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If x is an integer, is x|x|<2^x ?

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If x is an integer, is x|x|<2^x ? [#permalink] New post 18 Dec 2012, 07:31
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If x is an integer, is x|x|<2^x ?

(1) x < 0
(2) x = -10
[Reveal] Spoiler: OA
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Re: If x is an integer, is x|x|<2^x ? [#permalink] New post 18 Dec 2012, 07:35
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Walkabout wrote:
If x is an integer, is x|x|<2^x ?

(1) x < 0
(2) x= -10


If x is an integer, is x|x|<2^x ?

Notice that the RHS (right hand side) of the expression is always positive (2^x>0), but the LHS is positive when x>0 (x>0 --> x*|x|=x^2), negative when x<0 (x<0 --> x*|x|=-x^2) and equals to zero when x={0}.

(1) x < 0. According to the above x*|x|<0<2^x. Sufficient.

(2) x = -10. The same here x*|x|=-100<0<\frac{1}{2^{10}}. Sufficient.

Answer: D.
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DS from OG [#permalink] New post 30 Dec 2013, 10:42
If x is an integer, is x |x| < 2^x ?

(1) x < 0
(2) x = –10

DS from OG.
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Last edited by seabhi on 31 Dec 2013, 01:45, edited 1 time in total.
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Re: DS from OG [#permalink] New post 30 Dec 2013, 11:02
seabhi wrote:
If x is an integer, is x |x| < 2x ?

(1) x < 0
(2) x = –10

DS from OG.


OA is D for the following reasons:
When you first see a DS question, see if there is anyway to simplify the question stem
In this case, since |x| is positive, we can divide both sides by |x| giving us a new question stem --> is x < 2?

S1: x<0, therefore x must be <2 = sufficient
S2: x = -10 and -10 < 2 = sufficient

Let me know if this helps!
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Re: DS from OG [#permalink] New post 30 Dec 2013, 20:36
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bparrish89 wrote:
seabhi wrote:
If x is an integer, is x |x| < 2x ?

(1) x < 0
(2) x = –10

DS from OG.


OA is D for the following reasons:
When you first see a DS question, see if there is anyway to simplify the question stem
In this case, since |x| is positive, we can divide both sides by |x| giving us a new question stem --> is x < 2?

S1: x<0, therefore x must be <2 = sufficient
S2: x = -10 and -10 < 2 = sufficient

Let me know if this helps!



The OA is wrong here because of the following reasons:


(1) if x=-10 then -100<-20, on the other hand if x= -1, x<0 then the inequality changes from < to >, namely, -1 > -2 ; This statement is absolutely insufficient!


(2) This statement is obviously sufficient!


So, the correct answer is notD, but B
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Re: DS from OG [#permalink] New post 31 Dec 2013, 01:46
Apologies for the confusion, the Question has been corrected.
It was not 2x but 2^x
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Re: DS from OG [#permalink] New post 31 Dec 2013, 03:07
Expert's post
seabhi wrote:
If x is an integer, is x |x| < 2^x ?

(1) x < 0
(2) x = –10

DS from OG.


Merging similar topics. Please refer tot the solutions above. All OG13 questions are here: the-official-guide-quantitative-question-directory-143450.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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: DS from OG   [#permalink] 31 Dec 2013, 03:07
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