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Each problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.
'x' and 'y' are positive integers. Is x divisible by 7?
I. x/14 + y/15 is an integer.
II. x/7 + y/14 is an integer.
- a)Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.
- b)Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.
- c)Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.
- d)Either statement alone is sufficient.
- e)Both statements together are not sufficient to answer the question.
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Each problem consists of a question followed by 2 statements. Check w...
From Statement I:
x/14 + y/15 is an integer. But 14 and 15 are Co-prime numbers i.e., they do not have any common factor. Hence, x and y have to be divisible by 14 and 15 respectively.
Since x is divisible by 14, it is divisible by 7 as well.
From Statement II:
x7 + y14 is an integer.
But 7 and 14 are not Coprime.
x/7 + y/14 = (2x + y)14
So, whether x is divisible by 7 or not, cannot be concluded from Statement II.
Most Upvoted Answer
Each problem consists of a question followed by 2 statements. Check w...
Statement I: x/14 y/15 is an integer.
Statement II: x/7 y/14 is an integer.
To determine if x is divisible by 7, we need to find out if x is a multiple of 7.
Analysis of Statement I:
If x/14 y/15 is an integer, it implies that both x and y are divisible by their respective denominators.
Let's consider an example to understand this better. Suppose x = 28 and y = 15. In this case, x/14 = 28/14 = 2 and y/15 = 15/15 = 1. Both x/14 and y/15 are integers. Therefore, x is divisible by 7.
Now, let's consider another example. Suppose x = 35 and y = 15. In this case, x/14 = 35/14 = 2.5 and y/15 = 15/15 = 1. Both x/14 and y/15 are not integers. Therefore, x is not divisible by 7.
From the above analysis, we can see that Statement I alone is not sufficient to determine if x is divisible by 7.
Analysis of Statement II:
If x/7 y/14 is an integer, it implies that both x and y are divisible by their respective denominators.
Let's consider an example to understand this better. Suppose x = 21 and y = 14. In this case, x/7 = 21/7 = 3 and y/14 = 14/14 = 1. Both x/7 and y/14 are integers. Therefore, x is divisible by 7.
Now, let's consider another example. Suppose x = 35 and y = 14. In this case, x/7 = 35/7 = 5 and y/14 = 14/14 = 1. Both x/7 and y/14 are integers. Therefore, x is divisible by 7.
From the above analysis, we can see that Statement II alone is sufficient to determine if x is divisible by 7.
Conclusion:
Statement I alone is not sufficient to answer the question. Statement II alone is sufficient to answer the question. Therefore, the correct answer is option A: Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.
Statement II: x/7 y/14 is an integer.
To determine if x is divisible by 7, we need to find out if x is a multiple of 7.
Analysis of Statement I:
If x/14 y/15 is an integer, it implies that both x and y are divisible by their respective denominators.
Let's consider an example to understand this better. Suppose x = 28 and y = 15. In this case, x/14 = 28/14 = 2 and y/15 = 15/15 = 1. Both x/14 and y/15 are integers. Therefore, x is divisible by 7.
Now, let's consider another example. Suppose x = 35 and y = 15. In this case, x/14 = 35/14 = 2.5 and y/15 = 15/15 = 1. Both x/14 and y/15 are not integers. Therefore, x is not divisible by 7.
From the above analysis, we can see that Statement I alone is not sufficient to determine if x is divisible by 7.
Analysis of Statement II:
If x/7 y/14 is an integer, it implies that both x and y are divisible by their respective denominators.
Let's consider an example to understand this better. Suppose x = 21 and y = 14. In this case, x/7 = 21/7 = 3 and y/14 = 14/14 = 1. Both x/7 and y/14 are integers. Therefore, x is divisible by 7.
Now, let's consider another example. Suppose x = 35 and y = 14. In this case, x/7 = 35/7 = 5 and y/14 = 14/14 = 1. Both x/7 and y/14 are integers. Therefore, x is divisible by 7.
From the above analysis, we can see that Statement II alone is sufficient to determine if x is divisible by 7.
Conclusion:
Statement I alone is not sufficient to answer the question. Statement II alone is sufficient to answer the question. Therefore, the correct answer is option A: Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.
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Each problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.'x' and 'y' are positive integers. Is x divisible by 7?I. x/14 + y/15 is an integer.II. x/7 + y/14 is an integer.a)Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.b)Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.c)Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.d)Either statement alone is sufficient.e)Both statements together are not sufficient to answer the question.Correct answer is option 'A'. Can you explain this answer?
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Each problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.'x' and 'y' are positive integers. Is x divisible by 7?I. x/14 + y/15 is an integer.II. x/7 + y/14 is an integer.a)Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.b)Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.c)Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.d)Either statement alone is sufficient.e)Both statements together are not sufficient to answer the question.Correct answer is option 'A'. 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 Each problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.'x' and 'y' are positive integers. Is x divisible by 7?I. x/14 + y/15 is an integer.II. x/7 + y/14 is an integer.a)Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.b)Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.c)Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.d)Either statement alone is sufficient.e)Both statements together are not sufficient to answer the question.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Each problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.'x' and 'y' are positive integers. Is x divisible by 7?I. x/14 + y/15 is an integer.II. x/7 + y/14 is an integer.a)Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.b)Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.c)Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.d)Either statement alone is sufficient.e)Both statements together are not sufficient to answer the question.Correct answer is option 'A'. Can you explain this answer?.
Each problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.'x' and 'y' are positive integers. Is x divisible by 7?I. x/14 + y/15 is an integer.II. x/7 + y/14 is an integer.a)Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.b)Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.c)Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.d)Either statement alone is sufficient.e)Both statements together are not sufficient to answer the question.Correct answer is option 'A'. 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 Each problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.'x' and 'y' are positive integers. Is x divisible by 7?I. x/14 + y/15 is an integer.II. x/7 + y/14 is an integer.a)Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.b)Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.c)Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.d)Either statement alone is sufficient.e)Both statements together are not sufficient to answer the question.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Each problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.'x' and 'y' are positive integers. Is x divisible by 7?I. x/14 + y/15 is an integer.II. x/7 + y/14 is an integer.a)Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.b)Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.c)Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.d)Either statement alone is sufficient.e)Both statements together are not sufficient to answer the question.Correct answer is option 'A'. Can you explain this answer?.
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