GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
(x – 2y)(x + 2y) = 5 (2x – y)(2x + y) = 35
[#permalink]
07 Apr 2019, 07:33
07 Apr 2019, 07:33
1
Expert Reply
5
Bookmarks
00:00
Question Stats:
81% (01:49) correct
18% (02:28) wrong based on 75 sessions
Hide Show timer Statistics
\((x – 2y)(x + 2y) = 5\)
\((2x – y)(2x + y) = 35\)
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
\((2x – y)(2x + y) = 35\)
Quantity A |
Quantity B |
\(2x^2 - y^2\) |
\(x^2 - 2y^2\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: (x – 2y)(x + 2y) = 5 (2x – y)(2x + y) = 35
[#permalink]
07 Apr 2019, 07:47
07 Apr 2019, 07:47
2
Carcass wrote:
\((x – 2y)(x + 2y) = 5\)
\((2x – y)(2x + y) = 35\)
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
\((2x – y)(2x + y) = 35\)
Quantity A |
Quantity B |
\(2x^2 - y^2\) |
\(x^2 - 2y^2\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
GIVEN:
(x – 2y)(x + 2y) = 5
(2x – y)(2x + y) = 35
Expand and simplify each equation to get:
x² - 4y² = 5
4x² - y² = 35
ADD the two equations to get: 5x² - 5y² = 40
Divide both sides by 5 to get: x² - y² = 8
Rewrite each quantity as follows:
QUANTITY A: x² + x² - y²
QUANTITY B: x² - y² - y²
Add some brackets for clarity:
QUANTITY A: x² + (x² - y²)
QUANTITY B: (x² - y²) - y²
Replace x² - y² with 8 to get:
QUANTITY A: x² + 8
QUANTITY B: 8 - y²
Subtract 8 from both quantities to get:
QUANTITY A: x²
QUANTITY B: -y²
Since x and y cannot both equal 0, we know that x² is POSITIVE, and -y² is NEGATIVE
So, Quantity A must be greater.
Answer: A
Cheers,
Brent
Re: (x 2y)(x + 2y) = 5 (2x y)(2x + y) = 35
[#permalink]
04 Aug 2022, 10:26
04 Aug 2022, 10:26
1
My solution was to solve both the given equations by elimination,
End up with
\(x^2 = 7\)
\(y^2 = \frac{1}{2}\)
Quantity A = 13.5
Quantity B = 7 - <something positive>
So, the answer is A
End up with
\(x^2 = 7\)
\(y^2 = \frac{1}{2}\)
Quantity A = 13.5
Quantity B = 7 - <something positive>
So, the answer is A
