Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 12 Feb 2016, 21:12

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:
Manager
Joined: 22 Mar 2009
Posts: 79
Schools: Darden:Tepper:UCUIC:Kenan Flager:Nanyang:NUS:ISB:UCI Merage:Emory
WE 1: 3
Followers: 2

Kudos [?]: 23 [2] , given: 7

If r is not equal to 0, is r^2/|r| < 1? (1) r > -1 (2) [#permalink]  27 Jun 2010, 11:43
2
KUDOS
00:00

Difficulty:

25% (medium)

Question Stats:

68% (01:58) correct 32% (01:34) wrong based on 348 sessions
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

_________________

Second cut is the deepest cut!!!:P

Math Expert
Joined: 02 Sep 2009
Posts: 31303
Followers: 5364

Kudos [?]: 62515 [3] , given: 9457

Re: Mod of R - DS [#permalink]  27 Jun 2010, 12:10
3
KUDOS
Expert's post
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

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.

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.
_________________
Manhattan GMAT Instructor
Joined: 27 Aug 2009
Posts: 153
Location: St. Louis, MO
Schools: Cornell (Bach. of Sci.), UCLA Anderson (MBA)
Followers: 158

Kudos [?]: 324 [0], given: 6

Re: Mod of R - DS [#permalink]  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)?"
_________________

Emily Sledge | Manhattan GMAT Instructor | St. Louis

Manhattan GMAT Discount | Manhattan GMAT Course Reviews | Manhattan GMAT Reviews

Intern
Joined: 14 Jun 2010
Posts: 16
Location: Singapore
Concentration: Strategy
Schools: Fuqua '14 (S)
WE: Information Technology (Consulting)
Followers: 0

Kudos [?]: 5 [0], given: 2

Re: Mod of R - DS [#permalink]  27 Jun 2010, 22:21
C, value of 'r' shall fall in the range -1 and 1 for a single solution to exist.
Manager
Joined: 22 Mar 2009
Posts: 79
Schools: Darden:Tepper:UCUIC:Kenan Flager:Nanyang:NUS:ISB:UCI Merage:Emory
WE 1: 3
Followers: 2

Kudos [?]: 23 [0], given: 7

Re: Mod of R - DS [#permalink]  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

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.

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!!!
_________________

Second cut is the deepest cut!!!:P

Manager
Joined: 29 Mar 2010
Posts: 142
Location: United States
GMAT 1: 590 Q28 V38
GPA: 2.54
WE: Accounting (Hospitality and Tourism)
Followers: 1

Kudos [?]: 77 [0], given: 16

Re: If r is not equal to 0, is r^2/|r| < 1? (1) r > -1 (2) [#permalink]  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
_________________

4/28 GMATPrep 42Q 36V 640

Senior Manager
Joined: 06 Aug 2011
Posts: 405
Followers: 2

Kudos [?]: 139 [0], given: 82

Re: Mod of R - DS [#permalink]  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

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.

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 ???
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Math Expert
Joined: 02 Sep 2009
Posts: 31303
Followers: 5364

Kudos [?]: 62515 [0], given: 9457

Re: Mod of R - DS [#permalink]  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

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.

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.
_________________
Senior Manager
Joined: 23 Jan 2013
Posts: 489
Schools: Cambridge'16
Followers: 2

Kudos [?]: 40 [0], given: 36

Re: If r is not equal to 0, is r^2/|r| < 1? (1) r > -1 (2) [#permalink]  06 Nov 2014, 00:36
kylexy wrote:
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.

r^2/|r|<1 ---> r^2<|r|

Logically, the only way when any number squared is less than the same number not squared is when the number is between -1 and 1

S1. r>-1 only one part of interval, so INSUFFICIENT

S2. r<1 again, only one part of interval, INSUFFICIENT

S1+S2 gives full interval, SUFFICIENT

C
Re: If r is not equal to 0, is r^2/|r| < 1? (1) r > -1 (2)   [#permalink] 06 Nov 2014, 00:36
Similar topics Replies Last post
Similar
Topics:
1 If r > 0, is r^(1/2) an integer? 2 20 Dec 2015, 04:11
6 If r + s = 4, is s < 0? (1) -4 > -r (2) r > 2s + 2 6 28 Jul 2015, 00:43
9 If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 16 22 Feb 2012, 02:01
8 Is r > s ? (1) -r + s < 0 (2) r < | s | 10 29 Jan 2012, 17:54
Is 1/p > r/(r^2+2) ? 1. p = r 2. r > 0 Can 6 20 Mar 2010, 22:17
Display posts from previous: Sort by