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18 Oct 2021, 10:13
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D
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Difficulty:
25%
(medium)
Question Stats:
74% (01:12) correct
26%
(01:01)
wrong
based on 73
sessions
History
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Time
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What is the value of \(x\)?
(1) \(4(2x - 1.5y) - 3(1.5x - 2y) = -4.235\)
(2) \(3(2y - 1.5x) - 4(1.5y - 2x) = -4.235\)
(1) \(4(2x - 1.5y) - 3(1.5x - 2y) = -4.235\)
(2) \(3(2y - 1.5x) - 4(1.5y - 2x) = -4.235\)
18 Oct 2021, 11:28
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What is the value of \(x\)?
(1) \(4(2x - 1.5y) - 3(1.5x - 2y) = -4.235\)
Can we eliminate y.
\(4(2x - 1.5y) - 3(1.5x - 2y) = -4.235\)
\(4*2x - 4*1.5y- 3*1.5x +3* 2y= -4.235\)
y gets eliminated, so we will be able to get value of x.
Sufficient
(2) \(3(2y - 1.5x) - 4(1.5y - 2x) = -4.235\) Can we eliminate y.
\(3(2y - 1.5x) - 4(1.5y - 2x) = -4.235\)
\(4*2x - 4*1.5y- 3*1.5x +3* 2y= -4.235\)
y gets eliminated, so we will be able to get value of x.
Sufficient
D
(1) \(4(2x - 1.5y) - 3(1.5x - 2y) = -4.235\)
Can we eliminate y.
\(4(2x - 1.5y) - 3(1.5x - 2y) = -4.235\)
\(4*2x - 4*1.5y- 3*1.5x +3* 2y= -4.235\)
y gets eliminated, so we will be able to get value of x.
Sufficient
(2) \(3(2y - 1.5x) - 4(1.5y - 2x) = -4.235\) Can we eliminate y.
\(3(2y - 1.5x) - 4(1.5y - 2x) = -4.235\)
\(4*2x - 4*1.5y- 3*1.5x +3* 2y= -4.235\)
y gets eliminated, so we will be able to get value of x.
Sufficient
D
18 Oct 2021, 11:35
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BrentGMATPrepNow
I created this question to highlight a common misconception about linear equations.
Many students will look at the first equation and conclude that, since the equation has two variables, there's no way to determine the value of x.
However, if you simplify the first equation, you'll find that there's only one variable.
The same applies to the second equation.
Target question: What is the value of \(x\)?
Statement 1: \(4(2x - 1.5y) - 3(1.5x - 2y) = -4.235\)
Expand to get: \(8x-6y - 4.5x + 6y = -4.235\)
Simplify: \(3.5x = -4.235\)
At this point, we can see that \(x = \frac{-4.235}{3.5}\), which means statement 1 is sufficient.
Aside: On test day, we'd never waste valuable time actually calculating\(\frac{-4.235}{3.5}\).
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: \(3(2y - 1.5x) - 4(1.5y - 2x) = -4.235\)
Expand to get: \(6y - 4.5x - 6y + 8x = -4.235\)
Simplify: \(3.5x = -4.235\)
This equation is identical to the simplified equation in statement 1.
So, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
