[Math Revolution GMAT math practice question]
If (|x|-2)(x-1)=0, then x=?
$$1)\ x>0$$
$$2)\ -1\le x\le1$$
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If (|x|-2)(x-1)=0, then x=?
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Max@Math Revolution
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Target question: What is the value of x?Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
If (|x| - 2)(x - 1) = 0, then x = ?
$$1)\ x>0$$
$$2)\ -1\le x\le1$$
Given: (|x| - 2)(x - 1) = 0
This tells us that EITHER: |x| - 2 OR x - 1 = 0
If |x| - 2 = 0, then x = 2 OR x = -2
If x - 1 = 0, then x = 1
So, there are 3 possible values of x:
i. x = 2
ii. x = -2
iii. x = 1
Statement 1: x > 0
When we examine the 3 possible values of x, we see that two values are greater than 0
It COULD be the case that x = 2, or it COULD be the case that x = 1,
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: -1 ≤ x ≤ 1
When we examine the 3 possible values of x, we see that only one value satisfies statement 2 (x = 1)
So, it MUST be the case that x = 1
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Max@Math Revolution
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=>
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.
Original condition:
(|x|-2)(x-1)=0
=> |x| = 2 or x = 1
=> x = 2, x = -2 or x = 1
Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.
Condition 1)
By condition 1) (x > 0), the possible solutions are x = 1 and x = 2.
Since we don't have a unique solution, condition 1) is not sufficient.
Condition 2)
By condition 2) (-1 ≤ x ≤ 1), the only possible solution is x = 1.
Since we have a unique solution, condition 2) is sufficient.
Therefore, B is the answer.
Answer: B
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.
Original condition:
(|x|-2)(x-1)=0
=> |x| = 2 or x = 1
=> x = 2, x = -2 or x = 1
Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.
Condition 1)
By condition 1) (x > 0), the possible solutions are x = 1 and x = 2.
Since we don't have a unique solution, condition 1) is not sufficient.
Condition 2)
By condition 2) (-1 ≤ x ≤ 1), the only possible solution is x = 1.
Since we have a unique solution, condition 2) is sufficient.
Therefore, B is the answer.
Answer: B
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[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
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