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

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

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05 Sep 2013, 11:17
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Difficulty:

65% (hard)

Question Stats:

63% (02:17) correct 38% (02:28) wrong based on 138 sessions

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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.

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Joined: 14 Aug 2013
Posts: 34
Location: United States
Concentration: Finance, Strategy
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Re: If b=a+4, then for which of the folloing  [#permalink]

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05 Sep 2013, 11:39
2
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!
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Joined: 02 Sep 2009
Posts: 52344
Re: If b=a+4, then for which of the folloing  [#permalink]

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05 Sep 2013, 11:47
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
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Re: If b=a+4, then for which of the folloing  [#permalink]

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07 Sep 2013, 05:33
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
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Posts: 52344
Re: If b=a+4, then for which of the folloing  [#permalink]

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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 $$x=a+2$$ --> $$(x-a)^2 + (x-a-4)^2=(a+2-a)^2 + (a+2-a-4)^2=8$$.

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

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05 Apr 2018, 00:31
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).

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Re: If b=a+4, then for which of the folloing &nbs [#permalink] 05 Apr 2018, 00:31
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