Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 18 Aug 2014
Posts: 7

If x > 0.9, which of the following could be the value of x? [#permalink]
Show Tags
Updated on: 12 Jan 2015, 03:53
1
This post received KUDOS
9
This post was BOOKMARKED
Question Stats:
52% (00:56) correct 48% (01:11) wrong based on 370 sessions
HideShow timer Statistics
If x > 0.9, which of the following could be the value of x? A. √0.81 B. √0.9 C. (0.9)^2 D. (0.9)(0.99) E. 1  √0.01 If you decide to choose B, please tell me why E doesn't work, since the \sqrt{0.01} can be negative and the entire answer choice becomes greater than 1. However, B can be negative, which is smaller than 0.9.
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by pohkid on 11 Sep 2014, 19:42.
Last edited by Bunuel on 12 Jan 2015, 03:53, edited 3 times in total.
Added the OA.



Intern
Joined: 12 May 2014
Posts: 15
Location: United States
Concentration: Strategy, Operations
GMAT Date: 10222014
GPA: 1.9
WE: Engineering (Energy and Utilities)

Re: If x > 0.9, which of the following could be the value of x? [#permalink]
Show Tags
11 Sep 2014, 21:18
1
This post received KUDOS
1
This post was BOOKMARKED
I went with B initially but after reading your query its clear that the right answer should be "BOTH B & E" as the question asks about which "could" be the value of x....Both are equally possible values of x and hence, this may be one of those questions which doesn't have the right answer choice....
kudos:)



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8030
Location: Pune, India

Re: If x > 0.9, which of the following could be the value of x? [#permalink]
Show Tags
11 Sep 2014, 21:45
5
This post received KUDOS
Expert's post
6
This post was BOOKMARKED
pohkid wrote: If x > 0.9, which of the following could be the value of x?
A. √0.81 B. √0.9 C. (0.9)2 D. (0.9)(0.99) E. 1  √0.01
If you decide to choose B, please tell me why E doesn't work, since the \sqrt{0.01} can be negative and the entire answer choice becomes greater than 1. However, B can be negative, which is smaller than 0.9. You are missing a critical point here: \(\sqrt{x}\) implies the principal square root i.e. the positive square root of x only. For example: \(\sqrt{9} = 3\) only. \(\sqrt{9}\) is not 3. When the question wants the negative square root, it will be written as \(\sqrt{9} = 3\). It might be against what you might have learnt in school but by convention (and certainly as far as GMAT is concerned), \(\sqrt{x}\) implies the positive square root only. On the same lines, \(\sqrt{x^2} = x\) (only the positive value of x) Therefore, √0.9 is a positive value greater than 0.9 and √0.01 has only one value which is 0.1 so option (E) becomes 10.1 = 0.9. It is not greater than 0.9 Answer (B) only.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Intern
Joined: 12 May 2014
Posts: 15
Location: United States
Concentration: Strategy, Operations
GMAT Date: 10222014
GPA: 1.9
WE: Engineering (Energy and Utilities)

Re: If x > 0.9, which of the following could be the value of x? [#permalink]
Show Tags
11 Sep 2014, 21:57
I agree. Though a bit odd for us but the GMAT convention is in fact what you have said...



Intern
Joined: 18 Aug 2014
Posts: 7

Re: If x > 0.9, which of the following could be the value of x? [#permalink]
Show Tags
12 Sep 2014, 00:27
VeritasPrepKarishma wrote: pohkid wrote: If x > 0.9, which of the following could be the value of x?
A. √0.81 B. √0.9 C. (0.9)2 D. (0.9)(0.99) E. 1  √0.01
If you decide to choose B, please tell me why E doesn't work, since the \sqrt{0.01} can be negative and the entire answer choice becomes greater than 1. However, B can be negative, which is smaller than 0.9. You are missing a critical point here: \(\sqrt{x}\) implies the principal square root i.e. the positive square root of x only. For example: \(\sqrt{9} = 3\) only. \(\sqrt{9}\) is not 3. When the question wants the negative square root, it will be written as \(\sqrt{9} = 3\). It might be against what you might have learnt in school but by convention (and certainly as far as GMAT is concerned), \(\sqrt{x}\) implies the positive square root only. On the same lines, \(\sqrt{x^2} = x\) (only the positive value of x) Therefore, √0.9 is a positive value greater than 0.9 and √0.01 has only one value which is 0.1 so option (E) becomes 10.1 = 0.9. It is not greater than 0.9 Answer (B) only. Thanks for your explanation. Would you say on the GMAT, we would always care about the positive root only and ignore the negative root?



