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The problems below contain a question and two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the questions.
Q. If 'x' is an integer, is x/2 an even integer?
I. x is multiple of 2
II. x is multiple of 4
I. x is multiple of 2
II. x is multiple of 4
The correct answer is
- a)If Statement I alone is sufficient but Statement II alone is not sufficient.
- b)If Statement II alone is sufficient but Statement I atone is not sufficient.
- c)If both statements I and II together are sufficient but neither of statements alone is sufficient.
- d)If Statement I and II together are not sufficient.
Correct answer is option 'B'. Can you explain this answer?
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The problems below contain a question and two statements giving certai...
Statement I: x is a multiple of 2.
Statement II: x is a multiple of 4.
To determine whether x/2 is an even integer, we need to know if x is even or odd. Let's evaluate each statement separately:
Statement I: x is a multiple of 2.
If x is a multiple of 2, it means that x is even. In this case, x/2 will also be an even integer, since dividing an even number by 2 will always result in an even number. Therefore, Statement I alone is sufficient to answer the question.
Statement II: x is a multiple of 4.
If x is a multiple of 4, it means that x could be even or odd. For example, 4 is a multiple of 4 and is even, while 8 is also a multiple of 4 and is also even. However, if x is odd (e.g. 9), then x/2 would not be an even integer. Therefore, Statement II alone is not sufficient to answer the question.
Combined:
When we consider both statements together, we know that x is a multiple of both 2 and 4. This implies that x must be a multiple of the least common multiple of 2 and 4, which is 4. Therefore, x must be even. Since x is even, x/2 will also be an even integer. Thus, both statements together are sufficient to answer the question.
Therefore, the correct answer is option b) If Statement II alone is sufficient but Statement I alone is not sufficient.
Statement II: x is a multiple of 4.
To determine whether x/2 is an even integer, we need to know if x is even or odd. Let's evaluate each statement separately:
Statement I: x is a multiple of 2.
If x is a multiple of 2, it means that x is even. In this case, x/2 will also be an even integer, since dividing an even number by 2 will always result in an even number. Therefore, Statement I alone is sufficient to answer the question.
Statement II: x is a multiple of 4.
If x is a multiple of 4, it means that x could be even or odd. For example, 4 is a multiple of 4 and is even, while 8 is also a multiple of 4 and is also even. However, if x is odd (e.g. 9), then x/2 would not be an even integer. Therefore, Statement II alone is not sufficient to answer the question.
Combined:
When we consider both statements together, we know that x is a multiple of both 2 and 4. This implies that x must be a multiple of the least common multiple of 2 and 4, which is 4. Therefore, x must be even. Since x is even, x/2 will also be an even integer. Thus, both statements together are sufficient to answer the question.
Therefore, the correct answer is option b) If Statement II alone is sufficient but Statement I alone is not sufficient.
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The problems below contain a question and two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the questions.Q. If x is an integer, is x/2 an even integer?I. x is multiple of 2II. x is multiple of 4The correct answer isa)If Statement I alone is sufficient but Statement II alone is not sufficient.b)If Statement II alone is sufficient but Statement I atone is not sufficient.c)If both statements I and II together are sufficient but neither of statements alone is sufficient.d)If Statement I and II together are not sufficient.Correct answer is option 'B'. Can you explain this answer?
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