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If x > 0.9, which of the following could be the value of x?

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Joined: 18 Aug 2014
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If x > 0.9, which of the following could be the value of x? [#permalink]

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Updated on: 12 Jan 2015, 03:53
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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

[Reveal] Spoiler:
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.
[Reveal] Spoiler: OA

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.
Intern
Joined: 12 May 2014
Posts: 15
Location: United States
Concentration: Strategy, Operations
Schools: IIMC'17
GMAT Date: 10-22-2014
GPA: 1.9
WE: Engineering (Energy and Utilities)
Re: If x > 0.9, which of the following could be the value of x? [#permalink]

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11 Sep 2014, 21:18
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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:)
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Re: If x > 0.9, which of the following could be the value of x? [#permalink]

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11 Sep 2014, 21:45
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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 1-0.1 = 0.9. It is not greater than 0.9

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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 Schools: IIMC'17 GMAT Date: 10-22-2014 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 1-0.1 = 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 1-0.1 = 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 1-0.1 = 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. _________________ 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/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 11500 Location: United States (CA) GMAT 1: 800 Q51 V49 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 "square-rooting" are 'opposite' functions, what happens when you SQUARE-ROOT a positive fraction? √(1/9) = √(1)/√(9) = 1/3 Square-rooting 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: [Reveal] Spoiler: C 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 Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: If x > 0.9, which of the following could be the value of x? [#permalink]

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12 Jan 2015, 23:30
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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

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Re: If x > 0.9, which of the following could be the value of x? [#permalink]

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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 "square-rooting" are 'opposite' functions, what happens when you SQUARE-ROOT a positive fraction?

√(1/9) = √(1)/√(9) = 1/3

Square-rooting 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...

[Reveal] Spoiler:
C

GMAT assassins aren't born, they're made,
Rich

You sir, are a legend.... Thanks a bunch
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Joined: 15 Mar 2016
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Re: If x > 0.9, which of the following could be the value of x? [#permalink]

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

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07 Mar 2017, 07:37
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Expert's post
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.

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Re: If x > 0.9, which of the following could be the value of x? [#permalink]

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