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The question is followed by two statements, A and B. Answer the question using the following instructions:
Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.
Mark option (2) if the question can be answered by using statement B alone but not by using statement A alone.
Mark option (3) if the question can be answered by using either statement alone.
Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.
Mark option (5) if the question cannot be answered on the basis of the two statements.
Mark option (2) if the question can be answered by using statement B alone but not by using statement A alone.
Mark option (3) if the question can be answered by using either statement alone.
Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.
Mark option (5) if the question cannot be answered on the basis of the two statements.
Q.What is the first term of an arithmetic progression consisting of positive integers only?
A. Sum of the squares of the second and the third term is 130.
B. The sixth term is divisible by three.
A. Sum of the squares of the second and the third term is 130.
B. The sixth term is divisible by three.
- a)1
- b)2
- c)3
- d)4
- e)5
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The question is followed by two statements, A and B. Answer the questi...
Using statement A alone:
Sum of squares of only two pair of positive integers (i.e. (7, 9) and (3, 11)) is equal to 130.
So the second and third terms can be (7, 9), (9, 7) or (11, 3).
So the second and third terms can be (7, 9), (9, 7) or (11, 3).
(3, 11) is not possible, as in that case the first term of the AP will become negative.
But still we cannot find exact value of second and third term of an AP. Hence, no conclusion can be drawn about the first term of an AP.
Hence, statement A alone is not sufficient to answer the question.
Using statement B alone: This does not provide any useful information about the first term of the AP. Hence, statement B alone is not sufficient to answer the question.
Using both the statements together:
But still we cannot find exact value of second and third term of an AP. Hence, no conclusion can be drawn about the first term of an AP.
Hence, statement A alone is not sufficient to answer the question.
Using statement B alone: This does not provide any useful information about the first term of the AP. Hence, statement B alone is not sufficient to answer the question.
Using both the statements together:
From statement A it is clear that the second and third terms can be (7, 9), (9, 7) or (11, 3).
The different possible APs are
The different possible APs are
5, 7, 9, 11, 13, 15,... (possible)
11, 9, 7, 5, 3, 1 (sixth term is not divisible by 3, not possible)
19, 11, 3, -5, -13, -21 (sixth term is not positive, not possible)
Hence, the first term of the AP will be 5.
Hence, question can be answered using both the statements together.
Hence, option 4.
Hence, question can be answered using both the statements together.
Hence, option 4.
(9, 7) and (11,3) does have negative common difference. But that doesn't mean that these AP will be negative at some point. Because we don't know the number of elements in these series we can't assume them as infinte series or finite series.
AP could be,
AP could be,
11,9, 7 ,..., 1 and 19, 11,3.
Most Upvoted Answer
The question is followed by two statements, A and B. Answer the questi...
Statement A: The sum of the squares of the second and the third term is 130.
Statement B: The sixth term is divisible by three.
To find the first term of an arithmetic progression, we need information about the common difference and at least one value in the progression. Let's analyze each statement separately and then combine them to determine if we can answer the question.
Analysis of Statement A:
Let's assume that the common difference of the arithmetic progression is 'd' and the first term is 'a'.
The second term will be a + d, and the third term will be a + 2d.
According to the statement, (a + d)^2 + (a + 2d)^2 = 130.
Expanding the equation, we get a^2 + 6ad + 5d^2 - 130 = 0.
This is a quadratic equation in terms of 'a' and 'd', but we cannot solve for the individual values of 'a' and 'd' with this equation alone.
Hence, statement A alone is not sufficient to answer the question.
Analysis of Statement B:
The sixth term is a + 5d.
According to the statement, (a + 5d) is divisible by 3.
This means that a + 5d is a multiple of 3, but we do not have any information about the value of 'a' or 'd' individually.
Hence, statement B alone is not sufficient to answer the question.
Combining Statements A and B:
From statement A, we have the equation a^2 + 6ad + 5d^2 - 130 = 0.
From statement B, we have the condition a + 5d is divisible by 3.
By solving these two equations simultaneously, we can find the values of 'a' and 'd'.
Once we find the values of 'a' and 'd', we can determine the first term of the arithmetic progression.