Intern
Joined: 22 Aug 2010
Posts: 6

Re: If x > 0.9, which of the following could be the value of x? [#permalink]
Show Tags
12 Jan 2015, 03:36
1
This post received KUDOS
VeritasPrepKarishma wrote: pohkid wrote: If x > 0.9, which of the following could be the value of x?
A. √0.81 B. √0.9 C. (0.9)2 D. (0.9)(0.99) E. 1  √0.01
If you decide to choose B, please tell me why E doesn't work, since the \sqrt{0.01} can be negative and the entire answer choice becomes greater than 1. However, B can be negative, which is smaller than 0.9. You are missing a critical point here: \(\sqrt{x}\) implies the principal square root i.e. the positive square root of x only. For example: \(\sqrt{9} = 3\) only. \(\sqrt{9}\) is not 3. When the question wants the negative square root, it will be written as \(\sqrt{9} = 3\). It might be against what you might have learnt in school but by convention (and certainly as far as GMAT is concerned), \(\sqrt{x}\) implies the positive square root only. On the same lines, \(\sqrt{x^2} = x\) (only the positive value of x) Therefore, √0.9 is a positive value greater than 0.9 and √0.01 has only one value which is 0.1 so option (E) becomes 10.1 = 0.9. It is not greater than 0.9 Answer (B) only. HI, Thanks for the explanation. I seem to be missing another critical point. Why can't the answer be C? (0.9)2 = 1.8 1.8 > 0.9



Math Expert
Joined: 02 Sep 2009
Posts: 44636

Re: If x > 0.9, which of the following could be the value of x? [#permalink]
Show Tags
12 Jan 2015, 03:54
sm1510 wrote: VeritasPrepKarishma wrote: pohkid wrote: If x > 0.9, which of the following could be the value of x?
A. √0.81 B. √0.9 C. (0.9)2 D. (0.9)(0.99) E. 1  √0.01
If you decide to choose B, please tell me why E doesn't work, since the \sqrt{0.01} can be negative and the entire answer choice becomes greater than 1. However, B can be negative, which is smaller than 0.9. You are missing a critical point here: \(\sqrt{x}\) implies the principal square root i.e. the positive square root of x only. For example: \(\sqrt{9} = 3\) only. \(\sqrt{9}\) is not 3. When the question wants the negative square root, it will be written as \(\sqrt{9} = 3\). It might be against what you might have learnt in school but by convention (and certainly as far as GMAT is concerned), \(\sqrt{x}\) implies the positive square root only. On the same lines, \(\sqrt{x^2} = x\) (only the positive value of x) Therefore, √0.9 is a positive value greater than 0.9 and √0.01 has only one value which is 0.1 so option (E) becomes 10.1 = 0.9. It is not greater than 0.9 Answer (B) only. HI, Thanks for the explanation. I seem to be missing another critical point. Why can't the answer be C? (0.9)2 = 1.8 1.8 > 0.9
It's (0.9)^2 = 0.81 < 0.9 not (0.9)*2. Edited the stem.
_________________
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
Joined: 22 Aug 2010
Posts: 6

If x > 0.9, which of the following could be the value of x? [#permalink]
Show Tags
12 Jan 2015, 05:49
Bunuel wrote: sm1510 wrote: HI, Thanks for the explanation. I seem to be missing another critical point. Why can't the answer be C? (0.9)2 = 1.8 1.8 > 0.9
It's (0.9)^2 = 0.81 < 0.9 not (0.9)*2. Edited the stem. Great! Makes much more sense now. We could also use the process of elimination and eliminate all other options that equal to 0.9 or are <0.9 That's if someone, like me, were confused about the root of 0.9 Thanks



