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M20-33

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M20-33 [#permalink]

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New post 16 Sep 2014, 01:09
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A
B
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D
E

Difficulty:

  65% (hard)

Question Stats:

58% (01:26) correct 42% (01:19) wrong based on 110 sessions

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Kudos [?]: 132991 [0], given: 12402

Expert Post
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Re M20-33 [#permalink]

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New post 16 Sep 2014, 01:09
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Official Solution:


"Is \(|x+1| \lt 2\)?" means "is \(-2 \lt x+1 \lt 2\)?" or "is \(-3 \lt x \lt 1\)?"

(1) \((x-1)^2 \lt 1\). This statement tells that \(-\sqrt{1} \lt x-1 \lt \sqrt{1}\) or \(0 \lt x \lt 2\). So, we can have an YES as well as a NO answer (for example consider \(x=1\) and \(x=1.1\)). Not sufficient.

(2) \(x^2-2 \lt 0\). This statement tells that \(-\sqrt{2} \lt x \lt \sqrt{2}\). Since \(\sqrt{2} \approx 1.4\), then we still can have an YES as well as a NO answer (consider the same example \(x=1\) and \(x=1.1\)). Not sufficient.

(1)+(2) From (1) and (2) we have that \(0 \lt x \lt \sqrt{2}\) and we still can have an YES as well as a NO answer (naturally the example from above works here as well). Not sufficient.


Answer: E
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Resources:
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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.


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Re: M20-33 [#permalink]

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New post 08 Jul 2015, 14:05
Bunuel wrote:
Official Solution:


"Is \(|x+1| \lt 2\)?" means "is \(-2 \lt x+1 \lt 2\)?" or "is \(-3 \lt x \lt 1\)?"

(1) \((x-1)^2 \lt 1\). This statement tells that \(-\sqrt{1} \lt x-1 \lt \sqrt{1}\) or \(0 \lt x \lt 2\). So, we can have an YES as well as a NO answer (for example consider \(x=1\) and \(x=1.1\)). Not sufficient.

(2) \(x^2-2 \lt 0\). This statement tells that \(-\sqrt{2} \lt x \lt \sqrt{2}\). Since \(\sqrt{2} \approx 1.4\), then we still can have an YES as well as a NO answer (consider the same example \(x=1\) and \(x=1.1\)). Not sufficient.

(1)+(2) From (1) and (2) we have that \(0 \lt x \lt \sqrt{2}\) and we still can have an YES as well as a NO answer (naturally the example from above works here as well). Not sufficient.


Answer: E



Hi Bunuel,

One question... From statement 1 and 2, did you apply the x2−2<0 is equal to ¡x! < 2 (Absolute vale of x) because yo knew both sides are positive???

Thanks a lot.

Regards.

Luis Navarro
Looking for 700

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Re: M20-33 [#permalink]

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New post 09 Jul 2015, 02:03
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Expert's post
luisnavarro wrote:
Bunuel wrote:
Official Solution:


"Is \(|x+1| \lt 2\)?" means "is \(-2 \lt x+1 \lt 2\)?" or "is \(-3 \lt x \lt 1\)?"

(1) \((x-1)^2 \lt 1\). This statement tells that \(-\sqrt{1} \lt x-1 \lt \sqrt{1}\) or \(0 \lt x \lt 2\). So, we can have an YES as well as a NO answer (for example consider \(x=1\) and \(x=1.1\)). Not sufficient.

(2) \(x^2-2 \lt 0\). This statement tells that \(-\sqrt{2} \lt x \lt \sqrt{2}\). Since \(\sqrt{2} \approx 1.4\), then we still can have an YES as well as a NO answer (consider the same example \(x=1\) and \(x=1.1\)). Not sufficient.

(1)+(2) From (1) and (2) we have that \(0 \lt x \lt \sqrt{2}\) and we still can have an YES as well as a NO answer (naturally the example from above works here as well). Not sufficient.


