Last visit was: 30 Dec 2024, 12:05 It is currently 30 Dec 2024, 12:05
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

x is any non-negative integer

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30557
Own Kudos [?]: 36906 [1]
Given Kudos: 26108
Send PM
x is any non-negative integer [#permalink] New post   27 Jan 2021, 06:14
Expert Reply
1
Bookmarks
00:00

Question Stats:

50% (00:45) correct 50% (00:33) wrong based on 12 sessions

Hide Show timer Statistics

x is any non-negative integer

Quantity A
Quantity B
The minimum value of \(4x^2+1\)
The minimum value of \(5x^2+1\)



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.

Kudos for the right answer and explanation
ShowHide Answer
Official Answer
C
Most Helpful Community Reply
User avatar
D
KarunMendiratta
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Own Kudos [?]: 3277 [1]
Given Kudos: 172
Location: India
WE:Education (Education)
Send PM
Re: x is any non-negative integer [#permalink] New post   30 May 2021, 00:28
1
Carcass wrote:
x is any non-negative integer

Quantity A
Quantity B
The minimum value of \(4x^2+1\)
The minimum value of \(5x^2+1\)



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.

Kudos for the right answer and explanation


Both the equations given here are Quadratic Functions (Parabola)

The minimum value i.e. the y-value (only when a > 0) of a Parabola occurs at it's vertex

x-coordinate of the vertex = \(\frac{-b}{2a}\), which is same for both the equations

\(4x^2 + 0x + 1\)
x-coordinate of the vertex = \(\frac{-0}{8} = 0\)

\(5x^2 + 0x + 1\)
x-coordinate of the vertex = \(\frac{-0}{10} = 0\)

Now, on plugging the x-coordinates back into the equation, we have same y-coordinates as 1

Col. A: 1
Col. B: 1

Hence, option C

You can also try to draw the graph of both the functions and notice that they have same vertex!
Attachments

Parabolas.png
Parabolas.png [ 92.12 KiB | Viewed 2104 times ]

General Discussion
User avatar
D
rx10
Retired Moderator
Joined: 02 Dec 2020
Posts: 1831
Own Kudos [?]: 2149 [2]
Given Kudos: 140
GRE 1: Q168 V157

GRE 2: Q167 V161
Send PM
Re: x is any non-negative integer [#permalink] New post   27 Jan 2021, 07:32
2
x is a non-negative, so \(x>=0\)

We need min value so we will take x = 0

Qt A = Qt B = 1

Answer C
avatar
S
COolguy101
Senior Manager
Senior Manager
Joined: 23 Jan 2021
Posts: 294
Own Kudos [?]: 172 [1]
Given Kudos: 81
Concentration: , International Business
Send PM
Re: x is any non-negative integer [#permalink] New post   29 May 2021, 18:36
1
Carcass wrote:
x is any non-negative integer

Quantity A
Quantity B
The minimum value of \(4x^2+1\)
The minimum value of \(5x^2+1\)



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.

Kudos for the right answer and explanation


In Quantity A , \(4x^2 + 1 \) and similarly in \(5x^2 + 1\) Quantity B



subtracting 1 from both sides,
\(4x^2 \) in Quantity A and \(5x^2\) in Quantity B


since, \(x^2 \)is always positive, hence , we can safely divide by it.
then 4 remain in quantity A and 5 remain Quantity B.

Hence, quantity B is greater..
Carcass sir, please add OA for this particular question.
Prep Club for GRE Bot
gmatclubot
Re: x is any non-negative integer [#permalink]
29 May 2021, 18:36
Moderators:
adewale223
GRE Instructor
88 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1116 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