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11500
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: If x > 0.9, which of the following could be the value of x? [#permalink]
Show Tags
12 Jan 2015, 16:39
7
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
Hi All, This question is built around a great Number Property rule that you might see on Test Day (although its usage is relatively rare). When dealing with positive fractions (0 < X < 1).....what happens when you SQUARE a positive fraction? eg (1/3)^2 = (1/3)(1/3) = 1/9 Squaring a positive fraction makes the result SMALLER. Since "squaring" and "squarerooting" are 'opposite' functions, what happens when you SQUAREROOT a positive fraction? √(1/9) = √(1)/√(9) = 1/3 Squarerooting a positive fraction makes the result BIGGER. In this question, you'll notice that the answer choices revolve around the use of 0.9 I want to focus on Answers B and C Without doing the math, what happens when you SQUARE 0.9.....? The result will get SMALLER. Without doing the math, what happens when you SQAURE ROOT 0.9....? The result will get BIGGER. Since the question is asking which of the following values could be X (meaning....could be greater than 0.9), we don't have to do any more work... 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!***********************



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: If x > 0.9, which of the following could be the value of x? [#permalink]
Show Tags
12 Jan 2015, 23:30
1
This post received KUDOS
x > 0.9 10x > 9 If the value of x comes up 1 or greater than 1, then the above equation hold true \(\sqrt{0.81} = 0.9\) > will not satisfy \(\sqrt{0.90} = \sqrt{\frac{9}{10}} = \frac{3}{\sqrt{10}}\) > Answer would be greater than 1 Answer = B
_________________
Kindly press "+1 Kudos" to appreciate



Intern
Joined: 11 Nov 2015
Posts: 1

Re: If x > 0.9, which of the following could be the value of x? [#permalink]
Show Tags
07 Jan 2017, 07:58
EMPOWERgmatRichC wrote: Hi All, This question is built around a great Number Property rule that you might see on Test Day (although its usage is relatively rare). When dealing with positive fractions (0 < X < 1).....what happens when you SQUARE a positive fraction? eg (1/3)^2 = (1/3)(1/3) = 1/9 Squaring a positive fraction makes the result SMALLER. Since "squaring" and "squarerooting" are 'opposite' functions, what happens when you SQUAREROOT a positive fraction? √(1/9) = √(1)/√(9) = 1/3 Squarerooting a positive fraction makes the result BIGGER. In this question, you'll notice that the answer choices revolve around the use of 0.9 I want to focus on Answers B and C Without doing the math, what happens when you SQUARE 0.9.....? The result will get SMALLER. Without doing the math, what happens when you SQAURE ROOT 0.9....? The result will get BIGGER. Since the question is asking which of the following values could be X (meaning....could be greater than 0.9), we don't have to do any more work... Final Answer: GMAT assassins aren't born, they're made, Rich You sir, are a legend.... Thanks a bunch



Intern
Joined: 15 Mar 2016
Posts: 6

Re: If x > 0.9, which of the following could be the value of x? [#permalink]
Show Tags
02 Mar 2017, 17:20
Does anyone know what source this question comes from? OG, Kaplan, Veritas?



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2447
Location: United States (CA)

Re: If x > 0.9, which of the following could be the value of x? [#permalink]
Show Tags
07 Mar 2017, 07:37
pohkid wrote: If x > 0.9, which of the following could be the value of x?
A. √0.81 B. √0.9 C. (0.9)^2 D. (0.9)(0.99) E. 1  √0.01 We are given that x > 0.9 and need to determine a value for x. We may recall that when we take the square root of a decimal that is between 0 and 1, the result is larger than the original number inside the root. Thus, since √0.9 > 0.9, we know that √0.9 could be x. Answer: B
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



NonHuman User
Joined: 09 Sep 2013
Posts: 6655

Re: If x > 0.9, which of the following could be the value of x? [#permalink]
Show Tags
20 Mar 2018, 10:49
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). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If x > 0.9, which of the following could be the value of x?
[#permalink]
20 Mar 2018, 10:49






