December 10, 2018 December 10, 2018 10:00 PM PST 11:00 PM PST Practice the one most important Quant section  Integer properties, and rapidly improve your skills. December 11, 2018 December 11, 2018 09:00 PM EST 10:00 PM EST Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51071

Question Stats:
59% (01:39) correct 41% (01:40) wrong based on 225 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 51071

Re M1918
[#permalink]
Show Tags
16 Sep 2014, 00:06



Retired Moderator
Status: I Declare War!!!
Joined: 02 Apr 2014
Posts: 237
Location: United States
Concentration: Finance, Economics
GMAT Date: 03182015
WE: Asset Management (Investment Banking)

Re: M1918
[#permalink]
Show Tags
24 Jul 2016, 17:10
Bunuel wrote: Official Solution:
If \(b=a+4\), then for which of the following values of \(x\) is the expression \((xa)^2 + (xb)^2\) the smallest?
A. \(a1\) B. \(a\) C. \(a + 2\) D. \(a + 3\) E. \(a + 5\)
Since \(b=a+4\) then \((xa)^2 + (xb)^2=(xa)^2 + (xa4)^2\). Now, plug each option for \(x\) to see which gives the least value. The least value of the expression is for \(x=a+2\): \((xa)^2 + (xa4)^2=(a+2a)^2 + (a+2a4)^2=8\).
Answer: C hi please throw some light how you picked the least value for x as a2? any pattern or logic via looking at answer choices? thanks



Intern
Joined: 27 Jul 2016
Posts: 8
Location: India
GPA: 3.15

Re: M1918
[#permalink]
Show Tags
27 Jul 2016, 22:07
There's a simple trick for guys who are having a problem with finding the maximum or the minimum value question(and it saves a lot of time)
differentiate the equation and then equate to zero. the values of X will be either maximun or minimum value. to determine whether its max or min put any number for x(i prefer 0). Dont worry about point of inflexion as it wont be asked in GMAT. For simple differentiation rules look up google. Its pretty simple.



Intern
Joined: 17 May 2016
Posts: 29

Re: M1918
[#permalink]
Show Tags
02 Aug 2016, 00:46
ABHISHEK8998 wrote: There's a simple trick for guys who are having a problem with finding the maximum or the minimum value question(and it saves a lot of time)
differentiate the equation and then equate to zero. the values of X will be either maximun or minimum value. to determine whether its max or min put any number for x(i prefer 0). Dont worry about point of inflexion as it wont be asked in GMAT. For simple differentiation rules look up google. Its pretty simple. Abshishek, thank you for the tip, could you please detail your solution ? Many thanks in advance, Best regards,



Intern
Joined: 23 Apr 2016
Posts: 22
Location: Finland
Concentration: General Management, International Business
GPA: 3.65

Re: M1918
[#permalink]
Show Tags
14 Oct 2016, 09:28
nickimonckomif you diffrentiate (xa)^2 + (xb)^2, you get 2(xa)+2(xb) Now if you equate this with 0 2(xa)+2(xb) = 0 gives you x = (a+b)/2, if you plug b = a+4, you get x = a+2



Intern
Joined: 23 Jun 2016
Posts: 14

Re: M1918
[#permalink]
Show Tags
17 Dec 2016, 04:37
nickimonckom wrote: ABHISHEK8998 wrote: There's a simple trick for guys who are having a problem with finding the maximum or the minimum value question(and it saves a lot of time)
differentiate the equation and then equate to zero. the values of X will be either maximun or minimum value. to determine whether its max or min put any number for x(i prefer 0). Dont worry about point of inflexion as it wont be asked in GMAT. For simple differentiation rules look up google. Its pretty simple. Abshishek, thank you for the tip, could you please detail your solution ? Many thanks in advance, Best regards, Your strategy helps. Could you please specify how to determine whether it is min value or max value in more detail. Thanks is advance.



Senior CR Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1376
Location: Viet Nam

Re: M1918
[#permalink]
Show Tags
17 Dec 2016, 10:08
Bunuel wrote: If \(b=a+4\), then for which of the following values of \(x\) is the expression \((xa)^2 + (xb)^2\) the smallest?
A. \(a1\) B. \(a\) C. \(a + 2\) D. \(a + 3\) E. \(a + 5\) We could use AMGM inequality to solve this easily. \((xa)^2+(xb)^2=(xa)^2+(bx)^2 \geq \frac{1}{2}[(xa)+(bx)]^2=\frac{1}{2}(ba)^2=\frac{4^2}{2}=8\) \(min((xa)^2+(xb)^2)=8 \iff xa=bx \iff x=\frac{a+b}{2}=a+2\) The answer is C
_________________
Actual LSAT CR bank by Broall
How to solve quadratic equations  Factor quadratic equations Factor table with sign: The useful tool to solve polynomial inequalities Applying AMGM inequality into finding extreme/absolute value
New Error Log with Timer



Intern
Joined: 15 Jan 2014
Posts: 34
Location: India
Concentration: Technology, Strategy
GPA: 2.5
WE: Information Technology (Consulting)

