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Question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question:
Is quadrilateral PQRS a rhombus but not Square?
I: Area of PQRS is 65 cm2 and length of one diagonal is 5 cm.
II: All sides of quadrilateral PQRS are equal and length of one diagonal is 26 cm.
- a)Statement (I) alone is sufficient, but statement (II) alone is not sufficient.
- b)Statement (II) alone is sufficient, but statement (I) alone is not sufficient.
- c)Both statements together are sufficient, but neither statement alone is sufficient.
- d)Either statement alone is sufficient.
- e)Statements (I) and (II) together are not sufficient.
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Question below consists of a question and two statements numbered I a...
From I: Area of PQRS = 65 cm2 and length of one diagonal = 5 cm.
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We cannot determine the property of PQRS.
So, I alone is not sufficient.
From II: All sides are equal. With this information we can conclude the PQRS is a rhombus, but it also can be Square.
Length of one diagonal is given.
So, II alone is not sufficient.
From I and II:
Length of diagonal is 5 cm and 26 cm.
All sides are equal and length of both the diagonals are not the same. So, PQRS is a rhombus but not Square.
Area of rhombus = ½ × (product of the lengths of the diagonals)
=> ½ × (5× 26) = 65 cm2
Area of PQRS is the same as given in statement I. So PQRS must be a rhombus.
So, I and II together are sufficient.
Most Upvoted Answer
Question below consists of a question and two statements numbered I a...
Statement (I) alone is not sufficient to answer the question.
Explanation:
To determine whether quadrilateral PQRS is a rhombus but not a square, we need more information.
- The area of a rhombus can be calculated using the formula:
Area = (diagonal1 * diagonal2) / 2
However, statement (I) only provides the area of PQRS as 65 cm² and the length of one diagonal as 5 cm. Without the length of the other diagonal or any information about the sides, we cannot conclusively determine if PQRS is a rhombus but not a square.
Statement (II) alone is not sufficient to answer the question.
Explanation:
Statement (II) provides information about the sides and one diagonal of quadrilateral PQRS, but it does not provide information about the other diagonal.
- All sides of a rhombus are equal, so if all sides of PQRS are equal as stated in statement (II), it could be a rhombus.
- However, a square is a special type of rhombus where all sides are equal and all angles are right angles. Without information about the angles or the other diagonal, we cannot determine if PQRS is a square or just a rhombus.
Both statements together are sufficient to answer the question.
Explanation:
By combining the information from both statements, we can determine if PQRS is a rhombus but not a square.
- Statement (I) gives the area of PQRS as 65 cm² and the length of one diagonal as 5 cm.
- Statement (II) states that all sides of PQRS are equal and the length of one diagonal is 26 cm.
From statement (I), we can calculate the length of the other diagonal using the formula for the area of a rhombus.
Area = (diagonal1 * diagonal2) / 2
65 = (5 * diagonal2) / 2
diagonal2 = 26 cm
By combining the length of both diagonals from statements (I) and (II), we can determine if PQRS is a rhombus.
- If both diagonals are equal, then PQRS is a rhombus.
- If both diagonals are not equal, then PQRS is not a rhombus.
Since both statements together provide the necessary information to determine if PQRS is a rhombus but not a square, the correct answer is option 'C' - Both statements together are sufficient, but neither statement alone is sufficient.
Explanation:
To determine whether quadrilateral PQRS is a rhombus but not a square, we need more information.
- The area of a rhombus can be calculated using the formula:
Area = (diagonal1 * diagonal2) / 2
However, statement (I) only provides the area of PQRS as 65 cm² and the length of one diagonal as 5 cm. Without the length of the other diagonal or any information about the sides, we cannot conclusively determine if PQRS is a rhombus but not a square.
Statement (II) alone is not sufficient to answer the question.
Explanation:
Statement (II) provides information about the sides and one diagonal of quadrilateral PQRS, but it does not provide information about the other diagonal.
- All sides of a rhombus are equal, so if all sides of PQRS are equal as stated in statement (II), it could be a rhombus.
- However, a square is a special type of rhombus where all sides are equal and all angles are right angles. Without information about the angles or the other diagonal, we cannot determine if PQRS is a square or just a rhombus.
Both statements together are sufficient to answer the question.
Explanation:
By combining the information from both statements, we can determine if PQRS is a rhombus but not a square.
- Statement (I) gives the area of PQRS as 65 cm² and the length of one diagonal as 5 cm.
- Statement (II) states that all sides of PQRS are equal and the length of one diagonal is 26 cm.
From statement (I), we can calculate the length of the other diagonal using the formula for the area of a rhombus.
Area = (diagonal1 * diagonal2) / 2
65 = (5 * diagonal2) / 2
diagonal2 = 26 cm
By combining the length of both diagonals from statements (I) and (II), we can determine if PQRS is a rhombus.
