If AC = BC and CD = DE Then, in Terms of x, the Value of y is GMAT Problem Solving

Question: If AC = BC and CD = DE then, in terms of x, the value of y is

Note: Figure not drawn to scale

1. x
2. 180 - 2x
3. 90 - 2x
4. 4x - 180
5. 45 + x/4

“If AC = BC and CD = DE then, in terms of x, the value of y is”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide”. 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:
This question can be solved by only one approach
When we add the given information to the diagram we get:

In an isosceles triangle, the angles opposite the equal sides are always equal.

This means ∠A = x°

Also, since the angles in a triangle must add to 180°, we know that ∠ACB = 180 - 2x

The angles in the other triangle are a little trickier, so, let's label them k to get the following diagram:

Since the angles in a triangle must add to 180°, we can write: k + k + y = 180

Simplify: 2k + y = 180

Subtract y from both sides: 2k = 180 - y

Divide both sides by 2 to get: : k = (180 - y)/2

So, we can add this information to our diagram:

Finally, since opposite angles are equal, we can write the following equation: 180 - 2x = k = (180 - y)/2 [we need to solve this equation for y]

Multiply both sides of the equation by 2 to get: 360 - 4x = 180 - y

Subtract 180 from both sides of the equation to get: 180 - 4x = -y

Multiply both sides of the equation by -1 to get: -180 + 4x = y, which can be rearranged as follows: y = 4x - 180

Correct Answer: D

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