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# Is (1 + 0.01r)(1 - 0.01s) > 1 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 52284
Is (1 + 0.01r)(1 - 0.01s) > 1 ?  [#permalink]

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13 Apr 2018, 00:24
00:00

Difficulty:

65% (hard)

Question Stats:

56% (02:19) correct 44% (02:16) wrong based on 71 sessions

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Is $$(1 + 0.01r)(1 - 0.01s) > 1$$ ?

(1) $$r > s$$

(2) $$0.01rs < r - s$$

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Math Expert
Joined: 02 Aug 2009
Posts: 7201
Re: Is (1 + 0.01r)(1 - 0.01s) > 1 ?  [#permalink]

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13 Apr 2018, 01:35
Bunuel wrote:
Is $$(1 + 0.01r)(1 - 0.01s) > 1$$ ?

(1) $$r > s$$

(2) $$0.01rs < r - s$$

$$(1 + 0.01r)(1 - 0.01s) > 1............1+0.01r-0.01s-0.0001rs>1...............0.01r-0.01s-0.0001rs>0...............r-s>0.01rs$$

so basically we have to say whether r-s>0.01rs

let's see the statements..
(1) $$r > s$$
just says that r-s>0...
insuff

(2) $$0.01rs < r - s$$
this is exactly what we were looking for..
suff

B
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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

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Intern
Joined: 24 Oct 2017
Posts: 46
Re: Is (1 + 0.01r)(1 - 0.01s) > 1 ?  [#permalink]

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13 Apr 2018, 21:15
Hello chetan2u,
(1+0.01r)(1−0.01s)=1+.01[(r-s)-0.01rs]
If we will take r<s
Suppose r=10 s=20
Then 1+.01[(r-s)-0.01rs]=0.88
And if r=20 and s=10
Then 1+.01[(r-s)-0.01rs]=1.08
Hence option c is correct
Math Expert
Joined: 02 Aug 2009
Posts: 7201
Re: Is (1 + 0.01r)(1 - 0.01s) > 1 ?  [#permalink]

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13 Apr 2018, 21:21
1
GYANENDRA88 wrote:
Hello chetan2u,
(1+0.01r)(1−0.01s)=1+.01[(r-s)-0.01rs]
If we will take r<s
Suppose r=10 s=20
Then 1+.01[(r-s)-0.01rs]=0.88
And if r=20 and s=10
Then 1+.01[(r-s)-0.01rs]=1.08
Hence option c is correct

$$0.01rs<r−s$$...
if r = 10 and s = 20..
$$0.01*10*20 <10-20.......2<-10$$????.... not valid as per statement II
_________________

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

Director
Joined: 02 Oct 2017
Posts: 735
Re: Is (1 + 0.01r)(1 - 0.01s) > 1 ?  [#permalink]

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27 Apr 2018, 21:45
Resolving equation

1+0.01[(r-s)-0.1rs]

I) r>s

3>2 value of equation less than 1
3>-2 value of equation greater then 1
Insufficient

II)this equation makes bracket greater than 1 in equation
So value >1
Sufficient

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Manager
Joined: 24 Mar 2018
Posts: 174
Re: Is (1 + 0.01r)(1 - 0.01s) > 1 ?  [#permalink]

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07 Jun 2018, 05:23
Bunuel chetan2u

Can you please elaborate how 1 is insufficient
On solveing the given equation we get
r-s>0.01rs
in this equation if we take any value of r greater than s it satisfy the above equation.
Math Expert
Joined: 02 Aug 2009
Posts: 7201
Re: Is (1 + 0.01r)(1 - 0.01s) > 1 ?  [#permalink]

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07 Jun 2018, 08:51
teaserbae wrote:
Bunuel chetan2u

Can you please elaborate how 1 is insufficient
On solveing the given equation we get
r-s>0.01rs
in this equation if we take any value of r greater than s it satisfy the above equation.

No it does not..
Take huge value for r and s but very less difference between the two..
Say r=100 and s=99...
So r-s=100-99=1..
But 0.01rs=0.01*100*99=99..
Here r-s<0.01rs as 1<99
_________________

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

Re: Is (1 + 0.01r)(1 - 0.01s) > 1 ? &nbs [#permalink] 07 Jun 2018, 08:51
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