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

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27 Jun 2010, 12:43

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67% (02:01) correct
33% (01:25) wrong based on 469 sessions

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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.

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 \(\frac{(-2)^2}{|-2|}=2>1\).

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

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!!!
_________________

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 ???
_________________

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

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 \(\frac{(-2)^2}{|-2|}=2>1\).

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

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06 Nov 2014, 01:36

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

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