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A certain calculating machine has only three operation

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A certain calculating machine has only three operation

by swerve » Fri Aug 16, 2019 2:41 pm

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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

The OA is D
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by Ian Stewart » Sun Aug 18, 2019 5:58 am
We start with the number "2", and according to the instructions in the question, we double that number, subtract one, double the result, subtract one, over and over. If you carry out the instructions, you end up with 65.

The result is odd, so if we're going to arrive at 65 following a different sequence of instructions, the final instruction could never be "D", since we'd get an even result applying D (doubling) to an integer. So only A, D or E could be right. In answer A, we'll end up subtracting "1" six times from an even number at the end (because there are six "R" operations following a "D"), so answer A will also produce an even result and cannot get us to 65. So the answer must be D or E. In each case, we'll double our starting number "2" a few times and then add one. We want the doubling to therefore get us to 64, and since we're starting with 2, and (2)(2^5) = 64, we want to double our number five times. So answer D is correct.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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