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25 Mar 2022, 04:15
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
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Question Stats:
89% (01:22) correct
11%
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What is the smallest value of x for which \((\frac{12}{x} + 36)(4 - x^2) = 0\) ?
A. -3
B. -2
C. -1/2
D. -1/4
E. 2
A. -3
B. -2
C. -1/2
D. -1/4
E. 2
25 Mar 2022, 06:21
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One of the factors on the left side will need to be equal to zero. If 4 - x^2 = 0, then x^2 = 4 and x = 2 or x = -2. If 12/x + 36 = 0, then, dividing by 12, 1/x + 3 = 0, so 1/x = -3 and x = -1/3. Of the three possible values of x, -2 is the smallest.
25 Mar 2022, 06:54
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Bunuel
What is the smallest value of x for which \((\frac{12}{x} + 36)(4 - x^2) = 0\) ?
A. -3
B. -2
C. -1/2
D. -1/4
E. 2
A. -3
B. -2
C. -1/2
D. -1/4
E. 2
STRATEGY: Upon reading any GMAT Problem Solving question, we should always ask, Can I use the answer choices to my advantage?
In this case, we can easily test the answer choices, starting from the smallest answer choice.
Now let's give ourselves up to 20 seconds to identify a faster approach.
In this case, we can also solve the equation.
I think solving the equation will be faster, so.....
Given: \((\frac{12}{x} + 36)(4 - x^2) = 0\)
Factor the difference of squares: \((\frac{12}{x} + 36)(2 + x)(2 - x) = 0\)
So \(\frac{12}{x} + 36 = 0\), \(2 + x = 0\), or \(2 - x = 0\).
At this point, we can use the answer choices to our advantage.
Since we're looking for the smallest possible solution, let's see if answer choice A (\(x = -3\)), the smallest option, is a solution to any of our three equations. It isn't.
Next, we can see that answer choice B (\(x = -2\)) is a solution to the equation \(2 + x = 0\)
So the correct answer must be B
