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16 Sep 2014, 00:38
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For all positive integers \(m\), \(\&m = m - 1\) when \(m\) is odd and \(\&m = m + 2\) when \(m\) is even. What is the value of \(\&(...\&(\&(\&(15)))...)\), where \(\&\) is used 99 times?
A. 120
B. 180
C. 210
D. 225
E. 250
A. 120
B. 180
C. 210
D. 225
E. 250
16 Sep 2014, 00:38
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Official Solution:
For all positive integers \(m\), \(\&m = m - 1\) when \(m\) is odd and \(\&m = m + 2\) when \(m\) is even. What is the value of \(\&(...\&(\&(\&(15)))...)\), where \(\&\) is used 99 times?
A. 120
B. 180
C. 210
D. 225
E. 250
Since 15 is odd, then \(\&15 = 15-1=14\).
Now, we need to calculate \(\&(...\&(\&(\&(14)))...)\), where \(\&\) is used 98 times.
Since 14 is even, each \(\&\) just adds 2 to the previous result. Therefore, \(\&(...\&(\&(\&(14)))...)\), where \(\&\) is used 98 times, equals to \(14 + 2*98 = 210\).
Answer: C
For all positive integers \(m\), \(\&m = m - 1\) when \(m\) is odd and \(\&m = m + 2\) when \(m\) is even. What is the value of \(\&(...\&(\&(\&(15)))...)\), where \(\&\) is used 99 times?
A. 120
B. 180
C. 210
D. 225
E. 250
Since 15 is odd, then \(\&15 = 15-1=14\).
Now, we need to calculate \(\&(...\&(\&(\&(14)))...)\), where \(\&\) is used 98 times.
Since 14 is even, each \(\&\) just adds 2 to the previous result. Therefore, \(\&(...\&(\&(\&(14)))...)\), where \(\&\) is used 98 times, equals to \(14 + 2*98 = 210\).
Answer: C
27 Jun 2023, 01:37
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
