Last visit was: 06 Apr 2025, 06:11 It is currently 06 Apr 2025, 06:11
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

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

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

Track
Your Progress

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

Practice
Pays

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
PREVIOUS TOPIC
NEXT TOPIC

Both x and y are positive integers.

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 31474
Own Kudos [?]: 37667 [6]
Given Kudos: 26234
Send PM
Both x and y are positive integers. [#permalink] New post   09 Apr 2019, 02:16
1
Expert Reply
5
Bookmarks
00:00

Question Stats:

77% (01:51) correct 22% (02:07) wrong based on 88 sessions

Hide Show timer Statistics

Both x and y are positive integers. If \(x^2 + 2xy + y^2 = 49\) and x\(^2 −   y^2 = − 7\), then \(y =  \)

A. 2

B. 3

C. 4

D. 5

E. 7
ShowHide Answer
Official Answer
C
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12345 [2]
Given Kudos: 136
Send PM

Top Member of the Month
Re: Both x and y are positive integers. [#permalink] New post   09 Apr 2019, 06:26
2
Carcass wrote:
Both x and y are positive integers. If \(x^2 + 2xy + y^2 = 49\) and x\(^2 −   y^2 = − 7\), then \(y =  \)

A. 2

B. 3

C. 4

D. 5

E. 7


GIVEN: x² + 2xy + y² = 49
Factor to get: (x + y)² = 49

So, EITHER x + y = 7 OR x + y = -7
Since we're told that x and y are POSITIVE, we can be certain that x + y = 7


GIVEN: x² - y² = −7
Factor to get: (x + y)(x - y) = -7
Replace x + y with 7 to get: (7)(x - y) = -7
So, we know that x - y = -1

We now have two linear equations:
x + y = 7
x - y = -1

Subtract the BOTTOM equation from the TOP equation to get: 2y = 8
Solve: y = 8/2 = 4

Answer: C

Cheers,
Brent
User avatar
bumpbot
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 5228
Own Kudos [?]: 77 [0]
Given Kudos: 0
Send PM
Re: Both x and y are positive integers. [#permalink] New post   22 Dec 2024, 11:28
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Prep Club for GRE Bot
gmatclubot
Re: Both x and y are positive integers. [#permalink]
22 Dec 2024, 11:28
Moderators:
adewale223
GRE Instructor
108 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1131 posts
VibhuAnurag
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact