If b=a+4, then for which of the folloing : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 19 Jan 2017, 06:10

# LIVE NOW:

Chat with Admission Manager and Current Student of NUS SIngapore - Join Chat Room to Participate.

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If b=a+4, then for which of the folloing

Author Message
TAGS:

### Hide Tags

Manager
Joined: 14 Jun 2011
Posts: 85
Followers: 2

Kudos [?]: 34 [1] , given: 15

If b=a+4, then for which of the folloing [#permalink]

### Show Tags

05 Sep 2013, 11:17
1
KUDOS
1
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

56% (02:44) correct 44% (02:18) wrong based on 80 sessions

### HideShow timer Statistics

If b=a+4, then for which of the following values of x is the expression (x−a)^2+(x−b)^2 the smallest?

A) a−1
B) a
C) a+2
D) a+3
E) a+5

I know that we can solve this question by plugging in the option values. I want to know the smart way to choose which option to plug in first.
[Reveal] Spoiler: OA

_________________

Kudos always encourages me

Intern
Joined: 14 Aug 2013
Posts: 35
Location: United States
Concentration: Finance, Strategy
GMAT Date: 10-31-2013
GPA: 3.2
WE: Consulting (Consumer Electronics)
Followers: 2

Kudos [?]: 74 [2] , given: 4

Re: If b=a+4, then for which of the folloing [#permalink]

### Show Tags

05 Sep 2013, 11:39
2
KUDOS
lets take a= 0 ; then b=4 and the equation becomes x^2+(x-4)^2. The minimum value of this function occurs when
x^2 = (x-4)^2 as both of these functions are increasing functions.

Solving this we get x=2 it is minimum. for a=0 option c is gives the value of x as 2.

hope it helps!
Math Expert
Joined: 02 Sep 2009
Posts: 36554
Followers: 7078

Kudos [?]: 93170 [1] , given: 10553

Re: If b=a+4, then for which of the folloing [#permalink]

### Show Tags

05 Sep 2013, 11:47
1
KUDOS
Expert's post
swati007 wrote:
If b=a+4, then for which of the following values of x is the expression (x−a)^2+(x−b)^2 the smallest?

A) a−1
B) a
C) a+2
D) a+3
E) a+5

I know that we can solve this question by plugging in the option values. I want to know the smart way to choose which option to plug in first.

Discussed here: m19-q18-120286.html
_________________
Manager
Status: Persevering
Joined: 15 May 2013
Posts: 225
Location: India
GMAT Date: 08-02-2013
GPA: 3.7
WE: Consulting (Consulting)
Followers: 1

Kudos [?]: 86 [0], given: 34

Re: If b=a+4, then for which of the folloing [#permalink]

### Show Tags

07 Sep 2013, 05:33
1
This post was
BOOKMARKED
Maxima and minima

Used derivatives here

(x-a)^2+(x-b)^2

First derivative=> 2*(x-a)+2*(x-b) =0 =>x=(a+b)/2 ;substitute b=> x=a+2
_________________

--It's one thing to get defeated, but another to accept it.

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13447
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: If b=a+4, then for which of the folloing [#permalink]

### Show Tags

26 Dec 2014, 06:28
Hello from the GMAT Club BumpBot!

Thanks to another GMAT 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.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 36554
Followers: 7078

Kudos [?]: 93170 [0], given: 10553

Re: If b=a+4, then for which of the folloing [#permalink]

### Show Tags

26 Dec 2014, 06:40
swati007 wrote:
If b=a+4, then for which of the following values of x is the expression (x−a)^2+(x−b)^2 the smallest?

A) a−1
B) a
C) a+2
D) a+3
E) a+5

I know that we can solve this question by plugging in the option values. I want to know the smart way to choose which option to plug in first.

If $$b=a+4$$, then for which of the following values of $$x$$ is the expression $$(x-a)^2 + (x-b)^2$$ the smallest?

A. $$a-1$$
B. $$a$$
C. $$a+2$$
D. $$a+3$$
E. $$a+5$$

Since $$b=a+4$$ then $$(x-a)^2 + (x-b)^2=(x-a)^2 + (x-a-4)^2$$. Now, plug each option for $$x$$ to see which gives the least value.

The least value of the expression if for $$x=a+2$$ --> $$(x-a)^2 + (x-a-4)^2=(a+2-a)^2 + (a+2-a-4)^2=8$$.

_________________
Re: If b=a+4, then for which of the folloing   [#permalink] 26 Dec 2014, 06:40
Similar topics Replies Last post
Similar
Topics:
3 The factorial expression 13!/7! is not divisible by which of the follo 5 02 Jun 2016, 03:46
2 Considering the positions on the number line above, which of the follo 4 16 May 2016, 01:34
8 An even and an odd integer are multiplied together. Which of the follo 10 17 Apr 2015, 03:48
10 If k is an integer and k^2 - 4 > 45, then which of the follo 6 28 Sep 2013, 02:42
2 For the numbers on the number line above, which of the follo 3 10 Feb 2013, 00:43
Display posts from previous: Sort by