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If \(45x = 121y\), which of the following must be true?
I. \(x > y\)
II. \(x^2 > y^2\)
III. \(\frac{x}{11}\) is an integer
A. I only
B. II only
C. III only
D. I and III only
E. None of the above
I. \(x > y\)
II. \(x^2 > y^2\)
III. \(\frac{x}{11}\) is an integer
A. I only
B. II only
C. III only
D. I and III only
E. None of the above
11 Mar 2023, 02:32
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Official Solution:
If \(45x = 121y\), which of the following must be true?
I. \(x > y\)
II. \(x^2 > y^2\)
III. \(\frac{x}{11}\) is an integer
A. I only
B. II only
C. III only
D. I and III only
E. None of the above
It is important to note that the problem does not specify that \(x\) and \(y\) are necessarily integers, nor does it require \(x\) and \(y\) to be necessarily positive. Therefore, when evaluating each option, it is essential to keep in mind that these variables may take on non-integer or non-positive values!
I. \(x > y\).
This statement is not always true, as \(x\) and \(y\) are not necessarily positive. For instance, consider \(x = -121\) and \(y=-45\), or \(x = 0\) and \(y=0\).
II. \(x^2 > y^2\).
This statement is also not always true. For example, consider \(x = y = 0\).
III. \(\frac{x}{11}\) is an integer.
This statement is also not always true, as \(x\) and \(y\) are not necessarily integers. For instance, consider \(x = \frac{1}{45}\) and \(y=\frac{1}{121}\).
Answer: E
If \(45x = 121y\), which of the following must be true?
I. \(x > y\)
II. \(x^2 > y^2\)
III. \(\frac{x}{11}\) is an integer
A. I only
B. II only
C. III only
D. I and III only
E. None of the above
It is important to note that the problem does not specify that \(x\) and \(y\) are necessarily integers, nor does it require \(x\) and \(y\) to be necessarily positive. Therefore, when evaluating each option, it is essential to keep in mind that these variables may take on non-integer or non-positive values!
I. \(x > y\).
This statement is not always true, as \(x\) and \(y\) are not necessarily positive. For instance, consider \(x = -121\) and \(y=-45\), or \(x = 0\) and \(y=0\).
II. \(x^2 > y^2\).
This statement is also not always true. For example, consider \(x = y = 0\).
III. \(\frac{x}{11}\) is an integer.
This statement is also not always true, as \(x\) and \(y\) are not necessarily integers. For instance, consider \(x = \frac{1}{45}\) and \(y=\frac{1}{121}\).
Answer: E
03 Jul 2024, 07:38
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The catch in most of these "which of the following must be true?" questions is the limit assigned to the type of value the variable can take/ hold/ posess.
Questions without any such limit generally favour the more absolute answer choice i.e., all of the above, none of these.
This question is a great example!
Questions without any such limit generally favour the more absolute answer choice i.e., all of the above, none of these.
This question is a great example!
