Question: Which of the following lines are parallel to line x = 4 – 2y?

1. y = 2x + 4
2. y = - 2x - 4
3. \(\frac{x}{2}-y=4\)
4. \(y+\frac{x}{2}=4\)
5. \(2y=2-\frac{1}{2}x\)

“How many five digit numbers can be formed using the digits 0, 1, 2, 3, 4, and 5 which are divisible by 3, without repeating the digits?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

Approach Solution 1

Rewrite x = 4 – 2y as y = \(2-\frac{1}{2}x\) , so the slope if this line is – \(\frac{1}{2}\). Now, since the parallel lines have the same slope then a line parallel to the given line must also have the same slope.

From the above options, we can see that option D best satisfies this as:

\(y+\frac{x}{2}=4\) is the same as \(y=4-\frac{1}{2}x\)

Correct option: D

Approach Solution 2

Two lines are parallel if they have same slope.

Slope of the line:

x = 4 – 2y

4 – x = 2y

2 + ( \(-\frac{1}{2}x\)) = y

Comparing it with y = mx + c gives us m (slope) as \(-\frac{1}{2}\)

A quick scan through the options will make you realise C or D are likely choices. Once you solve D is the right answer with slope as \(-\frac{1}{2}\)

Correct option: D

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