A student initially draws a rectangle ABCF. Later, he draws an adjacent trapezium FCDE in which side ED is parallel to side FC and drops perpendiculars EG and DH on FC. The dimensions of each side of the polygon ABCDEF, in centimeters, are shown on the figure above. What is the value of x?(1) The area of the polygon ABCHDEG is 332 square centimeters(2) If sides AE and BD are joined, the area of the quadrilateral ABDE will be 266 square centimetersa)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 'D'. Can you explain this answer?

EduRev

All Courses

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

GMAT Exam > GMAT Questions > A student initially draws a rectangle ABCF. L...

Join the Discussion on the App

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 'D'. Can you explain this answer?

FREE This question is part of

Test: Rectangles And Squares- 2

Attempt Test

Attempt this Test

Verified Answer

A student initially draws a rectangle ABCF. Later, he draws an adjacen...

Step 1 & 2: Understand Question and Draw Inference

Given

Rectangle ABCF
- Since opposite sides of a rectangle are equal,
  - CF = AB = 15 cm and
  - AF = BC = 20 cm
Trapezium EDCF
- ED parallel to FC
- CF = 15 cm
- ED = 4 cm
- CD = 10 cm

To find: x = ?

Step 3 : Analyze Statement 1 independent

The area of the polygon ABCHDEG is 332 square centimeters
To make use of this fact, let’s first try to understand how the area of this figure will be found.

Area of the figure
- = area of rectangle EDHG + area of rectangle ABCF
Since ED is parallel to FC, both perpendiculars EG and DH will have the same length. Let this length be h.
Let CH = y.
Since EDHG forms a rectangle, GH = 4
So, FG = FC – (GH + HC)
- That is, FG = 15 – (4 + y)
- FG = 11 – y
So, area of the figure = 4h + 20 * 15
Substituting the value of area in the above equation: 4h + 20 * 15 = 332

Also, by applying Pythagoras Theorem in right triangle DHC,

So, y = 6 (rejecting the negative value as length cannot be negative)

And, in right triangle EHF, we get:
- (11-y)²+ h² = x²
- Substituting y = 6 and h = 8 in this equation, we get:
  - 5² + 8² = x²
- That is, x² = 89
- So, x = √89 (rejecting the negative value since length cannot be negative)
  Thus, Statement 1 is sufficient to determine the length of x.

Step 4 : Analyze Statement 2 independent

If sides AE and BD are joined, the area of the quadrilateral ABDE will be 266 square centimeters
- In quadrilateral ABDE, sides AB and ED are parallel (since both ED and AB are parallel to FC)
  - This means, ABDE is a trapezium

Substituting the known value of this area in the above equation:
Since this is a linear equation with only one unknown, we can use it to find a unique value of h.
Once we know the value of h, we can find the value of x using similar analysis as done in Statement 1 above.

So, Statement 2 is sufficient to determine a unique value of x.

Step 5: Analyze Both Statements Together (if needed)

Since we’ve already arrived at unique answers in each of Steps 3 and 4, this
step is not required
Answer: Option D

View all questions of this test

View all answers Start learning for free

< Previous Question Next Question >

Explore Courses for GMAT exam

Similar GMAT Doubts

The area of a rectangle is 28 square centimeter. What is the perimeter of the rectangle?(1) If the length of the rectangle is increased by 10 centimeter and the breadth is decreased by 5 centimeter, the perimeter of the rectangle is eight times the original length of the rectangle.(2) If the length of the rectangle is increased by 350% and the breadth is increased to 350% of the original breadth, the perimeter of the rectangle is 63 centimeters more than the original perimeter of the rectangle.

View answer

The base of a rectangular block has an area of 60 square centimeters. Is the block a cube?(1) The area of the front face of the block is 60 square centimeters.(2) The area of a side of the block is 60 square centimeters.

View answer

How many books will fit into a drawer?(1) Each book has a volume of 10 cubic centimeters.(2) The drawer is 300 centimeters by 30 centimeters by 20 centimeters and has the shape of a rectangular solid.

View answer

Square ABCD and Trapezium PQRS lie between the parallel lines l and m as shown in the figure above. If the area of the square ABCD and trapezium PQRS is equal to 64 square centimeters each, what is the length in centimeters of PQ?

View answer

A right circular cylinder of height 1 meter and radius 92 centimeters is to be used to store cubes of side length 3 cm each. If in each layer of cubes stored in the cylinder, the cubes are arranged such that the top view of the layer is a square, what is the maximum number of cubes that can be stored in the cylinder? (1 meter = 100 centimeters)

View answer

Top Courses for GMATView all

GMAT Focus Edition Mock Test Series 2024

Top Courses for GMAT

View all

A student initially draws a rectangle ABCF. Later, he draws an adjacent trapezium FCDE in which side ED is parallel to side FC and drops perpendiculars EG and DH on FC. The dimensions of each side of the polygon ABCDEF, in centimeters, are shown on the figure above. What is the value of x?(1) The area of the polygon ABCHDEG is 332 square centimeters(2) If sides AE and BD are joined, the area of the quadrilateral ABDE will be 266 square centimetersa)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 'D'. Can you explain this answer?

