It is currently 16 Dec 2017, 11:01

Close

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
Your Progress

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

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

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If g(x)= x^2 – 4bx + 9b^2, where b is any positive integer, then

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

2 KUDOS received
PS Forum Moderator
avatar
P
Joined: 25 Feb 2013
Posts: 625

Kudos [?]: 312 [2], given: 39

Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
If g(x)= x^2 – 4bx + 9b^2, where b is any positive integer, then [#permalink]

Show Tags

New post 17 Sep 2017, 07:04
2
This post received
KUDOS
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

47% (01:29) correct 53% (01:50) wrong based on 97 sessions

HideShow timer Statistics

If \(g(x) = x^2 – 4bx + 9b^2\), where \(b\) is any positive integer, then which of the following must be true

A.) \(g(x) < -b\)

B.) \(g(x) < 0\)

C.) \(0 < g(x) < 4b\)

D.) \(g(x) ≥ 4b\)

E.) \(g(x) ≥ 5b^2\)
[Reveal] Spoiler: OA

Last edited by niks18 on 18 Sep 2017, 08:25, edited 1 time in total.

Kudos [?]: 312 [2], given: 39

1 KUDOS received
Manager
Manager
avatar
S
Joined: 22 Apr 2017
Posts: 76

Kudos [?]: 30 [1], given: 59

Location: India
Schools: MBS '20 (S)
GPA: 3.7
GMAT ToolKit User
Re: If g(x)= x^2 – 4bx + 9b^2, where b is any positive integer, then [#permalink]

Show Tags

New post 18 Sep 2017, 08:32
1
This post received
KUDOS
niks18 wrote:
If \(g(x) = x^2 – 4bx + 9b^2\), where \(b\) is any positive integer, then which of the following must be true

A.) \(g(x) < -b\)

B.) \(g(x) < 0\)

C.) \(0 < g(x) < 4b\)

D.) \(g(x) ≥ 4b\)

E.) \(g(x) ≥ 5b^2\)





g(x)= x^2-4bx+9b^2--> (x-2b)^2+5b^2.
Since b is a positive integer, value of g(x) will always be greater than 5b^2 as (x-2b)^2 will alwz be positive.
Hence for min value of b i.e 1, g(x)=5b^2.
Hence E. g(x)>=5b^2

Kudos [?]: 30 [1], given: 59

1 KUDOS received
PS Forum Moderator
avatar
P
Joined: 25 Feb 2013
Posts: 625

Kudos [?]: 312 [1], given: 39

Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: If g(x)= x^2 – 4bx + 9b^2, where b is any positive integer, then [#permalink]

Show Tags

New post 18 Sep 2017, 10:11
1
This post received
KUDOS
1
This post was
BOOKMARKED
niks18 wrote:
If \(g(x) = x^2 – 4bx + 9b^2\), where \(b\) is any positive integer, then which of the following must be true

A.) \(g(x) < -b\)

B.) \(g(x) < 0\)

C.) \(0 < g(x) < 4b\)

D.) \(g(x) ≥ 4b\)

E.) \(g(x) ≥ 5b^2\)


OE

\(g(x) = x^2 – 4bx + 4b^2+5b^2\)

or, \(g(x) = (x – 2b)^2+5b^2\),

Now, \((x-2b)^2≥0\), for all values of \(x\). Adding \(5b^2\) to both sides of the inequality we get

\((x-2b)^2+5b^2≥5b^2\)

Or, \(g(x)≥5b^2\)

Option E

Kudos [?]: 312 [1], given: 39

Manager
Manager
avatar
B
Joined: 06 Aug 2017
Posts: 74

Kudos [?]: 15 [0], given: 30

GMAT 1: 610 Q48 V24
Re: If g(x)= x^2 – 4bx + 9b^2, where b is any positive integer, then [#permalink]

Show Tags

New post 23 Sep 2017, 02:27
niks18 wrote:
If \(g(x) = x^2 – 4bx + 9b^2\), where \(b\) is any positive integer, then which of the following must be true

A.) \(g(x) < -b\)

B.) \(g(x) < 0\)

C.) \(0 < g(x) < 4b\)

D.) \(g(x) ≥ 4b\)

E.) \(g(x) ≥ 5b^2\)


Answer is E as follows.

\(g(x) = x^2 – 4bx + 9b^2\)

Since the above is a quadratic equation, its maxima/minima will be at (-)-4d/2 = 2b. Also since b is a +ve integer 2b will be +ve. Hence as per the rule the quadratic equation will have minimum value at x=2b.
Putting the value of 2b back into the equation will yield g(2b) = \((2b)^2\) - 4b*(2b) + 9\(b^2\) = 5\(b^2\)
_________________

-------------------------------------------------------------------------------
Kudos are the only way to tell whether my post is useful.

GMATPREP1: Q47 V36 - 680
Veritas Test 1: Q43 V34 - 630
Veritas Test 2: Q46 V30 - 620

Kudos [?]: 15 [0], given: 30

Re: If g(x)= x^2 – 4bx + 9b^2, where b is any positive integer, then   [#permalink] 23 Sep 2017, 02:27
Display posts from previous: Sort by

If g(x)= x^2 – 4bx + 9b^2, where b is any positive integer, then

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.