GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 31 May 2020, 06:25

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Which of the following is NOT equivalent to 49a^2 = 9b^2 - 4?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 64249
Which of the following is NOT equivalent to 49a^2 = 9b^2 - 4?  [#permalink]

### Show Tags

13 Nov 2014, 08:47
00:00

Difficulty:

5% (low)

Question Stats:

90% (00:58) correct 10% (01:06) wrong based on 135 sessions

### HideShow timer Statistics

Tough and Tricky questions: Algebra.

Which of the following is NOT equivalent to $$49a^2 = 9b^2 - 4$$?

A. $$49a^2 + 4 = 9b^2$$
B. $$98a^2 = 18b^2 - 8$$
C. $$49a^2 = (3b - 2)(3b + 2)$$
D. $$a^2 = \frac{9b^2 - 4}{7^2}$$
E. $$7a = 3b - 2$$

Kudos for a correct solution.

_________________
Manager
Joined: 10 Sep 2014
Posts: 96
Re: Which of the following is NOT equivalent to 49a^2 = 9b^2 - 4?  [#permalink]

### Show Tags

13 Nov 2014, 09:10
I chose to put everything on one side of the equal sign.

49a^2 - 9b^2 - 4 = 0

Answer A: move everything to one side to get 49^2 - 9b^2 - 4 = 0, not equivalent

Manager
Joined: 21 Jul 2014
Posts: 117
Re: Which of the following is NOT equivalent to 49a^2 = 9b^2 - 4?  [#permalink]

### Show Tags

13 Nov 2014, 09:13
1
Bunuel wrote:

Tough and Tricky questions: Algebra.

Which of the following is NOT equivalent to $$49a^2 = 9b^2 - 4$$?

A. $$49a^2 + 4 = 9b^2$$
B. $$98a^2 = 18b^2 - 8$$
C. $$49a^2 = (3b - 2)(3b + 2)$$
D. $$a^2 = \frac{9b^2 - 4}{7^2}$$
E. $$7a = 3b - 2$$

Kudos for a correct solution.

I tried to look for the common traps people face when they simplify equations. My attention went to choice E.

The reason is because it tries to simplify by square root-ing the equation, but the square root of $$9b^2 - 4$$ does not equal $$3b - 2$$. It factors to $$(3b+2)(3b-2)$$.

Therefore I know it is not equivalent to the equation in the question stem.

If I really wanted to validate that the other choices are in fact wrong, most of them require very simple algebraic operations to prove which can be done without pen and paper even.

A) Just add +4 to both sides.
B) Multiply both sides by 2.
C) Factor the right side of the equation. (This is what answer choice E tries to trap with.)
D) Divide both sides by 49,
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1708
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Which of the following is NOT equivalent to 49a^2 = 9b^2 - 4?  [#permalink]

### Show Tags

13 Nov 2014, 20:13
3
1

Original Equation

$$49a^2 = 9b^2 - 4$$

Option A, B, C, D are same as the original equation.... adjusting terms of LHS/RHS, multiply by 2 etc...

Option E

Square root the original equation

$$7a = \sqrt{9b^2 - 4} = \sqrt{(3b+2)(3b-2)}$$ .... This only far the equation can go
Intern
Joined: 20 Jan 2013
Posts: 33
Re: Which of the following is NOT equivalent to 49a^2 = 9b^2 - 4?  [#permalink]

### Show Tags

14 Nov 2014, 05:20
1
We just need to adjust equation as per the options and verify.

49a^2 = 9b^2 - 4 => 49a^2 + 4 = 9b^2 ----> Option a

Multiply by 2,
98a^2 = 18b^2 - 8 ----> Option b

49a^2 = 9b^2 - 4 => 49a^2 = (3b + 2)(3b - 2) ---> option c

a^2 = 9b^2 - 4 / 49 => a^2 = 9b^2 - 4 /7^2 ---- > option d

Take square root on both the sides
7a = $$\sqrt{9b^2 - 4}$$ = $$\sqrt{(3b+2)(3b-2)}$$ => This is not equal to 7a = 3b - 2

Math Expert
Joined: 02 Sep 2009
Posts: 64249
Re: Which of the following is NOT equivalent to 49a^2 = 9b^2 - 4?  [#permalink]

### Show Tags

14 Nov 2014, 08:25
Bunuel wrote:

Tough and Tricky questions: Algebra.

Which of the following is NOT equivalent to $$49a^2 = 9b^2 - 4$$?

