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A sequence An satisfies An+3=An+8. What is the remainder whe

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by Max@Math Revolution » Thu Jan 17, 2019 12:52 am

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[Math Revolution GMAT math practice question]1.17

A sequence An satisfies An+3=An+8. What is the remainder when A99 is divided by 8?

1) A1=1
2) A2=2
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Source: — Data Sufficiency |
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by Max@Math Revolution » Sun Jan 20, 2019 5:24 pm
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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

The initial condition, An+3=An+8, tells us that every third term has the same remainder when it is divided by 8.
By condition 1), A1 = 1, A4 = 9, A7 = 17, ... , A97 = 257, A100 = 265 .... Each of these terms has remainder 1 when it is divided by 8.
By condition 2), A2 = 2, A5 = 10, A8 = 18, ... , A98 = 258, A101 = 266 .... Each of these terms has remainder 2 when it is divided by 8.

A99 does not appear in either of these lists. Thus, both conditions together do not provide enough information to find the remainder when A99 is divided by 8. Therefore, E is the answer.

Note: in order to find the remainder when A99 is divided by 8, we need the value of A3. Thus, we need the values of 3 variables, and we are given only 2, so E should be the answer.

Therefore, the correct answer is E.
Answer: E
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