GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Oct 2019, 01:20

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

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

Author Message
TAGS:

Hide Tags

Manager
Joined: 14 Jun 2011
Posts: 65
If b=a+4, then for which of the folloing  [#permalink]

Show Tags

05 Sep 2013, 12:17
3
5
00:00

Difficulty:

55% (hard)

Question Stats:

62% (02:15) correct 38% (02:25) wrong based on 195 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.

_________________
Kudos always encourages me
Intern
Joined: 14 Aug 2013
Posts: 31
Location: United States
Concentration: Finance, Strategy
GMAT Date: 10-31-2013
GPA: 3.2
WE: Consulting (Consumer Electronics)
Re: If b=a+4, then for which of the folloing  [#permalink]

Show Tags

05 Sep 2013, 12:39
3
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: 58375
Re: If b=a+4, then for which of the folloing  [#permalink]

Show Tags

05 Sep 2013, 12:47
1
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: 146
Location: India
GMAT Date: 08-02-2013
GPA: 3.7
WE: Consulting (Consulting)
Re: If b=a+4, then for which of the folloing  [#permalink]

Show Tags

07 Sep 2013, 06:33
2
1
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.
Math Expert
Joined: 02 Sep 2009
Posts: 58375
Re: If b=a+4, then for which of the folloing  [#permalink]

Show Tags

26 Dec 2014, 07:40
1
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 $$x=a+2$$ --> $$(x-a)^2 + (x-a-4)^2=(a+2-a)^2 + (a+2-a-4)^2=8$$.

_________________
SVP
Joined: 03 Jun 2019
Posts: 1689
Location: India
Re: If b=a+4, then for which of the folloing  [#permalink]

Show Tags

27 Aug 2019, 10:12
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.

Given: b=a+4

Asked: For which of the following values of x is the expression (x−a)^2+(x−b)^2 the smallest?

(x−a)^2+(x−b)^2 = 2x^2 - 2(a+b)x + a^2 + b^2 = 2{x^2 - (a+b)x + (a+b)^2/4} - (a+b)^2/2 + a^2 + b^2 = 2(x - (a+b)/2))^2 + - (a+b)^2/2 + a^2 + b^2

For the expression to be the smallest
x = (a+b)/2 = (2a +4)/2 = a + 2

IMO C
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
Re: If b=a+4, then for which of the folloing   [#permalink] 27 Aug 2019, 10:12
Display posts from previous: Sort by