Hence, combining both statements A and B, we can answer the question.
Therefore, the correct answer is option (4) - The question can be answered by using both the statements together but not by either of the statements alone.
Statement B: The sixth term is divisible by three.
To find the first term of an arithmetic progression, we need information about the common difference and at least one value in the progression. Let's analyze each statement separately and then combine them to determine if we can answer the question.
Analysis of Statement A:
Let's assume that the common difference of the arithmetic progression is 'd' and the first term is 'a'.
The second term will be a + d, and the third term will be a + 2d.
According to the statement, (a + d)^2 + (a + 2d)^2 = 130.
Expanding the equation, we get a^2 + 6ad + 5d^2 - 130 = 0.
This is a quadratic equation in terms of 'a' and 'd', but we cannot solve for the individual values of 'a' and 'd' with this equation alone.
Hence, statement A alone is not sufficient to answer the question.
Analysis of Statement B:
The sixth term is a + 5d.
According to the statement, (a + 5d) is divisible by 3.
This means that a + 5d is a multiple of 3, but we do not have any information about the value of 'a' or 'd' individually.
Hence, statement B alone is not sufficient to answer the question.
Combining Statements A and B:
From statement A, we have the equation a^2 + 6ad + 5d^2 - 130 = 0.
From statement B, we have the condition a + 5d is divisible by 3.
By solving these two equations simultaneously, we can find the values of 'a' and 'd'.
Once we find the values of 'a' and 'd', we can determine the first term of the arithmetic progression.
Hence, combining both statements A and B, we can answer the question.
Therefore, the correct answer is option (4) - The question can be answered by using both the statements together but not by either of the statements alone.
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The question is followed by two statements, A and B. Answer the question using the following instructions:Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.Mark option (2) if the question can be answered by using statement B alonebut not by using statement A alone.Mark option (3) if the question can be answered by using either statement alone.Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.Mark option (5) if the question cannot be answered on the basis of the two statements.Q.What is the first term of an arithmetic progression consisting of positive integers only?A. Sum of the squares of the second and the third term is 130.B. The sixth term is divisible by three.a)1b)2c)3d)4e)5Correct answer is option 'D'. Can you explain this answer?
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The question is followed by two statements, A and B. Answer the question using the following instructions:Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.Mark option (2) if the question can be answered by using statement B alonebut not by using statement A alone.Mark option (3) if the question can be answered by using either statement alone.Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.Mark option (5) if the question cannot be answered on the basis of the two statements.Q.What is the first term of an arithmetic progression consisting of positive integers only?A. Sum of the squares of the second and the third term is 130.B. The sixth term is divisible by three.a)1b)2c)3d)4e)5Correct answer is option 'D'. 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 The question is followed by two statements, A and B. Answer the question using the following instructions:Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.Mark option (2) if the question can be answered by using statement B alonebut not by using statement A alone.Mark option (3) if the question can be answered by using either statement alone.Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.Mark option (5) if the question cannot be answered on the basis of the two statements.Q.What is the first term of an arithmetic progression consisting of positive integers only?A. Sum of the squares of the second and the third term is 130.B. The sixth term is divisible by three.a)1b)2c)3d)4e)5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The question is followed by two statements, A and B. Answer the question using the following instructions:Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.Mark option (2) if the question can be answered by using statement B alonebut not by using statement A alone.Mark option (3) if the question can be answered by using either statement alone.Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.Mark option (5) if the question cannot be answered on the basis of the two statements.Q.What is the first term of an arithmetic progression consisting of positive integers only?A. Sum of the squares of the second and the third term is 130.B. The sixth term is divisible by three.a)1b)2c)3d)4e)5Correct answer is option 'D'. Can you explain this answer?.
