Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 17 Jun 2013
Posts: 24

If x is a positive number and a=√x∗x−x, [#permalink]
Show Tags
03 Feb 2014, 05:41
4
This post was BOOKMARKED
Question Stats:
53% (00:46) correct 47% (00:57) wrong based on 217 sessions
HideShow timer Statistics
If x is a positive number and a=√x∗x−x, which of the following must be true? I. a is even II. a is positive III. a is an integer A)I only B)II only C)III only D)I and II E) None of the above
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 44419

Re: If x is a positive number and a=√x∗x−x, [#permalink]
Show Tags
03 Feb 2014, 05:50
gmatgambler wrote: If x is a positive number and a=√x∗x−x, which of the following must be true?
I. a is even
II. a is positive
III. a is an integer
A)I only B)II only C)III only D)I and II E) None of the above If \(x\) is a positive number and \(a=\sqrt{x} * x  x\), which of the following must be true?I. \(a\) is even II. \(a\) is positive III. \(a\) is an integer A. I only B. II only C. III only D. I and II E. None of the above Note that we are asked "which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer. If \(x=\frac{1}{4}\) then \(a=\sqrt{x} * x  x=\frac{1}{2}*\frac{1}{4}\frac{1}{4}=\frac{1}{8}\). Now, \(\frac{1}{8}\) is not an integer at all (hence not even) and also not positive, so none of the options MUST be true. Answer: E.
_________________
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



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8003
Location: Pune, India

Re: If x is a positive number and a=√x∗x−x, [#permalink]
Show Tags
03 Feb 2014, 22:44
2
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
gmatgambler wrote: If x is a positive number and a=√x∗x−x, which of the following must be true?
I. a is even
II. a is positive
III. a is an integer
A)I only B)II only C)III only D)I and II E) None of the above Also, let me point out how we arrive at the numbers that we should try here. Given x is a positive number and \(a =\sqrt{x}*x  x\). \(\sqrt{x}\) makes us think of perfect squares. We try to put in a perfect square such as 4 and see that all conditions are met. So now we need to think of the cases when the condition may not be met. Let's figure out whether a must be positive. \(\sqrt{x}\) is positive and x is positive but for a to be positive, \(\sqrt{x}*x\) MUST be greater than x. Will \(\sqrt{x}*x\) be less than x in any case? It will be if \(\sqrt{x}\) is less than 1 i.e. a fraction. So this leads us to x = 1/4. We must try this value. When x = 1/4, we see that a is not positive, is not an integer and hence the question of even or odd doesn't arise. Answer (E)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Manager
Status: Kitchener
Joined: 03 Oct 2013
Posts: 95
Location: Canada
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)

If x is a positive number and a=√x∗x−x, [#permalink]
Show Tags
18 Jan 2015, 14:22
Bunuel wrote: gmatgambler wrote: If x is a positive number and a=√x∗x−x, which of the following must be true?
I. a is even
II. a is positive
III. a is an integer
A)I only B)II only C)III only D)I and II E) None of the above If \(x\) is a positive number and \(a=\sqrt{x} * x  x\), which of the following must be true?I. \(a\) is even II. \(a\) is positive III. \(a\) is an integer A. I only B. II only C. III only D. I and II E. None of the above Note that we are asked "which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer. If \(x=\frac{1}{4}\) then \(a=\sqrt{x} * x  x=\frac{1}{2}*\frac{1}{4}\frac{1}{4}=\frac{1}{8}\). Now, \(\frac{1}{8}\) is not an integer at all (hence not even) and also not positive, so none of the options MUST be true. Answer: E. [b][color=#0d004c]I did as Bunuel did where I used 1/4 as option and I subtrac 1/4 from 1/4 and then Multiple by sqrt 1/4 the result was always zero. So my answer was E because 0 is both even and integer abd there is no option include both A and C. Does my reason to chosen was true?
_________________
Click +1 Kudos if my post helped



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11312
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: If x is a positive number and a=√x∗x−x, [#permalink]
Show Tags
18 Jan 2015, 19:22
HI All, The "font" (and lack of parentheses) makes this question a little tough to interpret. I believe that the intent is the following: If X is POSITIVE, and A = (\sqrt{X})(X)  X which of the following MUST be true? Since the question asks what MUST be true, we can quickly eliminate possibilities by proving what is NOT always true (by TESTing VALUES) IF.... A = 1, then (\sqrt{1})(1)  1 = (1)(1)  1 = 0 This result is NOT positive. Eliminate Roman Numeral II and Answers B and D. IF.... A = 2, then (\sqrt{2})(2)  2 = NOT an integer. Eliminate Roman Numerals I and III and Answers A and C. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8003
Location: Pune, India

Re: If x is a positive number and a=√x∗x−x, [#permalink]
Show Tags
18 Jan 2015, 21:33
23a2012 wrote: Bunuel wrote: gmatgambler wrote: If x is a positive number and a=√x∗x−x, which of the following must be true?
I. a is even
II. a is positive
III. a is an integer
A)I only B)II only C)III only D)I and II E) None of the above If \(x\) is a positive number and \(a=\sqrt{x} * x  x\), which of the following must be true?I. \(a\) is even II. \(a\) is positive III. \(a\) is an integer A. I only B. II only C. III only D. I and II E. None of the above Note that we are asked "which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer. If \(x=\frac{1}{4}\) then \(a=\sqrt{x} * x  x=\frac{1}{2}*\frac{1}{4}\frac{1}{4}=\frac{1}{8}\). Now, \(\frac{1}{8}\) is not an integer at all (hence not even) and also not positive, so none of the options MUST be true. Answer: E. [b][color=#0d004c]I did as Bunuel did where I used 1/4 as option and I subtrac 1/4 from 1/4 and then Multiple by sqrt 1/4 the result was always zero. So my answer was E because 0 is both even and integer abd there is no option include both A and C. Does my reason to chosen was true? Multiplication/Division always comes before Addition/Subtraction. You cannot subtract x first and then multiply by root(x). The multiplication has to be done first because sequence of operators follows the rule of PEMDAS/BODMAS. I suggest you to check this out from a Math book or online.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Intern
Joined: 10 Jun 2014
Posts: 15

If x is a positive number and a=√x∗x−x, [#permalink]
Show Tags
01 Jan 2018, 17:16
We can aslo do the following. Just juggling of steps.
Given, a= sqrt(x)*xx => a= x(sqrt (x) 1) Then we start put to numbers for eg. x=1 => a=0. Cuts point 2 Put x>1, a may not be an integer and hence not even. Cuts point 1 and 3.
Ans is E.




If x is a positive number and a=√x∗x−x,
[#permalink]
01 Jan 2018, 17:16






