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The terms of the sequence {An}, where n is a positive intege

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[GMAT math practice question]

The terms of the sequence {An}, where n is a positive integer, satisfy A1=81, A2=82, A3=83, and An+3=An+4. Which of the following cannot be a value of An?

A. 801
B. 802
C. 803
D. 804
E. 805

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=>

The terms of the sequence can be divided into three groups:
A1 = 81, A4 = 85, A7 = 89, … : These have a remainder of 1 when they are divided by 4.
A2 = 82, A5 = 86, A8 = 90, … : These have a remainder of 2 when they are divided by 4.
A3 = 83, A6 = 87, A9 = 91, … : These have a remainder of 3 when they are divided by 4.
No term of the sequence is a multiple of 4.

Since 804 is a multiple of 4, it cannot be a term of the sequence.

Therefore, the answer is D.

Answer: D

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