Which of the following equations is NOT equivalent to

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swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Thu Sep 27, 2018 10:11 am

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$$\text{Which of the following equations is NOT equivalent to } 4x^2=y^2-9?$$
$$\text{A. } 4x^2+9=y^2$$
$$\text{B. } 4x^2-y^2=-9$$
$$\text{C. } 4x^2=(y+3)(y-3)$$
$$\text{D. } 2x=y-3$$
$$\text{E. } x^2=\frac{y^2-9}{4}$$
The OA is D.
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Source: Beat The GMAT — Problem Solving | Thu Sep 27, 2018 10:11 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Thu Sep 27, 2018 10:36 pm

swerve wrote:$$\text{Which of the following equations is NOT equivalent to } 4x^2=y^2-9?$$
$$\text{A. } 4x^2+9=y^2$$
$$\text{B. } 4x^2-y^2=-9$$
$$\text{C. } 4x^2=(y+3)(y-3)$$
$$\text{D. } 2x=y-3$$
$$\text{E. } x^2=\frac{y^2-9}{4}$$
The OA is D.
Source: GMAT Prep

The correct answer is option D: 2x = y – 3

Let's see how:

4x^2 = y^2 – 9

Taking the square root, we get

√(4x^2) = √(y^2 – 9)

2x = √[(y + 3)(y – 3)]

Note that √(y^2 – 9) ≠ y – 3.

The correct answer: D

Hope this helps!

-Jay
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Sep 28, 2018 3:19 am

swerve wrote:$$\text{Which of the following equations is NOT equivalent to } 4x^2=y^2-9?$$
$$\text{A. } 4x^2+9=y^2$$
$$\text{B. } 4x^2-y^2=-9$$
$$\text{C. } 4x^2=(y+3)(y-3)$$
$$\text{D. } 2x=y-3$$
$$\text{E. } x^2=\frac{y^2-9}{4}$$

If we plug y=-3 into 4x² = y²-9, we get:
4x² = (-3)² - 9
4x² = 0
x = 0.

Test x=0 and y=-3 in the answer choices.
When the question stem includes the phrase which of the following, the correct answer is likely to be D or E.
D: 2x = y-3
Plugging in x=0 and y=-3, we get:
2*0 = -3-3
0 = -6
Doesn't work.
Thus, D is NOT equivalent to the given equation.

The correct answer is D.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Oct 02, 2018 6:56 pm

swerve wrote:$$\text{Which of the following equations is NOT equivalent to } 4x^2=y^2-9?$$
$$\text{A. } 4x^2+9=y^2$$
$$\text{B. } 4x^2-y^2=-9$$
$$\text{C. } 4x^2=(y+3)(y-3)$$
$$\text{D. } 2x=y-3$$
$$\text{E. } x^2=\frac{y^2-9}{4}$$
The OA is D.
Source: GMAT Prep

Looking at our answer choices, we see that 2x = y - 3 is not equivalent to the given equation. If we were to square both sides of answer choice D, we’d have:

4x^2 = (y - 3)^2 or 4x^2 = y^2 - 6y + 9, which is not equivalent to 4x^2 = y^2 - 9.

Answer: D

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