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[GMAT math practice question]
If \(n\) is a positive integer, is \(n\) a prime number?
1) \(n\) is the least factor of \(77\) greater than \(1\)
2) \(n\) has exactly two factors
If \(n\) is a positive integer, is \(n\) a prime number?
1) \(n\) is the least factor of \(77\) greater than \(1\)
2) \(n\) has exactly two factors
Updated on: 04 Aug 2021, 02:51
Originally posted by MathRevolution on 10 Mar 2019, 18:18.
Last edited by MathRevolution on 04 Aug 2021, 02:51, edited 1 time in total.
Last edited by MathRevolution on 04 Aug 2021, 02:51, 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.
If data are symmetric, then the average and the median of the data are the same.
Condition 1):
If \(y\) is the mean of \(x, y\) and \(z\), then \(x, y, z\) are symmetric. To see this note that \(\frac{( x + y + z )}{3} = y\) implies that \(y = \frac{( x + z )}{2}\). So, \(2y = x + z\) and \(y – x = z – y,\) which means that \(x, y, z\) are symmetric.
Condition 1) is sufficient.
Condition 2):
\(z = 2y – x\) is equivalent to \(y – x = z – y\), which is equivalent to condition 1).
Condition 2) is sufficient.
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.
Therefore, D is the answer.
Answer: D
Updated on: 04 Aug 2021, 02:52
Originally posted by MathRevolution on 10 Mar 2019, 18:20.
Last edited by MathRevolution on 04 Aug 2021, 02:52, edited 1 time in total.
Last edited by MathRevolution on 04 Aug 2021, 02:52, 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.
Since we have \(1\) variable (\(n\)) and \(0\) equations, D is most likely to be the answer. So, we should consider each condition on its own first.
Condition 1)
The factors of \(77\) are \(1, 7, 11\) and \(77\). We have \(n = 7\) since the least factor of \(77\) other than \(1\) is \(7\).
Condition 1) is sufficient.
Condition 2)
\(n\) is a prime number, by definition, since it has exactly two factors.
Condition 2) is sufficient.
Therefore, D is the answer.
Answer: D
If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
