Question: What is the y- intercept of the graph of the equation y = 2|4x – 4| - 10?

1. -2
2. \(-\frac{1}{4}\)
3. 0
4. 2
5. \(\frac{1}{9}\)

Solution and Explanation

Approach Solution (1):

This question can be solved as:
y = 2|4x – 4| - 10
y = 2|0 – 4| - 10
y = 2|-4| - 10
y = 2(4) – 10
y = 8 – 10
y = -2

Correct option: A

Approach Solution (2):

Part of the question includes |4x – 4|, which is the absolute value of 4x – 4
This can either be (4x – 4) or –(4x – 4) which is (-4x + 4)
Plugging in these two different options into the original equation, I get two different answers:

y = 2(-4x + 4) – 10
y = -8x + 8 – 10
y = -8x – 2
y- Intercept here would be equal to b in the y = mx + b equation, so the answer would be -2.
y = 2(4x – 4) – 10
y = 8x – 8 – 10
y = -18

The y- intercept here would be -18.

Since only -2 is given in the option

Correct option: A

Approach Solution (3):

Take: y = 2|4x – 4| - 10
Plug in x = 0 to get: y = 2|4(0) – 4| - 10
Simplify: y = 2|0 – 4| - 10
Simplify: y = 2|-4| - 10
Simplify: y = 2(4) – 10 = 8 – 10 = -2
So, the point (0, -2) is a point on the graph of y = 2|4x – 4| - 10
So, the y-intercept is -2

Correct option: A

“What is the y- intercept of the graph of the equation y = 2|4x – 4| - 10?”- 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.

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