NEW HERE? LEARN MORE
closeclose
Last visit was: 06 May 2024, 22:08 It is currently 06 May 2024, 22:08
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

A function is defined for all positive numbers x as f(x) = ax^(1/2) +

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93060
Own Kudos [?]: 621755 [5]
Given Kudos: 81767
Send PM
CAT Tests Forum Quiz Mode
A function is defined for all positive numbers x as f(x) = ax^(1/2) + [#permalink] New post   17 Apr 2019, 00:42
5
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

81% (02:00) correct 19% (02:27) wrong based on 151 sessions
Hide Show timer Statistics
A function is defined for all positive numbers x as \(f(x) = a\sqrt{x} + b\). What is the value of f(3), if f(4) – f(1) = 2 and f(4) + f(1) = 10?


(A) 1

(B) 2

(C) \(2 \sqrt{3}\)

(D) \(2 \sqrt{3} + 2\)

(E) \(2 \sqrt{3} – 2\)
ShowHide Answer
Official Answer
D
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8026
Own Kudos [?]: 4115 [0]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User
A function is defined for all positive numbers x as f(x) = ax^(1/2) + [#permalink] New post   Updated on: 17 Apr 2019, 02:41
Bunuel wrote:
A function is defined for all positive numbers x as \(f(x) = a\sqrt{x} + b\). What is the value of f(3), if f(4) – f(1) = 2 and f(4) + f(1) = 10?

(A) 1
(B) 2
(C) 2 3
(D) 2 3 + 2
(E) 2 3 – 2


solve for expressions
we get a=2and b =2
so for f(3) = 2√3+ 2
IMO D

Originally posted by Archit3110 on 17 Apr 2019, 02:16.
Last edited by Archit3110 on 17 Apr 2019, 02:41, edited 1 time in total.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93060
Own Kudos [?]: 621755 [0]
Given Kudos: 81767
Send PM
CAT Tests Forum Quiz Mode
Re: A function is defined for all positive numbers x as f(x) = ax^(1/2) + [#permalink] New post   17 Apr 2019, 02:26
Expert Reply
Archit3110 wrote:
Bunuel wrote:
A function is defined for all positive numbers x as \(f(x) = a\sqrt{x} + b\). What is the value of f(3), if f(4) – f(1) = 2 and f(4) + f(1) = 10?

(A) 1
(B) 2
(C) 2 3
(D) 2 3 + 2
(E) 2 3 – 2


solve for expressions
we get a=1/2 and b =4
so for f(3) = √3/2+ 4

Bunuel ; answer options are not clear.. :|


_________________
Fixed that. Thank you.
User avatar
L
NandishSS
Director
Director
Joined: 06 Jan 2015
Posts: 737
Own Kudos [?]: 1586 [1]
Given Kudos: 579
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE:Information Technology (Computer Software)
Send PM
Re: A function is defined for all positive numbers x as f(x) = ax^(1/2) + [#permalink] New post   17 Apr 2019, 02:48
1
Kudos
Bunuel wrote:
A function is defined for all positive numbers x as \(f(x) = a\sqrt{x} + b\). What is the value of f(3), if f(4) – f(1) = 2 and f(4) + f(1) = 10?


(A) 1

(B) 2

(C) \(2 \sqrt{3}\)

(D) \(2 \sqrt{3} + 2\)

(E) \(2 \sqrt{3} – 2\)


f(4) – f(1) = 2 ==> \(a\sqrt{4} + b\) - \(a\sqrt{1} - b\) ==> 2a - a =2 ==> a=2

f(4) + f(1) = 10 ==> \(a\sqrt{4} + b\) + \(a\sqrt{1} + b\) ==> 6+2b =10 ==> b=2

Hence D

f(3) = \(2 \sqrt{3} + 2\)
avatar
enricosanchez
Intern
Intern
Joined: 28 Apr 2020
Posts: 4
Own Kudos [?]: 0 [0]
Given Kudos: 43
Send PM
Re: A function is defined for all positive numbers x as f(x) = ax^(1/2) + [#permalink] New post   01 May 2020, 04:13
How does \(a\sqrt{4} + b\) + \(a\sqrt{1} + b\) ==> 6+2b =10??

NandishSS wrote:
Bunuel wrote:
A function is defined for all positive numbers x as \(f(x) = a\sqrt{x} + b\). What is the value of f(3), if f(4) – f(1) = 2 and f(4) + f(1) = 10?


(A) 1

(B) 2

(C) \(2 \sqrt{3}\)

(D) \(2 \sqrt{3} + 2\)

(E) \(2 \sqrt{3} – 2\)


f(4) – f(1) = 2 ==> \(a\sqrt{4} + b\) - \(a\sqrt{1} - b\) ==> 2a - a =2 ==> a=2

f(4) + f(1) = 10 ==> \(a\sqrt{4} + b\) + \(a\sqrt{1} + b\) ==> 6+2b =10 ==> b=2

Hence D

f(3) = \(2 \sqrt{3} + 2\)
avatar
B
kaylaquijas
Intern
Intern
Joined: 05 Mar 2021
Posts: 20
Own Kudos [?]: 1 [0]
Given Kudos: 18
Send PM
Re: A function is defined for all positive numbers x as f(x) = ax^(1/2) + [#permalink] New post   21 Oct 2021, 06:55
Bunuel wrote:
A function is defined for all positive numbers x as \(f(x) = a\sqrt{x} + b\). What is the value of f(3), if f(4) – f(1) = 2 and f(4) + f(1) = 10?


(A) 1

(B) 2

(C) \(2 \sqrt{3}\)

(D) \(2 \sqrt{3} + 2\)

(E) \(2 \sqrt{3} – 2\)


Bunuel,

Why doesn't it work algebraically to add the two functions together?

f(4)-f(1)=2
+
f(4)+f(1)=10
-------------------

f(1) cancels out, leaving (2)*f(4) = 12, which reduces to f(4) = 6. When subbing 6 into the second equation, then f(1) = 4.

So I ended up with f(3) = 6([square_root]3) +4

Did I fall into some sort of trap by trying to solve it this way? I need to understand why this doesn't work so I don't do it again in the future.
GMAT Club Bot
gmatclubot
Re: A function is defined for all positive numbers x as f(x) = ax^(1/2) + [#permalink]
21 Oct 2021, 06:55
Moderators:
Bunuel
Math Expert
93060 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions