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Current Student Joined: 11 May 2008
Posts: 541
Is rs/(r + s) > 1/2 ?  [#permalink]

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4 00:00

Difficulty:   55% (hard)

Question Stats: 66% (02:06) correct 34% (01:35) wrong based on 116 sessions

### HideShow timer Statistics Is $$\frac{rs}{r + s} \gt \frac{1}{2}$$ ?

(1) $$r \gt 1$$ and $$s \gt 1$$
(2) $$r \gt 2$$ and $$s \gt 0$$
VP  Joined: 05 Jul 2008
Posts: 1176
Re: Is rs/(r + s) > 1/2 ?  [#permalink]

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Why is A incorrect? Did I miss any values?

1. r \gt 1 and s \gt 1

r=2 s=2 Y
r=2 s=3 Y
r=3 s=5 Y
r=2.5 s=3.5 value = 35/24 >1/2 Y
r=1.5 s=1.5 value = 3/4 > 1/2 Y

2. r \gt 2 and s \gt 0

r=3 s=1 Y
r=4 s=1 Y
r=3 s=3 Y
r=2.5 s=1.5 Value =15/16 Y
r=3.5 s=0.5 value = 7/16 N
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Re: Is rs/(r + s) > 1/2 ?  [#permalink]

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arjtryarjtry wrote:
Is $$\frac{rs}{r + s} \gt \frac{1}{2}$$ ?

1. $$r \gt 1$$ and $$s \gt 1$$
2. $$r \gt 2$$ and $$s \gt 0$$

rewrite the question stem
1/r +1/s<2

1) r>1 x>1
1/r +1/s <2 True
Suffcieint

2) r>2 and s>0

1/r +1/s can be >2 or <2

insuffcient

Will go with A.
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Current Student Joined: 11 May 2008
Posts: 541
Re: Is rs/(r + s) > 1/2 ?  [#permalink]

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sorry guys.... the ans is A. i got confused with soem other question. -1 to me... Director  Joined: 25 Aug 2007
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Re: Is rs/(r + s) > 1/2 ?  [#permalink]

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Is rs/(r+s)>1/2 ?

1. r>1 and s>1
2. r>2 and s>0

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient
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Re: Is rs/(r + s) > 1/2 ?  [#permalink]

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ykaiim wrote:
Is rs/(r+s)>1/2 ?

1. r>1 and s>1
2. r>2 and s>0

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

IMHO D

Statement 2:
Is rs/(r+s)>1/2 >>>> Is rs/(r+s)-1/2 >0 >>>> Is (2*r*s-(r+s))/(r+s) >0
Now given r and s both are positive...so r+s is positive >>> so denominator is positive..
lets have a look at numerator

so the question becomes Is (2*r*s-(r+s)) >0
Is 2rs + (r-s) > 0
Now |2rs| will be greater than |s-r|, So 2rs + (r-s) > 0. Sufficient

Statement 1:
Same way as mentioned above, this statement is sufficient.
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Re: Is rs/(r + s) > 1/2 ?  [#permalink]

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Try this:
S2. If r=2.1 and y=0.1, then
rs=0.21 and r+s=2.2
So, rs/(r+s)=0.21/2.2 < 1/2

What if r=4 and y=8, then
rs=32 and r+s=12
So, rs/(r+s)=32/12 > 1/2

So, Insuff.

Well, I just figured out that for r>1 and s>1 this expression holds true.

nverma wrote:
ykaiim wrote:
Is rs/(r+s)>1/2 ?

1. r>1 and s>1
2. r>2 and s>0

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

IMHO D

Statement 2:
Is rs/(r+s)>1/2 >>>> Is rs/(r+s)-1/2 >0 >>>> Is (2*r*s-(r+s))/(r+s) >0
Now given r and s both are positive...so r+s is positive >>> so denominator is positive..
lets have a look at numerator

so the question becomes Is (2*r*s-(r+s)) >0
Is 2rs + (r-s) > 0
Now |2rs| will be greater than |s-r|, So 2rs + (r-s) > 0. Sufficient

Statement 1:
Same way as mentioned above, this statement is sufficient.

