alright, either I'm totally confused right now or there's something wrong.

I made a drawing of the whole thing, these are the 2 triangles that could result from the points stated in A), so (10|10) or (10|-10). I've attached my drawing to this post.

Unless I made a mistake, this should be drawn to scale. Each division of the grid on the paper corresponds to 5 units. It is very obvious the area of the orange trinangle (the one resulting from point (-10|10)) is a lot larger than that of the blue triangle (resulting from point (10|10)). Also, if assuming the line connecting (5|0) and (25|0) is the base, it is clearly obvious that the heights of these two triangles are different, after all as far as i know the height should be a line from the point opposite to the base in an angle that is orthogonal to the base. Since the base is not a straight vertical line but rather askew, the point (-10|10) cant be simply mirrored to generate a triangle with an equal area.

Does that make sense? Did I make a mistake or is there a flaw in the question?

Before wasting time trying to solve either statements, remember that: if two statements provide identical information then the correct answer will be either D or E. It's plain to see that both statements are identical; hence, a question with identical statements can not be A, B, or C. (1) |x| = y = 10 (2) x = |y| = 10

Before wasting time trying to solve either statements, remember that: if two statements provide identical information then the correct answer will be either D or E. It's plain to see that both statements are identical; hence, a question with identical statements can not be A, B, or C. (1) |x| = y = 10 (2) x = |y| = 10

Answer = D, since each statement is sufficient.

This is small, but you might want to note that these two statements are not identical. Statement 1 implies that that the third vertex is either located at (-10,10) or at (10,10), while Statement 2 implies (10,-10) or (10,10). In this particular problem, due to how those three points would all have the same effect on the area formula, the two statements are redundant, but not identical.

Wha? Alright, either I'm totally confused right now or there's something wrong.

I made a drawing of the whole thing, these are the 2 triangles that could result from the points stated in A), so (10|10) or (10|-10). I've attached my drawing to this post.

Unless I made a mistake, this should be drawn to scale. Each division of the grid on the paper corresponds to 5 units. It is very obvious the area of the orange trinangle (the one resulting from point (-10|10)) is a lot larger than that of the blue triangle (resulting from point (10|10)). Also, if assuming the line connecting (5|0) and (25|0) is the base, it is clearly obvious that the heights of these two triangles are different, after all as far as i know the height should be a line from the point opposite to the base in an angle that is orthogonal to the base. Since the base is not a straight vertical line but rather askew, the point (-10|10) cant be simply mirrored to generate a triangle with an equal area.

Does that make sense? Did I make a mistake or is there a flaw in the question?

Dear JeeMath, in the premise said that point A (5;0) and C(25;0) which is gives you strait line on x-line (as the points has the same y-coordinate=0) hope you are just overlooked it
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