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In the figure shown above, point E is the intersection point of the diagnoals AC and BD of rectangle ABCD. Is AB greater than BC?
- AE = 5 cms and AB = 7.25 cm
- The perimeter of AEB is greater than the perimeter of BEC
- 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 'D'. Can you explain this answer?
Verified Answer
In the figure shown above, point E is the intersection point of the di...
Steps 1 & 2: Understand Question and Draw Inferences
In the given rectangle ABCD, we need to find if AB > BC, i.e., if the length is greater than the breadth.
Note that AC and BD are the diagonals of the rectangle and E is their point of intersection.
In right triangle ADC, by Pythagoras Theorem,
AD2 + DC2 = AC2 . . . (1)
Similarly, in right triangle DCB,
DC2 + BC2 = DB2 . . . (2)
Equation (1) – Equation (2):
AD2 – BC2 = AC2 – DB2
Being opposite sides of a rectangle, AD = BC
Therefore, the above equation becomes:
0 = AC2 – DB2Therefore, AC = DB.
Thus, we observe that the two diagonals of the rectangle are equal.
As we know that diagonals of a rectangle bisect each other, we can write
AE = BE = CE = DE = AC/2 = BD/2
(Now, it is also easy to notice that the rectangle is symmetrical about point E.
Therefore, point E will divide each diagonal in half. )
Step 3: Analyze Statement 1
Given AE = 5
- AC = 10
Also, given that AB = 7.25
Notice that ABC is a right angled triangle. Applying Pythagoras theorem
AC2 = AB2 + BC2
- BC2 = 102 – 7.252
Therefore, we can calculate the value of BC and so we can arrive at a unique answer on whether AB is greater than BC or not.
Statement 1 is sufficient to arrive at a unique answer.
Step 4: Analyze Statement 2
Perimeter of AEB > Perimeter of BEC
- AE + BE + AB > BE + CE + BC
- AB > BC (Since we already noted that AE = BE = CE = DE)
Statement 2 is sufficient to arrive at a unique answer.
Step 5: Analyze Both Statements Together (if needed)
We arrived at a unique answer in step 3 and step 4 above. Therefore, this step is not needed.
Correct Answer: D
Most Upvoted Answer
In the figure shown above, point E is the intersection point of the di...
Steps 1 & 2: Understand Question and Draw Inferences
In the given rectangle ABCD, we need to find if AB > BC, i.e., if the length is greater than the breadth.
Note that AC and BD are the diagonals of the rectangle and E is their point of intersection.
In right triangle ADC, by Pythagoras Theorem,
AD2 + DC2 = AC2 . . . (1)
Similarly, in right triangle DCB,
DC2 + BC2 = DB2 . . . (2)
Equation (1) – Equation (2):
AD2 – BC2 = AC2 – DB2
Being opposite sides of a rectangle, AD = BC
Therefore, the above equation becomes:
0 = AC2 – DB2Therefore, AC = DB.
Thus, we observe that the two diagonals of the rectangle are equal.
As we know that diagonals of a rectangle bisect each other, we can write
AE = BE = CE = DE = AC/2 = BD/2
(Now, it is also easy to notice that the rectangle is symmetrical about point E.
Therefore, point E will divide each diagonal in half. )
Step 3: Analyze Statement 1
Given AE = 5
- AC = 10
Also, given that AB = 7.25
Notice that ABC is a right angled triangle. Applying Pythagoras theorem
AC2 = AB2 + BC2
- BC2 = 102 – 7.252
Therefore, we can calculate the value of BC and so we can arrive at a unique answer on whether AB is greater than BC or not.
Statement 1 is sufficient to arrive at a unique answer.
Step 4: Analyze Statement 2
Perimeter of AEB > Perimeter of BEC
- AE + BE + AB > BE + CE + BC
- AB > BC (Since we already noted that AE = BE = CE = DE)
Statement 2 is sufficient to arrive at a unique answer.
Step 5: Analyze Both Statements Together (if needed)
We arrived at a unique answer in step 3 and step 4 above. Therefore, this step is not needed.
Correct Answer: D
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In the figure shown above, point E is the intersection point of the diagnoals AC and BD of rectangle ABCD. Is AB greater than BC? AE = 5 cms and AB = 7.25 cm The perimeter of AEB is greater than the perimeter of BECa)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 'D'. Can you explain this answer?
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In the figure shown above, point E is the intersection point of the diagnoals AC and BD of rectangle ABCD. Is AB greater than BC? AE = 5 cms and AB = 7.25 cm The perimeter of AEB is greater than the perimeter of BECa)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 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In the figure shown above, point E is the intersection point of the diagnoals AC and BD of rectangle ABCD. Is AB greater than BC? AE = 5 cms and AB = 7.25 cm The perimeter of AEB is greater than the perimeter of BECa)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 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the figure shown above, point E is the intersection point of the diagnoals AC and BD of rectangle ABCD. Is AB greater than BC? AE = 5 cms and AB = 7.25 cm The perimeter of AEB is greater than the perimeter of BECa)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 'D'. Can you explain this answer?.
In the figure shown above, point E is the intersection point of the diagnoals AC and BD of rectangle ABCD. Is AB greater than BC? AE = 5 cms and AB = 7.25 cm The perimeter of AEB is greater than the perimeter of BECa)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 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In the figure shown above, point E is the intersection point of the diagnoals AC and BD of rectangle ABCD. Is AB greater than BC? AE = 5 cms and AB = 7.25 cm The perimeter of AEB is greater than the perimeter of BECa)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 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the figure shown above, point E is the intersection point of the diagnoals AC and BD of rectangle ABCD. Is AB greater than BC? AE = 5 cms and AB = 7.25 cm The perimeter of AEB is greater than the perimeter of BECa)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 'D'. Can you explain this answer?.
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In the figure shown above, point E is the intersection point of the diagnoals AC and BD of rectangle ABCD. Is AB greater than BC? AE = 5 cms and AB = 7.25 cm The perimeter of AEB is greater than the perimeter of BECa)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 'D'. Can you explain this answer?, a detailed solution for In the figure shown above, point E is the intersection point of the diagnoals AC and BD of rectangle ABCD. Is AB greater than BC? AE = 5 cms and AB = 7.25 cm The perimeter of AEB is greater than the perimeter of BECa)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 'D'. Can you explain this answer? has been provided alongside types of In the figure shown above, point E is the intersection point of the diagnoals AC and BD of rectangle ABCD. Is AB greater than BC? AE = 5 cms and AB = 7.25 cm The perimeter of AEB is greater than the perimeter of BECa)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 'D'. Can you explain this answer? theory, EduRev gives you an
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