On the Graph above, When x = 1/2, y = 2; and when x = 1, y = 1 GMAT Problem Solving

Question:

On the graph above, when x = 1/2, y = 2; and when x = 1, y = 1. The graph is symmetric with respect to the vertical line at x = 2. According to the graph, when x = 3, y =

(A) -1
(B) -½
(C) 0
(D) ½
(E) 1

“On the graph above, when x = 1/2, y = 2; and when x = 1, y = 1. ” - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “The Official Guide for GMAT Review 2017 With Online Question”. 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.

Solution and Explanation

Approach Solution 1:

A mirror image of the other side makes up half of the entire graph. The graph indicates that (2,0) is the center coordinate. As a result, y at x=1 and y at x=3 are equal.

Correct Answer: E

Approach Solution 2:

The graph's symmetry along the vertical axis of x = 2 is revealed to be symmetric. Furthermore, we are informed that y = 1 when x = 1. When x is 3, the value of y must be determined. Remember that the distance between the line x = 2 and x = 3 are both one unit when x = 1 and x = 3, respectively.

When x is 1, the y-coordinate is 1. Therefore, when x is 3, the y-coordinate is ALSO 1. Once more, this is due to the graph's symmetry with respect to the line at x = 2.

Observing that the point (1,1) is actually being reflected over the line x = 2 is another way to approach this issue.

The line x = 2 is exactly one unit away from the point (1,1), as can be seen. The point (2,1) is actually on the line x = 2, exactly 1 unit from (1,1). By symmetry, however, the point that is precisely 1 unit to the right of (2,1) is (1,1) because it is exactly 1 unit to the LEFT of (2,1). (3,1). The y-coordinate is therefore 1.

Correct Answer: E

Approach Solution 3:

The parabola's graph, according to what is said, is symmetrical with respect to the vertical line at x = 2. Consider the fact that the point (0,3) is on the parabola as an example. This location lies two units to the left of the symmetry line.

 

A point 2 units to the right of the line of symmetry must therefore also exist. the location's coordinates are as follows: (4,3)

 

We are also informed that point (1,1) is on the parabola.
This location is one unit to the left of the symmetry line.

 

The point 1 unit to the right of the line of symmetry must therefore also exist.
The location's coordinates are as follows: (3,1)

Correct Answer: E

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