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15 Feb 2019, 01:19
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[GMAT math practice question]
(exponent) \(\frac{a^{n^2+n-1}}{a^{(n-1)(n+2)}}=?\)
\(1) n=5\)
\(2) a=5\)
(exponent) \(\frac{a^{n^2+n-1}}{a^{(n-1)(n+2)}}=?\)
\(1) n=5\)
\(2) a=5\)
Updated on: 08 Feb 2021, 03:48
Originally posted by MathRevolution on 17 Feb 2019, 18:31.
Last edited by MathRevolution on 08 Feb 2021, 03:48, edited 1 time in total.
Last edited by MathRevolution on 08 Feb 2021, 03:48, edited 1 time in total.
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MathRevolution
=>
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.
\(|a|<1\)
\(=> |a|^2 < 1\)
\(=> a^2 < 1\)
\(=> a^2-1 < 0\)
\(=> (a+1)(a-1) < 0\)
\(=> -1 < a < 1\)
Condition 1) is sufficient, since it is equivalent to the question.
Condition 2)
\(\frac{1}{(1-a^2)} > 0\)
\(=> (1-a^2) > 0\)
\(=> a^2-1 < 0\)
\(=> (a+1)(a-1) < 0\)
\(=> -1 < a < 1\)
Thus, condition 2) is sufficient, since it is also equivalent to the question.
Therefore, the answer is D.
Answer: D
FYI: Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.
17 Feb 2019, 18:34
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MathRevolution
=>
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.
\(\frac{a^{n^2+n-1}}{a^{(n-1)(n+2)}}\)=\(\frac{a^{n^2+n-1}}{a^{n^2+n-2}}= a^{n^2+n-1-n^2-n+2} =a^2-1 =a.\)
Asking for the value of \(\frac{a^{n^2+n-1}}{a^{(n-1)(n+2)}}\) is equivalent to asking for the value of a. Thus, condition 2) is sufficient, but condition 1) is not sufficient as it gives us no information about the value of a.
Therefore, the answer is B.
Answer: B