- If both diagonals are equal, then PQRS is a rhombus.
- If both diagonals are not equal, then PQRS is not a rhombus.
Since both statements together provide the necessary information to determine if PQRS is a rhombus but not a square, the correct answer is option 'C' - Both statements together are sufficient, but neither statement alone is sufficient.
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Question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question:Is quadrilateral PQRS a rhombus but not Square?I: Area of PQRS is 65 cm2 and length of one diagonal is 5 cm.II: All sides of quadrilateral PQRS are equal and length of one diagonal is 26 cm.a)Statement (I) alone is sufficient, but statement (II) alone is not sufficient.b)Statement (II) alone is sufficient, but statement (I) alone is not sufficient.c)Both statements together are sufficient, but neither statement alone is sufficient.d)Either statement alone is sufficient.e)Statements (I) and (II) together are not sufficient.Correct answer is option 'C'. Can you explain this answer?
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Question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question:Is quadrilateral PQRS a rhombus but not Square?I: Area of PQRS is 65 cm2 and length of one diagonal is 5 cm.II: All sides of quadrilateral PQRS are equal and length of one diagonal is 26 cm.a)Statement (I) alone is sufficient, but statement (II) alone is not sufficient.b)Statement (II) alone is sufficient, but statement (I) alone is not sufficient.c)Both statements together are sufficient, but neither statement alone is sufficient.d)Either statement alone is sufficient.e)Statements (I) and (II) together are not sufficient.Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question:Is quadrilateral PQRS a rhombus but not Square?I: Area of PQRS is 65 cm2 and length of one diagonal is 5 cm.II: All sides of quadrilateral PQRS are equal and length of one diagonal is 26 cm.a)Statement (I) alone is sufficient, but statement (II) alone is not sufficient.b)Statement (II) alone is sufficient, but statement (I) alone is not sufficient.c)Both statements together are sufficient, but neither statement alone is sufficient.d)Either statement alone is sufficient.e)Statements (I) and (II) together are not sufficient.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question:Is quadrilateral PQRS a rhombus but not Square?I: Area of PQRS is 65 cm2 and length of one diagonal is 5 cm.II: All sides of quadrilateral PQRS are equal and length of one diagonal is 26 cm.a)Statement (I) alone is sufficient, but statement (II) alone is not sufficient.b)Statement (II) alone is sufficient, but statement (I) alone is not sufficient.c)Both statements together are sufficient, but neither statement alone is sufficient.d)Either statement alone is sufficient.e)Statements (I) and (II) together are not sufficient.Correct answer is option 'C'. Can you explain this answer?.
Question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question:Is quadrilateral PQRS a rhombus but not Square?I: Area of PQRS is 65 cm2 and length of one diagonal is 5 cm.II: All sides of quadrilateral PQRS are equal and length of one diagonal is 26 cm.a)Statement (I) alone is sufficient, but statement (II) alone is not sufficient.b)Statement (II) alone is sufficient, but statement (I) alone is not sufficient.c)Both statements together are sufficient, but neither statement alone is sufficient.d)Either statement alone is sufficient.e)Statements (I) and (II) together are not sufficient.Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question:Is quadrilateral PQRS a rhombus but not Square?I: Area of PQRS is 65 cm2 and length of one diagonal is 5 cm.II: All sides of quadrilateral PQRS are equal and length of one diagonal is 26 cm.a)Statement (I) alone is sufficient, but statement (II) alone is not sufficient.b)Statement (II) alone is sufficient, but statement (I) alone is not sufficient.c)Both statements together are sufficient, but neither statement alone is sufficient.d)Either statement alone is sufficient.e)Statements (I) and (II) together are not sufficient.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question:Is quadrilateral PQRS a rhombus but not Square?I: Area of PQRS is 65 cm2 and length of one diagonal is 5 cm.II: All sides of quadrilateral PQRS are equal and length of one diagonal is 26 cm.a)Statement (I) alone is sufficient, but statement (II) alone is not sufficient.b)Statement (II) alone is sufficient, but statement (I) alone is not sufficient.c)Both statements together are sufficient, but neither statement alone is sufficient.d)Either statement alone is sufficient.e)Statements (I) and (II) together are not sufficient.Correct answer is option 'C'. Can you explain this answer?.
Solutions for Question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question:Is quadrilateral PQRS a rhombus but not Square?I: Area of PQRS is 65 cm2 and length of one diagonal is 5 cm.II: All sides of quadrilateral PQRS are equal and length of one diagonal is 26 cm.a)Statement (I) alone is sufficient, but statement (II) alone is not sufficient.b)Statement (II) alone is sufficient, but statement (I) alone is not sufficient.c)Both statements together are sufficient, but neither statement alone is sufficient.d)Either statement alone is sufficient.e)Statements (I) and (II) together are not sufficient.Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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