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13 May 2024, 07:58
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If \(©\) denotes one of three arithmetic operations, addition, subtraction, or division, and \(2©x > x©2\), where \(x\) is a positive integer, what is the value of \(x\)?
A. 0
B. 1
C. 2
D. 3
E. Cannot be determined from the given information
A. 0
B. 1
C. 2
D. 3
E. Cannot be determined from the given information
13 May 2024, 07:58
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Official Solution:
If \(©\) denotes one of three arithmetic operations, addition, subtraction, or division, and \(2©x > x©2\), where \(x\) is a positive integer, what is the value of \(x\)?
A. 0
B. 1
C. 2
D. 3
E. Cannot be determined from the given information
If \(©\) represents addition, we'd have \(2 + x > x + 2\), which is not true for any value of \(x\). Hence, \(©\) is not addition.
If \(©\) represents subtraction, we'd have \(2 - x > x - 2\), simplifying to \(x < 2\). Given that \(x\) is a positive integer, if \(©\) is subtraction, then \(x\) must be 1.
If \(©\) represents division, we'd have \(\frac{2}{x} > \frac{x}{2}\). Cross-multiplying (we can safely do that since \(x\) is a positive integer) gives \(x^2 < 4\), which narrows down to \(-2 < x < 2\). As \(x\) is a positive integer, \(x\) must be 1. Therefore, if \(©\) is division, \(x\) is 1.
In both viable cases (subtraction or division), \(x\) turns out to be 1.
Answer: B
If \(©\) denotes one of three arithmetic operations, addition, subtraction, or division, and \(2©x > x©2\), where \(x\) is a positive integer, what is the value of \(x\)?
A. 0
B. 1
C. 2
D. 3
E. Cannot be determined from the given information
If \(©\) represents addition, we'd have \(2 + x > x + 2\), which is not true for any value of \(x\). Hence, \(©\) is not addition.
If \(©\) represents subtraction, we'd have \(2 - x > x - 2\), simplifying to \(x < 2\). Given that \(x\) is a positive integer, if \(©\) is subtraction, then \(x\) must be 1.
If \(©\) represents division, we'd have \(\frac{2}{x} > \frac{x}{2}\). Cross-multiplying (we can safely do that since \(x\) is a positive integer) gives \(x^2 < 4\), which narrows down to \(-2 < x < 2\). As \(x\) is a positive integer, \(x\) must be 1. Therefore, if \(©\) is division, \(x\) is 1.
In both viable cases (subtraction or division), \(x\) turns out to be 1.
Answer: B
29 May 2025, 05:13
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