A. $$49a^2 + 4 = 9b^2$$
B. $$98a^2 = 18b^2 - 8$$
C. $$49a^2 = (3b - 2)(3b + 2)$$
D. $$a^2 = \frac{9b^2 - 4}{7^2}$$
E. $$7a = 3b - 2$$

Kudos for a correct solution.

Official Solution:

Which of the following is NOT equivalent to $$49a^2 = 9b^2 - 4$$?

A. $$49a^2 + 4 = 9b^2$$
B. $$98a^2 = 18b^2 - 8$$
C. $$49a^2 = (3b - 2)(3b + 2)$$
D. $$a^2 = \frac{9b^2 - 4}{7^2}$$
E. $$7a = 3b - 2$$

Four of the answer choices are equivalent to $$49a^2 = 9b^2 - 4$$, and one is not. Equations are said to be equivalent when the equations have the same solution.

In this case, equivalent equations will have the same value for $$a$$ and $$b$$ as in the original equation. Let's compare our equation to each choice.

Choice A: $$49a^2 + 4 = 9b^2$$ is the same as the original equation if 4 is added to both sides. Eliminate A.

Choice B: $$98a^2 = 18b^2 - 8$$ is the same as the original equation if both sides are multiplied by 2. Eliminate B.

Choice C: $$49a^2 = (3b - 2)(3b + 2)$$ correctly factors the original equation. Eliminate C.

Choice D: $$a^2 = \frac{9b^2 - 4}{7^2}$$ is the same as the original equation if both sides are divided by $$7^2$$ or $$49$$. Eliminate D.

Choice E: $$7a = 3b - 2$$ incorrectly calculates the square root of $$9b^{2} - 4$$. The square root of the left side of the equation is correctly calculated. However, the square root of $$9b^{2} - 4$$ isn't $$3b - 2$$. We can verify this by squaring $$3b - 2$$. If we do, we get $$9b^{2} - 12b + 4$$, which is not equivalent to $$9b^{2} - 4$$.

Choice E, which is not equivalent, is thus correct.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 64249
Re: Which of the following is NOT equivalent to 49a^2 = 9b^2 - 4?  [#permalink]

### Show Tags

14 Nov 2014, 08:26
Bunuel wrote:

Tough and Tricky questions: Algebra.

Which of the following is NOT equivalent to $$49a^2 = 9b^2 - 4$$?

A. $$49a^2 + 4 = 9b^2$$
B. $$98a^2 = 18b^2 - 8$$
C. $$49a^2 = (3b - 2)(3b + 2)$$
D. $$a^2 = \frac{9b^2 - 4}{7^2}$$
E. $$7a = 3b - 2$$

Kudos for a correct solution.

Similar question from OG13: which-of-the-following-equations-is-not-equivalent-to-10y-138730.html
_________________
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2800
Re: Which of the following is NOT equivalent to 49a^2 = 9b^2 - 4?  [#permalink]

### Show Tags

29 Sep 2017, 09:21
Bunuel wrote:

Which of the following is NOT equivalent to $$49a^2 = 9b^2 - 4$$?

A. $$49a^2 + 4 = 9b^2$$
B. $$98a^2 = 18b^2 - 8$$
C. $$49a^2 = (3b - 2)(3b + 2)$$
D. $$a^2 = \frac{9b^2 - 4}{7^2}$$
E. $$7a = 3b - 2$$

A. 49a^2 + 4 = 9b^2

If we subtract 4 from both sides of the equation, we have 49a^2 = 9b^2 - 4. This is equivalent.

B. 98a^2 = 18b^2 - 8

If we divide both sides of the equation by 2, we have 49a^2 = 9b^2 - 4. This is equivalent.

C. 49a^2 = (3b - 2)(3b + 2)

If we expand the right-hand side of the equation, we have 49a^2 = 9b^2 - 4. This is equivalent.

D. a^2 = (9b^2 - 4)/7^2

If we divide both sides of the equation by 7^2 = 49, we have 49a^2 = 9b^2 - 4. This is equivalent.

Thus, the correct answer must be E. However, let’s analyze it anyway.

E. 7a = 3b - 2

If we square both sides of the equation, we have (7a)^2 = (3b - 2)^2, or 49a^2 = 9b^2 - 12b + 4, which is not the same is 49a^2 = 9b^2 - 4.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
214 Reviews

5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE

NOW WITH GMAT VERBAL (PRE-BETA)

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: Which of the following is NOT equivalent to 49a^2 = 9b^2 - 4?   [#permalink] 29 Sep 2017, 09:21