Solution: To save time and improve accuracy on DS question in GMAT, learn, and apply a Variable Approach.
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.
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https://www.mathrevolution.com/gmat/lesson for details.
Now we will solve this DS question using the Variable Approach.
Let’s apply the 3 steps suggested previously.
Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.
We have to find the value of the positive integer ‘x’.
Follow the second and the third step: From the original condition, we have 1 variable (x). To match the number of variables with the number of equations, we need 1 equation. Since conditions (1) and (2) will provide 1 equation each, D would most likely be the answer.
Recall 3- Principles and Choose D as the most likely answer. Let’s look at each condition separately. We should remember that the remainder questions are solved by the direct substitution
Condition (1) tells us that when x divided by 3, the remainder is 2.
=> If x = 5, then the remainder will be ‘2’ when ‘5’ is divided by ‘3’
=> But if x = 17, then the remainder will be ‘2’ when ‘17’ is divided by ‘2’
The answer is not unique, and condition (1) alone is not sufficient according to Common Mistake Type 2 which states that the number of answers must be only one.
Condition (2) tells us that when \(x^2\) divided by 3, the remainder is 1
=> If x = 5, then remainder will be ‘1’ when ‘\(x^2\) = \(5^2\) = 25’ is divided by ‘3’
=> But if x = 17, then remainder will be ‘1’ when \(x^2\) = \(17^2\) = 289’ is divided by ‘3’
The answer is not unique, and condition (2) alone is not sufficient according to Common Mistake Type 2 which states that the number of answers must be only one.
Let’s look at both conditions combined together.
=> If x = 5, then the remainder will be ‘2’ when ‘5’ is divided by ‘3’ and the remainder will be ‘1’ when ‘\(x^2\) = \(5^2\) = 25’ is divided by ‘3’
=> But if x = 17, then the remainder will be ‘2’ when ‘17’ is divided by ‘2’ and the remainder will be ‘1’ when ‘\(x^2\) = \(17^2\) = 289’ is divided by ‘3’
The answer is not unique, both conditions (1) and (2) combined are not sufficient according to Common Mistake Type 2 which states that the number of answers must be only one.
Both conditions together are not sufficient.
Therefore, E is the correct answer.
Answer: E
