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15 May 2024, 01:30
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D
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Difficulty:
25%
(medium)
Question Stats:
81% (01:02) correct
19%
(01:15)
wrong
based on 93
sessions
History
Date
Time
Result
Not Attempted Yet
If \(©\) denotes one of three arithmetic operations, addition, subtraction, or division, and \(9©x = x\), where \(x\) is a positive integer, what is the value of \(x\)?
A. 0
B. 1
C. 2
D. 3
E. 4
A. 0
B. 1
C. 2
D. 3
E. 4
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02 Jun 2024, 02:00
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Official Solution:
If \(©\) denotes one of three arithmetic operations, addition, subtraction, or division, and \(9©x = x\), where \(x\) is a positive integer, what is the value of \(x\)?
A. 0
B. 1
C. 2
D. 3
E. 4
If \(©\) represents addition, we'd have \(9 + x = x\), which cannot be true for any value of \(x\). Hence, \(©\) is not addition.
If \(©\) represents subtraction, we'd have \(9 - x = x\), which simplifies to \(x = \frac{9}{2}\). However, since \(x\) must be a positive integer, \(©\) cannot be subtraction.
Therefore, \(©\) must represent division. In this case, \(\frac{9}{x} = x\), leading to \(x^2 = 9\). Since \(x\) is a positive integer, \(x\) must be 3.
Answer: D
If \(©\) denotes one of three arithmetic operations, addition, subtraction, or division, and \(9©x = x\), where \(x\) is a positive integer, what is the value of \(x\)?
A. 0
B. 1
C. 2
D. 3
E. 4
If \(©\) represents addition, we'd have \(9 + x = x\), which cannot be true for any value of \(x\). Hence, \(©\) is not addition.
If \(©\) represents subtraction, we'd have \(9 - x = x\), which simplifies to \(x = \frac{9}{2}\). However, since \(x\) must be a positive integer, \(©\) cannot be subtraction.
Therefore, \(©\) must represent division. In this case, \(\frac{9}{x} = x\), leading to \(x^2 = 9\). Since \(x\) is a positive integer, \(x\) must be 3.
Answer: D
General Discussion
15 May 2024, 01:56
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Bunuel
If \(©\) denotes one of three arithmetic operations, addition, subtraction, or division, and \(9©x = x\), where \(x\) is a positive integer, what is the value of \(x\)?
A. 0
B. 1
C. 2
D. 3
E. 4
A. 0
B. 1
C. 2
D. 3
E. 4
9 + x = x
9 * x = x
9 / x = x
9 - x = x
Out of the above operations, only \(\frac{9 }{ x} = x\) is valid.
\(x^2 = 9\)
\(x = 3\)
Option D
