In the rectangular coordinate system above, if OB BC then is the area of the triangle ABC lesser than 12 square units?(1) Point A lies above the line y = 5(2)The mid-point of B and C is (6, 0)a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'E'. Can you explain this answer?

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In the rectangular coordinate system above, if OB < BC then is the area of the triangle ABC lesser than 12 square units?

(1) Point A lies above the line y = 5

(2) The mid-point of B and C is (6, 0)

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c)
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d)
EACH statement ALONE is sufficient.
e)
Statements (1) and (2) TOGETHER are NOT sufficient.

Correct answer is option 'E'. Can you explain this answer?

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In the rectangular coordinate system above, if OB < BC then is the...

Steps 1 & 2: Understand Question and Draw Inferences

In order to determine any information about the area of a triangle, we must try to obtain information about its base and height since

the area of a triangle = (1/2)*base*height

If the base is taken as the length of line segment BC, then the height is the y-coordinate of point A.

Step 3: Analyze Statement 1

If the point A lies above the line y = 5 and the side BC lies on the x-axis, then the height of the triangle is more than 5 units. We have no information about the length of the base BC.

INSUFFICIENT.

Step 4: Analyze Statement 2

Let’s assume the coordinates of point B to be (b, 0) and the coordinates of point C to be (c, 0).

If the mid-point of B and C is (6, 0) then

(b+c)/2 = 6

c = 12 – b

Length of BC = 12 – b – b = 12 – 2b

Since OB < BC, we have

b < 12 – 2b

b < 4

We cannot infer anything about the base BC from this, apart from the fact that the length of BC will always be greater than 4 units.

There is also no information about the height of the triangle ABC.

INSUFFICIENT.

Step 5: Analyze Both Statements Together (if needed)

Combining statements (1) and (2),

We have Height > 5 and b < 4

We have information about the height but still we are unsure about the base BC and so we cannot conclude if the area of the triangle ABC is greater than 12 or less than 12.

INSUFFICIENT.

(E) is the correct answer.

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In the rectangular coordinate system above, if OB < BC then is the area of the triangle ABC lesser than 12 square units?(1) Point A lies above the line y = 5(2)The mid-point of B and C is (6, 0)a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'E'. Can you explain this answer?

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