Answer: E



Hi Bunuel,

One question... From statement 1 and 2, did you apply the x2−2<0 is equal to ¡x! < 2 (Absolute vale of x) because yo knew both sides are positive???

Thanks a lot.

Regards.

Luis Navarro
Looking for 700


You can take even roots (such as the square root) from an inequality IF both sides are non-negative (check here: inequalities-tips-and-hints-175001.html). Both sides of \((x-1)^2 \lt 1\) and \(x^2 \lt 2\) are non-negative, hence after taking the square root we'll get:

\(|x-1| \lt 1\) and \(x \lt \sqrt{2}\) (recall that \(\sqrt{x^2}=|x|\)).
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132991 [1], given: 12402

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Re: M20-33 [#permalink]

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New post 09 Jul 2015, 05:58
Bunuel wrote:
luisnavarro wrote:
Bunuel wrote:
Official Solution:


"Is \(|x+1| \lt 2\)?" means "is \(-2 \lt x+1 \lt 2\)?" or "is \(-3 \lt x \lt 1\)?"

(1) \((x-1)^2 \lt 1\). This statement tells that \(-\sqrt{1} \lt x-1 \lt \sqrt{1}\) or \(0 \lt x \lt 2\). So, we can have an YES as well as a NO answer (for example consider \(x=1\) and \(x=1.1\)). Not sufficient.

(2) \(x^2-2 \lt 0\). This statement tells that \(-\sqrt{2} \lt x \lt \sqrt{2}\). Since \(\sqrt{2} \approx 1.4\), then we still can have an YES as well as a NO answer (consider the same example \(x=1\) and \(x=1.1\)). Not sufficient.

(1)+(2) From (1) and (2) we have that \(0 \lt x \lt \sqrt{2}\) and we still can have an YES as well as a NO answer (naturally the example from above works here as well). Not sufficient.


Answer: E



Hi Bunuel,

One question... From statement 1 and 2, did you apply the x2−2<0 is equal to ¡x! < 2 (Absolute vale of x) because yo knew both sides are positive???

Thanks a lot.

Regards.

Luis Navarro
Looking for 700


You can take even roots (such as the square root) from an inequality IF both sides are non-negative (check here: inequalities-tips-and-hints-175001.html). Both sides of \((x-1)^2 \lt 1\) and \(x^2 \lt 2\) are non-negative, hence after taking the square root we'll get:

\(|x-1| \lt 1\) and \(x \lt \sqrt{2}\) (recall that \(\sqrt{x^2}=|x|\)).



Thanks a lot, I appreciate your help.

Regards.

Luis Navarro
Looking for 700

Kudos [?]: 2 [0], given: 22

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Re: M20-33 [#permalink]

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New post 28 Oct 2017, 01:10
The prompt asks us if x lies between -3 and 1. Check for each option. The answer is option E , i.e none of the two.
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Re: M20-33 [#permalink]

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New post 06 Nov 2017, 10:28
Hi Bunuel, for S1, I considered the following, could you please help me understand what mistake I made? Thank you very much.

(x−1)2<1
x2-2x+1<1
x2-2x<0
x(x-2)<0
x<0
x<2

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Re: M20-33 [#permalink]

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New post 06 Nov 2017, 10:38
nelliegu wrote:
Hi Bunuel, for S1, I considered the following, could you please help me understand what mistake I made? Thank you very much.

(x−1)2<1
x2-2x+1<1
x2-2x<0
x(x-2)<0
x<0
x<2


x(x - 2) < 0 --> x and x - 2 have the opposite signs.

x > 0 and x - 2 < 0 --> x > 0 and x < 2 --> 0 < x < 2.

x < 0 and x - 2 > 0 --> x < 0 and x > 2 --> no solution.

So, x(x - 2) < 0 holds true for 0 < x < 2.

9. Inequalities



For more check Ultimate GMAT Quantitative Megathread



Hope it helps.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132991 [0], given: 12402

Re: M20-33   [#permalink] 06 Nov 2017, 10:38
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