Share with a Friend

Answer this doubt

Question Description
A student initially draws a rectangle ABCF. Later, he draws an adjacent trapezium FCDE in which side ED is parallel to side FC and drops perpendiculars EG and DH on FC. The dimensions of each side of the polygon ABCDEF, in centimeters, are shown on the figure above. What is the value of x?(1) The area of the polygon ABCHDEG is 332 square centimeters(2) If sides AE and BD are joined, the area of the quadrilateral ABDE will be 266 square centimetersa)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 'D'. 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 A student initially draws a rectangle ABCF. Later, he draws an adjacent trapezium FCDE in which side ED is parallel to side FC and drops perpendiculars EG and DH on FC. The dimensions of each side of the polygon ABCDEF, in centimeters, are shown on the figure above. What is the value of x?(1) The area of the polygon ABCHDEG is 332 square centimeters(2) If sides AE and BD are joined, the area of the quadrilateral ABDE will be 266 square centimetersa)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 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A student initially draws a rectangle ABCF. Later, he draws an adjacent trapezium FCDE in which side ED is parallel to side FC and drops perpendiculars EG and DH on FC. The dimensions of each side of the polygon ABCDEF, in centimeters, are shown on the figure above. What is the value of x?(1) The area of the polygon ABCHDEG is 332 square centimeters(2) If sides AE and BD are joined, the area of the quadrilateral ABDE will be 266 square centimetersa)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 'D'. Can you explain this answer?.

Solutions for A student initially draws a rectangle ABCF. Later, he draws an adjacent trapezium FCDE in which side ED is parallel to side FC and drops perpendiculars EG and DH on FC. The dimensions of each side of the polygon ABCDEF, in centimeters, are shown on the figure above. What is the value of x?(1) The area of the polygon ABCHDEG is 332 square centimeters(2) If sides AE and BD are joined, the area of the quadrilateral ABDE will be 266 square centimetersa)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 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT. Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.

Here you can find the meaning of A student initially draws a rectangle ABCF. Later, he draws an adjacent trapezium FCDE in which side ED is parallel to side FC and drops perpendiculars EG and DH on FC. The dimensions of each side of the polygon ABCDEF, in centimeters, are shown on the figure above. What is the value of x?(1) The area of the polygon ABCHDEG is 332 square centimeters(2) If sides AE and BD are joined, the area of the quadrilateral ABDE will be 266 square centimetersa)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 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A student initially draws a rectangle ABCF. Later, he draws an adjacent trapezium FCDE in which side ED is parallel to side FC and drops perpendiculars EG and DH on FC. The dimensions of each side of the polygon ABCDEF, in centimeters, are shown on the figure above. What is the value of x?(1) The area of the polygon ABCHDEG is 332 square centimeters(2) If sides AE and BD are joined, the area of the quadrilateral ABDE will be 266 square centimetersa)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 'D'. Can you explain this answer?, a detailed solution for A student initially draws a rectangle ABCF. Later, he draws an adjacent trapezium FCDE in which side ED is parallel to side FC and drops perpendiculars EG and DH on FC. The dimensions of each side of the polygon ABCDEF, in centimeters, are shown on the figure above. What is the value of x?(1) The area of the polygon ABCHDEG is 332 square centimeters(2) If sides AE and BD are joined, the area of the quadrilateral ABDE will be 266 square centimetersa)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 'D'. Can you explain this answer? has been provided alongside types of A student initially draws a rectangle ABCF. Later, he draws an adjacent trapezium FCDE in which side ED is parallel to side FC and drops perpendiculars EG and DH on FC. The dimensions of each side of the polygon ABCDEF, in centimeters, are shown on the figure above. What is the value of x?(1) The area of the polygon ABCHDEG is 332 square centimeters(2) If sides AE and BD are joined, the area of the quadrilateral ABDE will be 266 square centimetersa)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 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A student initially draws a rectangle ABCF. Later, he draws an adjacent trapezium FCDE in which side ED is parallel to side FC and drops perpendiculars EG and DH on FC. The dimensions of each side of the polygon ABCDEF, in centimeters, are shown on the figure above. What is the value of x?(1) The area of the polygon ABCHDEG is 332 square centimeters(2) If sides AE and BD are joined, the area of the quadrilateral ABDE will be 266 square centimetersa)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 'D'. Can you explain this answer? tests, examples and also practice GMAT tests.

Explore Courses for GMAT exam