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Re: Is rs/(r + s) > 1/2 ?  [#permalink]

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IMO A

stmnt1 for r>1 and s>1 expression rs/(r+s) will be greater than 1/2. hence suff

stmnt2 is insuff

r=3 s = 0.1 then rs = 0.3 and r+s = 3.1
=> 0.3/3.1 <1/2

r= 3 and s = 10 then rs = 30 and r+s = 13
=> 30/13 >1/2 hence insuff
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Re: Is rs/(r + s) > 1/2 ?  [#permalink]

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kp1811 wrote:
IMO A

stmnt1 for r>1 and s>1 expression rs/(r+s) will be greater than 1/2. hence suff

stmnt2 is insuff

r=3 s = 0.1 then rs = 0.3 and r+s = 3.1
=> 0.3/3.1 <1/2

r= 3 and s = 10 then rs = 30 and r+s = 13
=> 30/13 >1/2 hence insuff

I agree with the above explanation and OA.

ykaiim - Can you confirm what is the OA for this question please?
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Re: Is rs/(r + s) > 1/2 ?  [#permalink]

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A.

St. 1 : the value of $$\frac{rs}{r+s}$$ is always > 1/2 --> suff
St. 2 : For some values of r and s, the fraction is < 1/2 and for some > 1/2 --> insuff
Manager  Joined: 16 Feb 2010
Posts: 128
Re: Is rs/(r + s) > 1/2 ?  [#permalink]

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imo A
what is the OA?
Intern  Joined: 11 May 2011
Posts: 1
Re: Is rs/(r + s) > 1/2 ?  [#permalink]

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Is (rs)/(r+s) > 1/2?
1. r>1 and s>1
2. r>2 and s>0

In the explanation, I don't understand how (rs)/(r+s) simplifies to 1/[(1/r) + (1/s)]
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Re: Is rs/(r + s) > 1/2 ?  [#permalink]

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Looking at it from rveverse way :

1/[(1/r) + (1/s)] = 1/[(r+s)/rs] = rs/(r+s).

Or you may divide numerator and denominator by rs:

=> rs/rs/(r+s)/rs = 1/(1/r + 1/s)

HTH.
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Re: Is rs/(r + s) > 1/2 ?  [#permalink]

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a r=s=2 gives LHS = 1 > RHS = 1/2
r=1.1=s gives LHS > RHS
a is sufficient.

b r=3 s=0.1 gives LHS = 0.3 < RHS

r=3 s=3 gives LHS > RHS.

Hence A is clean

rs/r+s = 1/[(r/rs)+s/(r+s)] = 1/[1/s+1/r]

means 1/[1/s+1/r] >1/2 means 1/s+ 1/r < 2 taking reciprocals

a for positive values of s and r >1 will give LHS < RHS always.
b for s=3 and r = 0.1 will give RHS <LHS.

a is clean
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Re: Is rs/(r + s) > 1/2 ?  [#permalink]

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Janakan wrote:
Is (rs)/(r+s) > 1/2?
1. r>1 and s>1
2. r>2 and s>0

Stmt1:r>1 and s>1. Adding, r+s>2. also, rs > 1. Since (r+s) and (rs) both are +ve, dividing rs by r+s
rs/r+s > 1/2 Sufficient.

Stmt2: r>2 and s>0. Adding, r+s>2. also, rs>0. hence rs/r+s > 0/2. or rs/r+s > 0 but can be greater than 1/2 or less than 1/2. Insufficient.

OA A.
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Re: Is rs/(r + s) > 1/2 ?  [#permalink]

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Is $$\frac{rs}{r + s} \gt \frac{1}{2}$$ ?

1. $$r \gt 1$$ and $$s \gt 1$$
2. $$r \gt 2$$ and $$s \gt 0$$

Hey all, can solve it by plugging in numbers. Would be happy to find an easy mathematical way if there is one.

thanks.
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Re: Is rs/(r + s) > 1/2 ?  [#permalink]

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x2suresh wrote:
arjtryarjtry wrote:
Is $$\frac{rs}{r + s} \gt \frac{1}{2}$$ ?

1. $$r \gt 1$$ and $$s \gt 1$$
2. $$r \gt 2$$ and $$s \gt 0$$

rewrite the question stem
1/r +1/s<2

1) r>1 x>1
1/r +1/s <2 True
Suffcieint

2) r>2 and s>0

1/r +1/s can be >2 or <2

insuffcient

Will go with A.

Why do you switch the inequality sign when you take the reciprocals in your work on statement 1?
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Re: Is rs/(r + s) > 1/2 ?  [#permalink]

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_________________ Re: Is rs/(r + s) > 1/2 ?   [#permalink] 22 Dec 2018, 19:09
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