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GMAT Inequalities is a high-frequency topic in GMAT Quant, but many students struggle because the concepts behave differently from standard algebra. Understanding the right rules, patterns, and edge cases can significantly improve both speed and accuracy.- May 06
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17 Oct 2020, 12:23
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
74% (00:56) correct
26%
(00:51)
wrong
based on 104
sessions
History
Date
Time
Result
Not Attempted Yet
17 Oct 2020, 14:31
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Factoring, Statement 1 tells us (x-1)(x-3) = 0, so x can be 1 or 3. Statement 2 tells us (x-1)^2 = 0, so x can only equal 1, and Statement 2 is sufficient, so the answer is B.
18 Oct 2020, 02:16
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Forget the conventional way to solve DS questions.
We will solve this DS question using the variable approach.
DS question with 1 variable: Let the original condition in a DS question contain 1 variable. Now, 1 variable would generally require 1 equation for us to be able to solve for the value of the variable.
We know that each condition would usually give us an equation, and Since we need 1 equation to match the numbers of variables and equations in the original condition, the logical answer is D.
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' .
Second and the third step of Variable Approach: 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.
Let’s take look at each condition separately.
Condition(1) tells us that \(x^2 - 4x + 3 = 0 \).
=> \(x^2 - 4x + 3 = 0 \) :
=> (x - 1)(x - 3) = 0
=> x = 1 or 3
Since the answer is not unique , Condition(1) alone is not sufficient by CMT 2.
Condition(2) tells us that \(x^2 - 2x + 1 = 0\).
=> \(x^2 - 2x + 1 = 0\) = \((x -1)^2 = 0\)
=> x = 1
Since the answer is unique , Condition(2) alone is sufficient by CMT 2.
Condition(2) alone is sufficient.
So, B is the correct answer.
Answer: B
We will solve this DS question using the variable approach.
DS question with 1 variable: Let the original condition in a DS question contain 1 variable. Now, 1 variable would generally require 1 equation for us to be able to solve for the value of the variable.
We know that each condition would usually give us an equation, and Since we need 1 equation to match the numbers of variables and equations in the original condition, the logical answer is D.
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' .
Second and the third step of Variable Approach: 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.
Let’s take look at each condition separately.
Condition(1) tells us that \(x^2 - 4x + 3 = 0 \).
=> \(x^2 - 4x + 3 = 0 \) :
=> (x - 1)(x - 3) = 0
=> x = 1 or 3
Since the answer is not unique , Condition(1) alone is not sufficient by CMT 2.
Condition(2) tells us that \(x^2 - 2x + 1 = 0\).
=> \(x^2 - 2x + 1 = 0\) = \((x -1)^2 = 0\)
=> x = 1
Since the answer is unique , Condition(2) alone is sufficient by CMT 2.
Condition(2) alone is sufficient.
So, B is the correct answer.
Answer: B
