In the given figure ABCD is a rectangle and EF -- AD. AEG and FEB are two triangles inscribed in the rectangle ABCD such that the area of triangle AEG is half of the area of triangle FEB. What is the area of rectangle ABCD?(1) EBCF is a square of side length 5 centimeters.(2) A line passing through point G and parallel to AB divides the rectangle ABCD into 2 equal halvesa)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer?

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a)
Statement (1) ALONE is sufficient, but statement (2) alone is
not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is
not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to
answer the question asked, but NEITHER statement ALONE
is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question
asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to
answer the question asked, and additional data specific to the
problem are needed.

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

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Test: Rectangles And Squares- 2

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In the given figure ABCD is a rectangle and EF || AD. AEG and FEB are ...

Step 1 & 2: Understand Question and Draw Inference

ABCD is a rectangle
- AB = CD and AD = BC
Area(ΔAEG) = ½ * Area(ΔFEB)
- ½ * AE * EG = ¼ * EB * EF

(Since EF || AD and ABCD is a rectangle, So, Angle(FEB) =90° »

AE is perpendicular to EG and EB is perpendicular to EF)

AE * EG = ½ * EB * EF

To Find: Area of rectangle ABCD

Area of ABCD = AB * AD
Thus to find the area of ABCD, we need to find the actual lengths of AB and AD.

Step 3 : Analyze Statement 1 independent

Statement 1 states that –
- EBCF is a square of side length 5 centimeters.
- As EBCF is a square, EB = BC =CF = FE = 5 centimeters
  - Area of rectangle ABCD = Area of (EBCF +AEFD) = (EB +AE*EF=25+AE*5).
- As we do not know the value of AE, we cannot find the area of rectangle ABCD.
Hence Statement 1 is insufficient to answer the question

Step 4 : Analyze Statement 2 independent

Statement 2 states that –
- A line passing through point G and parallel to AB divides the rectangle ABCD into 2 equal halves
- As the line passing through G divides the rectangle into 2 equal halves, the portion of the rectangle above this line segment and below this line segment should be symmetric.
- So, we can write EG = GF
Also, we know from our question statement analysis that AE * EG = ½ * EB * EF = ½ * EB * 2EG
- So, we have AE = EB

However, we do not know anything about the lengths of the sides of the rectangle. So, we cannot calculate the area of the rectangle ABCD

Hence Statement 2 is insufficient to answer the question.

Step 5: Analyze Both Statements Together (if needed)

From statement 1 we inferred –
- Area of rectangle ABCD = 25 + AE * 5, where EB = EB = BC =CF = FE = 5 centimeters
From statement 2 we inferred –
- AE = EB
Using both the statements we can infer that
- AE = 5 centimeters.
Thus, Area of rectangle ABCD = 25 + 5*5 = 50 cm
Hence by combining both the statement, we can find the area of the
rectangle and the correct answer is OPTION C

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In the given figure ABCD is a rectangle and EF || AD. AEG and FEB are two triangles inscribed in the rectangle ABCD such that the area of triangle AEG is half of the area of triangle FEB. What is the area of rectangle ABCD?(1) EBCF is a square of side length 5 centimeters.(2) A line passing through point G and parallel to AB divides the rectangle ABCD into 2 equal halvesa)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer?

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In the given figure ABCD is a rectangle and EF || AD. AEG and FEB are two triangles inscribed in the rectangle ABCD such that the area of triangle AEG is half of the area of triangle FEB. What is the area of rectangle ABCD?(1) EBCF is a square of side length 5 centimeters.(2) A line passing through point G and parallel to AB divides the rectangle ABCD into 2 equal halvesa)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In the given figure ABCD is a rectangle and EF || AD. AEG and FEB are two triangles inscribed in the rectangle ABCD such that the area of triangle AEG is half of the area of triangle FEB. What is the area of rectangle ABCD?(1) EBCF is a square of side length 5 centimeters.(2) A line passing through point G and parallel to AB divides the rectangle ABCD into 2 equal halvesa)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the given figure ABCD is a rectangle and EF || AD. AEG and FEB are two triangles inscribed in the rectangle ABCD such that the area of triangle AEG is half of the area of triangle FEB. What is the area of rectangle ABCD?(1) EBCF is a square of side length 5 centimeters.(2) A line passing through point G and parallel to AB divides the rectangle ABCD into 2 equal halvesa)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer?.

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AEG and FEB are two triangles inscribed in the rectangle ABCD such that the area of triangle AEG is half of the area of triangle FEB. What is the area of rectangle ABCD?(1) EBCF is a square of side length 5 centimeters.(2) A line passing through point G and parallel to AB divides the rectangle ABCD into 2 equal halvesa)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. 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What is the area of rectangle ABCD?(1) EBCF is a square of side length 5 centimeters.(2) A line passing through point G and parallel to AB divides the rectangle ABCD into 2 equal halvesa)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of In the given figure ABCD is a rectangle and EF || AD. AEG and FEB are two triangles inscribed in the rectangle ABCD such that the area of triangle AEG is half of the area of triangle FEB. What is the area of rectangle ABCD?(1) EBCF is a square of side length 5 centimeters.(2) A line passing through point G and parallel to AB divides the rectangle ABCD into 2 equal halvesa)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice In the given figure ABCD is a rectangle and EF || AD. AEG and FEB are two triangles inscribed in the rectangle ABCD such that the area of triangle AEG is half of the area of triangle FEB. What is the area of rectangle ABCD?(1) EBCF is a square of side length 5 centimeters.(2) A line passing through point G and parallel to AB divides the rectangle ABCD into 2 equal halvesa)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice GMAT tests.

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