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# If |r|*s=r^2,which of the following must be

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Math Expert
Joined: 02 Aug 2009
Posts: 7100
If |r|*s=r^2,which of the following must be  [#permalink]

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28 Jun 2018, 21:17
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Difficulty:

55% (hard)

Question Stats:

55% (01:08) correct 45% (01:03) wrong based on 347 sessions

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If |r|*s=$$r^2$$, which of the following must be true?
I. rs>0
II. r=s
III. $$s\geq{r}$$

A) I
B) II
C) III
D) I and II
E) I, II, and III

New tricky question

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Math Expert
Joined: 02 Aug 2009
Posts: 7100
Re: If |r|*s=r^2,which of the following must be  [#permalink]

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28 Jun 2018, 21:20
try the following question on the same line to judge yourself on inequalities and modulus
https://gmatclub.com/forum/is-r-s-s-r-269267.html
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Intern
Joined: 10 Oct 2017
Posts: 11
Re: If |r|*s=r^2,which of the following must be  [#permalink]

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28 Jun 2018, 23:10
|r|*s=r^2

so, s=-r, or s=+r

so, if s=-r, the sr is <0,
and r not equal to s,
but s will be either =r, or >-r.

so swill be always >=r
so ans C
Intern
Joined: 14 Nov 2016
Posts: 2
Re: If |r|*s=r^2,which of the following must be  [#permalink]

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29 Jun 2018, 01:58
can someome explain this pls...
|r| = always positive
|r|* s = r^2
lets assume s = (-2)^2 and r = - 4

is this case
1)rs = -16 False
2) r=s False
3) s ≥ r True

So option c
Math Expert
Joined: 02 Aug 2009
Posts: 7100
If |r|*s=r^2,which of the following must be  [#permalink]

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29 Jun 2018, 02:46
1
harmanbindra wrote:
can someome explain this pls...
|r| = always positive
|r|* s = r^2
lets assume s = (-2)^2 and r = - 4

is this case
1)rs = -16 False
2) r=s False
3) s ≥ r True

So option c

Hi...
$$|r|*s=r^2$$..
Now |r| and r^2 are always positive..
So positive*s=positive
Here s has to be positive
So two points
1) s is positive and r can be anything
2) numeric value of s and r is equal that is |r|=|s|

If r is negative, s>r and if r is positive, s=r
Thus s can never be <r
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Intern
Joined: 24 Aug 2018
Posts: 1
Re: If |r|*s=r^2,which of the following must be  [#permalink]

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16 Nov 2018, 07:19
Manager
Joined: 28 Jan 2018
Posts: 140
Location: Taiwan
GPA: 3.34
Re: If |r|*s=r^2,which of the following must be  [#permalink]

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08 Dec 2018, 01:03
If |r|*s=r^2, which of the following must be true?
I. rs>0
II. r=s
III. s≥r

My take is, since |r| and r^2 will always be >= 0 , s cannot be negative
(I) immediately out
(II) is also out because easy plug-in would show |-2| * 2 = (-2)^2
Re: If |r|*s=r^2,which of the following must be &nbs [#permalink] 08 Dec 2018, 01:03
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