Solution: To save time and improve accuracy on DS question in GMAT, learn, and apply 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.
Forget the conventional way to solve DS questions.
We will solve this DS question using the variable approach.
Remember the relation between the Variable Approach, and Common Mistake Types 3 and 4 (A and B)[Watch lessons on our website to master these approaches and tips]
Step 1: Apply Variable Approach (VA)
Step II: After applying VA, if C is the answer, check whether the question is key questions.
Step III: If the question is not a key question, choose C as the probable answer, but if the question is a key question, apply CMT 3 and 4 (A or B).
Step IV: If CMT3 or 4 (A or B) is applied, choose either A, B, or D.
Let's apply CMT (2), which says there should be only one answer for the condition to be sufficient. Also, this is an integer question and, therefore, we will have to apply CMT 3 and 4 (A or B).
To master the Variable Approach, visit
https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.
Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]
Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.
We have to find the value of ‘x’ - where 'x' and 'y' are integers
Second and the third step of Variable Approach: From the original condition, we have 2 variables (x and y). To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 1 equation each, C would most likely be the answer.
Let’s look at both conditions together.
They tells us that \(3^x\ +\ 5^y\ =\ 134\) and y = 3, from which we get \(3^x\ +\ 5^3\ =\ 134\) = 134.
=> 3x + 125 = 134
=> 3x = 134 - 125 = 9 = \(3^2\)
=> x = 3.
The answer is unique, so the conditions combines are sufficient according to Common Mistake Type 2 which states that the answer should be a unique value.
But we know that this is a key question [Integer question] and if we get an easy C as an answer, we will choose A or B.
Let’s take a look at each condition.
Condition (1) tells us that \(3^x\ +\ 5^y\ =\ 134\) .
=> If y = 1: 3x + 5 = 134
=> 3x = 129
However, 129 cannot be expressed as an exponent of 3 => y ≠ 1
=> If y = 3: 3x + 125 = 134
=> 3x = 9
=> x = 3
Thus, there is only one solution: x = 3
The answer is unique and condition (1) alone is sufficient according to Common Mistake Type 2 which states that the answer should be a unique value.
Condition(2) tells us that y = 3.
=> But x is unknown.
The answer is not a unique value therefore condition (2) alone is not sufficient according to Common Mistake Type 2 which states that the answer should be a unique value.
If the question has both C and A as its answer, then A is the answer rather than C according to the definition of DS questions.
Condition (1) alone is sufficient.
Therefore, A is the correct answer.
Answer: A
