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07 May 2020, 01:00
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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)!
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[GMAT math practice question]
\((x, y)\) satisfies \(|3x - 2y + 4| + |-x + 2y - 2| = 0\). What is \(2x - y\)?
A. \(\frac{1}{3} \)
B. \(\frac{-5}{2} \)
C. \(1\)
D. \(\frac{-4}{3}\)
E. \(\frac{5}{3}\)
\((x, y)\) satisfies \(|3x - 2y + 4| + |-x + 2y - 2| = 0\). What is \(2x - y\)?
A. \(\frac{1}{3} \)
B. \(\frac{-5}{2} \)
C. \(1\)
D. \(\frac{-4}{3}\)
E. \(\frac{5}{3}\)
10 May 2020, 18:59
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Both \(|3x - 2y + 4|\) and \(|-x + 2y - 2|\) are greater than or equal to \(0\) and the sum of them is \(0\), so both of them are \(0.\)
Then we have \(3x - 2y + 4 = 0\) and \(-x + 2y - 2 = 0.\)
Adding the \(2\) equations together gives us:
\(3x – 2y + 4 – x + 2y – 2 = 0 + 0\)
\(2x + 2 = 0\)
\(2x = -2\)
\(x = -1\)
Then \(3x – 2y + 4 = 0\) becomes:
\(3(-1) – 2y + 4 = 0\)
\(-2y + 1 = 0\)
\(-2y = -1\)
\(= \frac{1}{2}\)
We have \(x = -1, y = ½.\)
Thus, we have \(2x - y = 2(-1) – ½ = -2 – ½ = -5/2.\)
Therefore, B is the answer.
Answer: B
Both \(|3x - 2y + 4|\) and \(|-x + 2y - 2|\) are greater than or equal to \(0\) and the sum of them is \(0\), so both of them are \(0.\)
Then we have \(3x - 2y + 4 = 0\) and \(-x + 2y - 2 = 0.\)
Adding the \(2\) equations together gives us:
\(3x – 2y + 4 – x + 2y – 2 = 0 + 0\)
\(2x + 2 = 0\)
\(2x = -2\)
\(x = -1\)
Then \(3x – 2y + 4 = 0\) becomes:
\(3(-1) – 2y + 4 = 0\)
\(-2y + 1 = 0\)
\(-2y = -1\)
\(= \frac{1}{2}\)
We have \(x = -1, y = ½.\)
Thus, we have \(2x - y = 2(-1) – ½ = -2 – ½ = -5/2.\)
Therefore, B is the answer.
Answer: B
yashikaaggarwal
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07 May 2020, 04:44
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Modulus is either positive or negative or both positive or both negative.
|3x-2y+4|+|-x+2y-2|=0
Put the equation like.
|3x-2y+4|=-|-x+2y-2|
Now opening module you have to solve only two cases.
Because both positive sides or both negative sides will give same solution.
And one positive and one negative will give same solution irrespective of sides.
|3x-2y+4|=-|-x+2y-2| ------(1)
|3x-2y+4|= |-x+2y-2| ------(2)
Equation 1 will give X=-1 ----(3)
Equation two will give 2x-2y+3=0 -----(4)
Put value of 3 in 4
We will get y=1/2 -----(5)
Now putting value in 2x-y from 3&5
2(-1)-(1/2)= -5/2
Hence answer is option B
Posted from my mobile device
|3x-2y+4|+|-x+2y-2|=0
Put the equation like.
|3x-2y+4|=-|-x+2y-2|
Now opening module you have to solve only two cases.
Because both positive sides or both negative sides will give same solution.
And one positive and one negative will give same solution irrespective of sides.
|3x-2y+4|=-|-x+2y-2| ------(1)
|3x-2y+4|= |-x+2y-2| ------(2)
Equation 1 will give X=-1 ----(3)
Equation two will give 2x-2y+3=0 -----(4)
Put value of 3 in 4
We will get y=1/2 -----(5)
Now putting value in 2x-y from 3&5
2(-1)-(1/2)= -5/2
Hence answer is option B
Posted from my mobile device
