Last visit was: 23 Apr 2024, 10:45 It is currently 23 Apr 2024, 10:45
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 integers. Which of the following expression

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 28620
Own Kudos [?]: 33099 [1]
Given Kudos: 25172
Send PM
Both x and y are integers. Which of the following expression [#permalink] New post   30 Jul 2020, 13:37
Expert Reply
1
Bookmarks
00:00

Question Stats:

63% (01:29) correct 36% (01:21) wrong based on 69 sessions

Hide Show timer Statistics

Both x and y are integers. Which of the following expressions must be the square of an integer?

Indicate all such expressions.


A. \((x+y)(x-y)+8xy+17y^2\)

B. \(9x^4-12x^2y^2+4y^4\)

C. \(x^6+2x^3y^3+y^6\)
ShowHide Answer
Official Answer
A,B,C
User avatar
rishabhrbs96
Manager
Manager
Joined: 02 May 2020
Posts: 91
Own Kudos [?]: 138 [0]
Given Kudos: 0
Send PM
Re: Both x and y are integers. Which of the following expression [#permalink] New post   31 Jul 2020, 10:00
2
How come A is correct. If we take x=1 and y=1, expression A will be 8 which is not square of any integer.

B is correct because we can factorize it as (3x^2 - 2y^2)^2

C is correct because we can factorize it as (x^3 + y^3)^2

So, the answers should be B and C.
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 28620
Own Kudos [?]: 33099 [0]
Given Kudos: 25172
Send PM
Re: Both x and y are integers. Which of the following expression [#permalink] New post   03 Aug 2020, 10:40
Expert Reply
Fixed the typo in the first answer choice.

Thanks for your patient.

Regards
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 11679 [2]
Given Kudos: 136
Send PM

Top Member of the Month
Re: Both x and y are integers. Which of the following expression [#permalink] New post   03 Aug 2020, 15:32
2
Carcass wrote:
Both x and y are integers. Which of the following expressions must be the square of an integer?

Indicate all such expressions.


A. \((x+y)(x-y)+8xy+17y^2\)

B. \(9x^4-12x^2y^2+4y^4\)

C. \(x^6+2x^3y^3+y^6\)


A. Given: \((x+y)(x-y)+8xy+17y^2\)
Expand and simplify the first product: \(x^2-y^2+8xy+17y^2\)
Simplify: \(x^2+8xy+16y^2\)
Factor: \((x + 4y)(x + 4y) = (x + 4y)^2\)
WORKS!


B. Given: \(9x^4-12x^2y^2+4y^4\)
Factor to get: \((3x^2-2y^2)(3x^2-2y^2) = (3x^2-2y^2)^2\)
WORKS!


C. Given: \(x^6+2x^3y^3+y^6\)
Factor to get: \((x^3+y^3)(x^3+y^3) = (x^3+y^3)^2\)[/quote]
WORKS!

Answer: A, B, C

Cheers,
Brent
User avatar
S
pprakash786
Manager
Manager
Joined: 20 Jun 2019
Posts: 181
Own Kudos [?]: 220 [0]
Given Kudos: 41
GRE 1: Q160 V161

GRE 2: Q165 V159
Send PM
Re: Both x and y are integers. Which of the following expression [#permalink] New post   05 Aug 2020, 23:34
rishabhrbs96 wrote:
How come A is correct. If we take x=1 and y=1, expression A will be 8 which is not square of any integer.

B is correct because we can factorize it as (3x^2 - 2y^2)^2

C is correct because we can factorize it as (x^3 + y^3)^2

So, the answers should be B and C.


By your own analogy for A ((x+y)(x−y)+8xy+17y^2) becomes 2*0=0+8*1*1=8+17=25, which is 5^2.

Thanks!
User avatar
bumpbot
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 4411
Own Kudos [?]: 68 [0]
Given Kudos: 0
Send PM
Re: Both x and y are integers. Which of the following expression [#permalink] New post   21 Jan 2024, 13:18
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
[#permalink]
Moderators:
BrushMyQuant
Moderator
1085 posts
VibhuAnurag
GRE Instructor
218 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