Re: M1918
[#permalink]
Show Tags
17 Feb 2017, 17:49
Another way of doing this question : We can use this property : \((AB)^2 = A^2+B^22AB\) \(A = (x−a)^2\) ; \(B = (x−b)^2\) \((xax+b)^2 = (x−a)^2 + (x−b)^2 2(xa)(xb)\) ==> \((ba)^2 +2(xa)(xb) = (x−a)^2 + (x−b)^2\) Given ba = 4 ; \(16 +2(xa)(xb) = (x−a)^2 + (x−b)^2\) \(16 +2(xa)(xa4) = (x−a)^2 + (x−b)^2\) . Now we need to minimize this expression .So wil try to minimize value for \(2(xa)(xa4)\) to 0 or negative . \(x = a\) will make this value 0 and this will give 16 ; \(x=a+2\) will make above expression ve and will give the value less than 16 hence our answer. Also, notice that next value of \(x=a+3\) will make \(2(xa)(xa4)\) +ve and hence will make overall value bigger. Please +1 kudos if this post helps



Manager
Joined: 31 Jan 2017
Posts: 58
Location: India
Concentration: Strategy, Leadership
GPA: 4
WE: Project Management (Energy and Utilities)

Re: M1918
[#permalink]
Show Tags
27 Feb 2017, 08:41
Answer: C Expression= (x−a)^2+(x−b)^2 = 2x^2  2ax 2bx +a^2 + b^2 For extreme values of expression, d/dx(expression) =0 Differentiating, d/dx(expression) = 4x 2a 2b = 0 or, 4x= 2a+2b = 4a+8 [putting values of b=a+4] Therefore, x= a+2 It can be ascertained that this extreme value is minimum as d^2/dx^2(expression) = 4 (positive) Note: Differentiation is not tested on the GMAT, but following little information helps 1. d/dx(constant) = 0 2. d/dx(x^n) = n * x^(n1) 3. d/dx(c*x) = c ; where c = constant 4. Expression has extreme values at d/dx(expression)=0 ; d2/dx^2(expression) = positive signifies minimum value ; d2/dx^2(expression) = negative signifies maximum value
_________________
__________________________________ Kindly press "+1 Kudos" if the post helped



Intern
Joined: 18 Jul 2015
Posts: 18
WE: Analyst (Consumer Products)

We can also pick numbers to solve this problem. Below is the approach I used: Let's take \(a = 1\), hence \(b\) will be 5 (\(b = a + 4\)). Now substitute the value of \(a\) in each of the answer options to get the value of \(x\).
Equation: \((xa)^2 + (xb)^2\)
A) \(a1\), \(x=0\), substitute in the above equation; result will be \(26\) B) \(a\), \(x=1\), \(16\) C) \(a+2\), \(x=3\), 8  Smallest Value (Correct Ans.) D) \(a+3\), \(x=4\), \(10\) E) \(a+5\), \(x=6\), \(26\)



Intern
Joined: 20 Jul 2018
Posts: 2

Re: M1918
[#permalink]
Show Tags
20 Jul 2018, 13:50
(xa)^2 is a standard parabola moved to the right by a. (x(a+4))^2 is a standard parabola moved to the right by a + 4.
the total formula is the sum of these two parabolas, which is smallest in the middle between the two minima a and a + 4.



Manager
Joined: 01 Feb 2017
Posts: 170

Re: M1918
[#permalink]
Show Tags
28 Jul 2018, 14:03
Plug in: Assume a=2 APS, b=6 Expression: (x2)^2+(x6)^2 Expanding: 2(x^2+208x)
A) a1=1, expression value:2*13 B) a=2, expression value:2*8 C) a+2=4, expression value:2*4 D) a+3=5, expression value:2*5 E) a+5=7, expression value:2*13
Min value: Choice C
Posted from my mobile device



Intern
Joined: 10 Jul 2018
Posts: 4
GMAT 1: 600 Q47 V26 GMAT 2: 630 Q48 V28

Re: M1918
[#permalink]
Show Tags
31 Jul 2018, 16:42
If you draw a graph, you'll find out that the midpoint from a and a+4 will be where the x is lowest...
_________________
Official GMAT 1  600 v26 q47 Official GMAT 2  630 v27 q48 MCAT 1  610 v28 q47 MCAT 2  630 v29 q48 MCAT 3  680 v35 q48 MCAT 4  640 v33 q45 MCAT 5  660 v34 q46 MCAT 6  640 v31 q47 Veritas CAT 1  690 v34 q51 Official CAT 2  720 v37 q50 Official CAT 4  690 v32 q50 Official CAT 6  700 v34 q50 Veritas CAT 2  680 v34 q49



Intern
Joined: 08 Dec 2017
Posts: 2
Location: India
Concentration: Marketing, Strategy
GPA: 3.9
WE: Marketing (Education)

Re M1918
[#permalink]
Show Tags
13 Sep 2018, 08:32
I think this is a highquality question and I agree with explanation. Assume a = 0 (x)2+(x−4)2
1  10 0  16 2  8 3  10 5  26
So the answer is option C










