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Bunuel
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A certain calculating machine has only three operation buttons, D, R a 24 May 2022, 08:00
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Difficulty:

55% (hard)

Question Stats:

61% (02:36) correct 39% (03:03) wrong based on 31 sessions

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A certain calculating machine has only three operation buttons, D, R and A. The D operation doubles the number the machine displays, the R operation subtracts 1 from the number the machine displays, and the A operation adds 1 to the number the machine displays. If the machine initially displays the number 2, which of the following operation sequences (read from left to right) would lead to the same final displayed result as the sequence - D R D R D R D R D R D R ?

A. D D D D D D R R R R R R

B. R D R D R D R D R D R D

C. A D D D D D

D. D D D D D A

E. D D D D D D D A
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A certain calculating machine has only three operation buttons, D, R a 24 May 2022, 11:04
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Bunuel
A certain calculating machine has only three operation buttons, D, R and A. The D operation doubles the number the machine displays, the R operation subtracts 1 from the number the machine displays, and the A operation adds 1 to the number the machine displays. If the machine initially displays the number 2, which of the following operation sequences (read from left to right) would lead to the same final displayed result as the sequence - D R D R D R D R D R D R ?

A. D D D D D D R R R R R R

B. R D R D R D R D R D R D

C. A D D D D D

D. D D D D D A

E. D D D D D D D A

Breaking Down the Info:

Currently, we apply D then R 6 times in a row. This means we double and then subtract 1 six times. If we start from 2, we have:
2 -> 3 -> 5 -> 9 -> 17 -> 33 -> 65.

Therefore we need to find a choice that gives 65. We will certainly need a lot of D's as our starting point is still 2.

We can eliminate A and B as double 6 times in a row will give a much bigger number, and reversing the operation will certainly give a different number.

We can eliminate C as we will end up with an even number with C.

Choice D gives \(2 * 2^5 + 1 = 65\) so choice D is correct.

Answer: D
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Bunuel
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