December 20, 2018 December 20, 2018 10:00 PM PST 11:00 PM PST This is the most inexpensive and attractive price in the market. Get the course now! December 22, 2018 December 22, 2018 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51280

Question Stats:
79% (00:35) correct 21% (00:46) wrong based on 157 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 51280

Re M0103
[#permalink]
Show Tags
15 Sep 2014, 23:14
Official Solution:If \(x\) is a positive number and \(\frac{1}{2}*\sqrt{x} = 2x\), what is the value of \(x\)?A. \(0\) B. \(\frac{1}{16}\) C. \(\frac{1}{4}\) D. \(\frac{1}{2}\) E. \(1\) Backsolve. Plug answer (C) into the equation for \(x\): \(\frac{1}{2}*\frac{1}{2} = 2*\frac{1}{4}\). Solve both sides of the equation: \(\frac{1}{4} \neq \frac{1}{2}\). Continue plugging in the answers. Plugging answer (B) into the equation for \(x\) gives: \(\frac{1}{2}*\frac{1}{4} = 2*\frac{1}{16}\)or \(\frac{1}{8} = \frac{1}{8}.\) Another option is to solve the equation for \(x\). \(\frac{1}{2}*\sqrt{x} = 2x\). Since \(x\) is a positive number, i.e., \(x \gt 0\), square both sides of equation to get: \(\frac{1}{4} * x = 4x^2\) Multiply both sides by 4: \(x = 16x^2\) \(16x^2  x = 0\) \(x(16x1) = 0\) The roots of this equation are \(x = 0\) and \(x = \frac{1}{16}\). Since \(x \gt 0\), the correct answer is \(x = \frac{1}{16}\). Answer: B
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Status: Pursuit of Happiness
Joined: 10 Sep 2016
Posts: 30
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 590 Q44 V27 GMAT 2: 690 Q50 V34
GPA: 3.94

Re: M0103
[#permalink]
Show Tags
16 Oct 2016, 17:59
I understand why Choice B is a solution, but I don't understand why 0  Choice A  is not..  Need Kudos
_________________
If you find this post hepful, please press +1 Kudos



Math Expert
Joined: 02 Sep 2009
Posts: 51280

Re: M0103
[#permalink]
Show Tags
16 Oct 2016, 21:40



Intern
Status: Pursuit of Happiness
Joined: 10 Sep 2016
Posts: 30
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 590 Q44 V27 GMAT 2: 690 Q50 V34
GPA: 3.94

Re: M0103
[#permalink]
Show Tags
17 Oct 2016, 06:47
Bunuel wrote: moulayabdesslam wrote: I understand why Choice B is a solution, but I don't understand why 0  Choice A  is not..
 Need Kudos The stem says that x is a positive number and 0 is neither positive nor negative. Thanks! That's funny how one can miss such obvious information.  Need Kudos
_________________
If you find this post hepful, please press +1 Kudos



Intern
Joined: 26 Dec 2016
Posts: 20

Re: M0103
[#permalink]
Show Tags
26 Jan 2017, 03:22
BunuelI think there is a little Typo: Backsolve. Plug answer (C) into the equation for \(x\): \(\frac{1}{2}*\frac{1}{2} = 2*\frac{1}{2}\). If you plugin answer (C) it should be "Backsolve. Plug answer (C) into the equation for \(x\): \(\frac{1}{2}*\frac{1}{2} = 2*\frac{1}{ 4}\)."



Math Expert
Joined: 02 Sep 2009
Posts: 51280

Re: M0103
[#permalink]
Show Tags
26 Jan 2017, 05:49



Intern
Joined: 20 Aug 2017
Posts: 38
Location: United States (FL)
GPA: 3.4

Re: M0103
[#permalink]
Show Tags
26 Aug 2017, 16:07
Instead of going from 1/4∗x=4x^2 and multiplying both sides by 4 and solving for roots, why not simply divide both sides by x, since you know x is positive?
You would then get 1/4 = 4x, then x = 1/16.



Math Expert
Joined: 02 Sep 2009
Posts: 51280

Re: M0103
[#permalink]
Show Tags
27 Aug 2017, 03:03



Intern
Joined: 05 Oct 2013
Posts: 8

Re: M0103
[#permalink]
Show Tags
21 Sep 2017, 11:31
I am a little confused as to which one is the correct answer.
Is it now 1/4 or 1/16 ?
a) If you move 1/2 to RHS, square both sides and solve for x, then we would get 1/4. b) Instead, if we square both LHS and RHS as they are, then the answer would be 1/16.
Can you please clarify? Thanks.



Math Expert
Joined: 02 Sep 2009
Posts: 51280

Re: M0103
[#permalink]
Show Tags
21 Sep 2017, 11:35



Intern
Joined: 05 Oct 2013
Posts: 8

Re: M0103
[#permalink]
Show Tags
21 Sep 2017, 12:04
Sorry, I made a rookie mistake. I missed squaring 4 when squaring both sides of the equation and ended up with 1/4. 1/16 is correct, like you mentioned



Intern
Joined: 16 Mar 2007
Posts: 1

Re: M0103
[#permalink]
Show Tags
07 Jul 2018, 17:04
what about the negatives?



Math Expert
Joined: 02 Sep 2009
Posts: 51280

Re: M0103
[#permalink]
Show Tags
07 Jul 2018, 23:56










