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Updated on: 05 Jan 2023, 12:34
Originally posted by BrentGMATPrepNow on 05 Jan 2023, 11:11.
Last edited by BrentGMATPrepNow on 05 Jan 2023, 12:34, edited 1 time in total.
Last edited by BrentGMATPrepNow on 05 Jan 2023, 12:34, edited 1 time in total.
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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:
75%
(hard)
Question Stats:
40% (01:36) correct
60%
(01:41)
wrong
based on 60
sessions
History
Date
Time
Result
Not Attempted Yet
What is the value of x?
(1) \(x^2-10x=24\)
(2) \(\frac{4x}{x^2-2x}=\frac{2}{5}\)
(1) \(x^2-10x=24\)
(2) \(\frac{4x}{x^2-2x}=\frac{2}{5}\)
05 Jan 2023, 11:36
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BrentGMATPrepNow
Statement 1
\(x^2-10x=24\)
\(x^2-10x-24=0\)
\(x^2-12x+2x-24=0\)
\((x+2)(x-12)=0\)
Therefore x can be either -2 or x can be 12.
As we are getting two possible values of x, the statement is not sufficient.
Statement 2
\(\frac{4x}{x^2-2x}=\frac{2}{5}\)
\(20x = 2(x^2-2x)\)
Dividing by 2 on both sides of the equation
\(10x = x^2 - 2x\)
\(x^2 - 12x = 0\)
\(x(x-12) = 0\)
x = 0 or x = 12
Note: at x = 0, the value of denominator, \(x^2-2x\), becomes 0.
Hence x = 0 is not a valid value.
x = 12
This statement is sufficient.
Option B
16 Jan 2023, 15:45
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BrentGMATPrepNow
Target question: What is the value of x?
Statement 1: x² - 10x = 24
Since we have a quadratic equation here, let's set it equal to zero by subtracting 24 from both sides of the equation.
When we do this we get: x² - 10x - 24 = 0
Factor: (x - 12)(x + 2) = 0
So, EITHER x = 12 OR x = -2
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 4x/(x² - 2x) = 2/5
Cross multiply to get: (2)(x² - 2x) = (4x)(5)
Simplify: 2x² - 4x = 20x
Subtract 20x from both sides: 2x² - 24x = 0
Factor: 2x(x - 12) = 0
At this point, it certainly LOOKS like EITHER x = 0 OR x = 12. However, we must consider the fact that, in the original equation we have a rational expression in which x appears in both the numerator and denominator.
Now notice what happens if we plug x = 0 into the original equation.
We get: 4(0)/(0² - 2(0)) = 2/5, and upon simplification we get: 0/0 = 2/5, which is definitely not true.
In other words, x = 0 is NOT a solution to the original equation, which means x = 12 is the only possible solution.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