The question is followed by two statements, A and B. Answer the question using the following instructions:Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.Mark option (2) if the question can be answered by using statement B alonebut not by using statement A alone.Mark option (3) if the question can be answered by using either statement alone.Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.Mark option (5) if the question cannot be answered on the basis of the two statements.Q.What is the first term of an arithmetic progression consisting of positive integers only?A. Sum of the squares of the second and the third term is 130.B. The sixth term is divisible by three.a)1b)2c)3d)4e)5Correct answer is option 'D'. 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 The question is followed by two statements, A and B. Answer the question using the following instructions:Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.Mark option (2) if the question can be answered by using statement B alonebut not by using statement A alone.Mark option (3) if the question can be answered by using either statement alone.Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.Mark option (5) if the question cannot be answered on the basis of the two statements.Q.What is the first term of an arithmetic progression consisting of positive integers only?A. Sum of the squares of the second and the third term is 130.B. The sixth term is divisible by three.a)1b)2c)3d)4e)5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The question is followed by two statements, A and B. Answer the question using the following instructions:Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.Mark option (2) if the question can be answered by using statement B alonebut not by using statement A alone.Mark option (3) if the question can be answered by using either statement alone.Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.Mark option (5) if the question cannot be answered on the basis of the two statements.Q.What is the first term of an arithmetic progression consisting of positive integers only?A. Sum of the squares of the second and the third term is 130.B. The sixth term is divisible by three.a)1b)2c)3d)4e)5Correct answer is option 'D'. Can you explain this answer?.
Solutions for The question is followed by two statements, A and B. Answer the question using the following instructions:Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.Mark option (2) if the question can be answered by using statement B alonebut not by using statement A alone.Mark option (3) if the question can be answered by using either statement alone.Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.Mark option (5) if the question cannot be answered on the basis of the two statements.Q.What is the first term of an arithmetic progression consisting of positive integers only?A. Sum of the squares of the second and the third term is 130.B. The sixth term is divisible by three.a)1b)2c)3d)4e)5Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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Here you can find the meaning of The question is followed by two statements, A and B. Answer the question using the following instructions:Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.Mark option (2) if the question can be answered by using statement B alonebut not by using statement A alone.Mark option (3) if the question can be answered by using either statement alone.Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.Mark option (5) if the question cannot be answered on the basis of the two statements.Q.What is the first term of an arithmetic progression consisting of positive integers only?A. Sum of the squares of the second and the third term is 130.B. The sixth term is divisible by three.a)1b)2c)3d)4e)5Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The question is followed by two statements, A and B. Answer the question using the following instructions:Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.Mark option (2) if the question can be answered by using statement B alonebut not by using statement A alone.Mark option (3) if the question can be answered by using either statement alone.Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.Mark option (5) if the question cannot be answered on the basis of the two statements.Q.What is the first term of an arithmetic progression consisting of positive integers only?A. Sum of the squares of the second and the third term is 130.B. The sixth term is divisible by three.a)1b)2c)3d)4e)5Correct answer is option 'D'. Can you explain this answer?, a detailed solution for The question is followed by two statements, A and B. Answer the question using the following instructions:Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.Mark option (2) if the question can be answered by using statement B alonebut not by using statement A alone.Mark option (3) if the question can be answered by using either statement alone.Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.Mark option (5) if the question cannot be answered on the basis of the two statements.Q.What is the first term of an arithmetic progression consisting of positive integers only?A. Sum of the squares of the second and the third term is 130.B. The sixth term is divisible by three.a)1b)2c)3d)4e)5Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of The question is followed by two statements, A and B. Answer the question using the following instructions:Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.Mark option (2) if the question can be answered by using statement B alonebut not by using statement A alone.Mark option (3) if the question can be answered by using either statement alone.Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.Mark option (5) if the question cannot be answered on the basis of the two statements.Q.What is the first term of an arithmetic progression consisting of positive integers only?A. Sum of the squares of the second and the third term is 130.B. The sixth term is divisible by three.a)1b)2c)3d)4e)5Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The question is followed by two statements, A and B. Answer the question using the following instructions:Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.Mark option (2) if the question can be answered by using statement B alonebut not by using statement A alone.Mark option (3) if the question can be answered by using either statement alone.Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.Mark option (5) if the question cannot be answered on the basis of the two statements.Q.What is the first term of an arithmetic progression consisting of positive integers only?A. Sum of the squares of the second and the third term is 130.B. The sixth term is divisible by three.a)1b)2c)3d)4e)5Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice CAT tests.
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