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If r is not equal to 0, is r^2/|r| < 1? (1) r > -1 (2)

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If r is not equal to 0, is r^2/|r| < 1? (1) r > -1 (2) [#permalink] New post 27 Jun 2010, 11:43
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If r is not equal to 0, is r^2/|r| < 1?

(1) r > -1

(2) r < 1

AS far as i know the option B looks sufficient. Since, r<1, it can take values that are negative like -2 or fraction values like
1/2. in either case the value of r^2/ |R| is <1. The OA suggests other wise.
[Reveal] Spoiler: OA

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Re: Mod of R - DS [#permalink] New post 27 Jun 2010, 12:10
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kylexy wrote:
If r is not equal to 0, is r^2/|r| < 1?

(1) r > -1

(2) r < 1

Hi pls help me out with a detailed explanation :lol: :roll:

AS far as i know the option B looks sufficient. Since, r<1, it can take values that are negative like -2 or fraction values like
1/2. in either case the value of r^2/ |R| is <1. The OA suggests other wise.


Is \frac{r^2}{|r|}<1? --> reduce by |r| --> is |r|<1? or is -1<r<1?

Two statements together give us the sufficient info.

Answer: C.

You made a mistake in calculation for statement (2). Given r<1: for -1<r<1, for example if r=-\frac{1}{2}, then \frac{(-\frac{1}{2})^2}{|-\frac{1}{2}|}=\frac{1}{2}<1 but if r\leq{-1}, for example if r=-2, then \frac{(-2)^2}{|-2|}=2>1.

Hope it's clear.
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Re: Mod of R - DS [#permalink] New post 27 Jun 2010, 12:13
The first thing to note is that the question isn't testing sign. They tell us that r is not 0, and by definition, both r^2 and |r| are positive. So neither of these statements would be more useful than the other alone.

Since pos/pos = pos, we are ok doing a little creative manipulation of r^2/|r| = |(r*r)/r| = |r|. This move (putting the absolute value sign around the whole thing) isn't a rule to memorize or anything. I'm just ignoring sign temporarily, cancelling, then just assuring the positive result I need with the bars.

This question is really asking "Is r a fraction, or is it larger than 1 (in absolute value)?"
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Re: Mod of R - DS [#permalink] New post 27 Jun 2010, 22:21
C, value of 'r' shall fall in the range -1 and 1 for a single solution to exist.
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Re: Mod of R - DS [#permalink] New post 28 Jun 2010, 01:37
Bunuel wrote:
kylexy wrote:
If r is not equal to 0, is r^2/|r| < 1?

(1) r > -1

(2) r < 1

Hi pls help me out with a detailed explanation :lol: :roll:

AS far as i know the option B looks sufficient. Since, r<1, it can take values that are negative like -2 or fraction values like
1/2. in either case the value of r^2/ |R| is <1. The OA suggests other wise.


Is \frac{r^2}{|r|}<1? --> reduce by |r| --> is |r|<1? or is -1<r<1?

Two statements together give us the sufficient info.

Answer: C.

You made a mistake in calculation for statement (2). Given r<1: for -1<r<1, for example if r=-\frac{1}{2}, then \frac{(-\frac{1}{2})^2}{|-\frac{1}{2}|}=\frac{1}{2}<1 but if r\leq{-1}, for example if r=-2, then \frac{(-2)^2}{|-2|}=2>1.

Hope it's clear.


I guess i did make a mistake in the calc....my bad!!! thanks for the info bunuel!!!
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Re: If r is not equal to 0, is r^2/|r| < 1? (1) r > -1 (2) [#permalink] New post 18 Aug 2013, 19:48
I just did this question on MGMAT, and learning to use number lines as a tool to answer these questions.

And I got it going well so far. Here is how I did it.

First I simplified the statement, but this is how I did it.

Instead of using long drawn out algebra I made it into 2 conditions.

I made \frac{r^2}{|r|} < 1 into two conditions; first where, both r, and |r| is positive.

Creating the equation r<1, then I took the reverse and said that <-1 creating r>1

Then I took the absolute value into the picture and made it into and created r>1 and r>-1

Which makes it that the answer has to r is between -infinity and positive infinity.

And the only solution that satisfies those conditions is C.

I may have made an error in one of my rationales above but it works
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Re: Mod of R - DS [#permalink] New post 06 Feb 2014, 09:54
Bunuel wrote:
kylexy wrote:
If r is not equal to 0, is r^2/|r| < 1?

(1) r > -1

(2) r < 1

Hi pls help me out with a detailed explanation :lol: :roll:

AS far as i know the option B looks sufficient. Since, r<1, it can take values that are negative like -2 or fraction values like
1/2. in either case the value of r^2/ |R| is <1. The OA suggests other wise.


Is \frac{r^2}{|r|}<1? -->reduce by |r| --> is |r|<1? or is -1<r<1?

Two statements together give us the sufficient info.

Answer: C.

You made a mistake in calculation for statement (2). Given r<1: for -1<r<1, for example if r=-\frac{1}{2}, then \frac{(-\frac{1}{2})^2}{|-\frac{1}{2}|}=\frac{1}{2}<1 but if r\leq{-1}, for example if r=-2, then \frac{(-2)^2}{|-2|}=2>1.

Hope it's clear.


How r^2/lrl reduce to lrl only ???
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Re: Mod of R - DS [#permalink] New post 07 Feb 2014, 04:29
Expert's post
sanjoo wrote:
Bunuel wrote:
kylexy wrote:
If r is not equal to 0, is r^2/|r| < 1?

(1) r > -1

(2) r < 1

Hi pls help me out with a detailed explanation :lol: :roll:

AS far as i know the option B looks sufficient. Since, r<1, it can take values that are negative like -2 or fraction values like
1/2. in either case the value of r^2/ |R| is <1. The OA suggests other wise.


Is \frac{r^2}{|r|}<1? -->reduce by |r| --> is |r|<1? or is -1<r<1?

Two statements together give us the sufficient info.

Answer: C.

You made a mistake in calculation for statement (2). Given r<1: for -1<r<1, for example if r=-\frac{1}{2}, then \frac{(-\frac{1}{2})^2}{|-\frac{1}{2}|}=\frac{1}{2}<1 but if r\leq{-1}, for example if r=-2, then \frac{(-2)^2}{|-2|}=2>1.

Hope it's clear.


How r^2/lrl reduce to lrl only ???


r^2=|r|*|r| --> \frac{r^2}{|r|} --> \frac{|r|*|r|}{|r|} --> |r|.

Hope it's clear.
_________________

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: Mod of R - DS   [#permalink] 07 Feb 2014, 04:29
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