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17 Jan 2020, 02:42
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A
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Difficulty:
45%
(medium)
Question Stats:
68% (01:57) correct
32%
(01:53)
wrong
based on 127
sessions
History
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Time
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Is \(\frac{rs}{r + s} \gt \frac{1}{2}\) ?
(1) \(r > 1\) and \(s > 1\)
(2) \(r > 2\) and \(s > 0\)
Are You Up For the Challenge: 700 Level Questions
(1) \(r > 1\) and \(s > 1\)
(2) \(r > 2\) and \(s > 0\)
Are You Up For the Challenge: 700 Level Questions
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Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
https://gmatclub.com/forum/data-sufficiency-ds-141/
https://gmatclub.com/forum/data-sufficiency-ds-141/
17 Jan 2020, 03:20
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Is \(\frac{rs}{(r+s)} > \frac{1}{2}\) ???
—> \(\frac{(2rs —r—s)}{2(r+s)}=\\
\frac{( rs+ rs—r—s)}{2(r+s)} = \\
\frac{(r(s—1) + s(r—1))}{2(r+s)} >0\) ??
(Statement1): r >1 and s >1
—> r—1>0, s—1 > 0 and r+ s > 2
\(\frac{(r(s—1) + s(r—1))}{2(r+s)}\) is always greater than zero
Sufficient
(Statement2): r >2 and s >0
if r = 3 and s= 0.5, then
—> \(\frac{3*0.5}{ (3+0.5)} = \frac{1.5}{3.5}= (\frac{3}{2})/(\frac{7}{2})= \frac{3}{7} <\frac{1}{2}\) (No)
If r=3 and s= 2, then
—> \(\frac{3*2}{(3+2)}= \frac{6}{5} > \frac{1}{2}\) (Yes)
Insufficient
The answer is A
Posted from my mobile device
—> \(\frac{(2rs —r—s)}{2(r+s)}=\\
\frac{( rs+ rs—r—s)}{2(r+s)} = \\
\frac{(r(s—1) + s(r—1))}{2(r+s)} >0\) ??
(Statement1): r >1 and s >1
—> r—1>0, s—1 > 0 and r+ s > 2
\(\frac{(r(s—1) + s(r—1))}{2(r+s)}\) is always greater than zero
Sufficient
(Statement2): r >2 and s >0
if r = 3 and s= 0.5, then
—> \(\frac{3*0.5}{ (3+0.5)} = \frac{1.5}{3.5}= (\frac{3}{2})/(\frac{7}{2})= \frac{3}{7} <\frac{1}{2}\) (No)
If r=3 and s= 2, then
—> \(\frac{3*2}{(3+2)}= \frac{6}{5} > \frac{1}{2}\) (Yes)
Insufficient
The answer is A
Posted from my mobile device
17 Jan 2020, 03:56
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Is \(\frac{rs}{r + s} \gt \frac{1}{2}\) ?
(1) \(r > 1\) and \(s > 1\)
let r=1+a and s=1+b, then is \(\frac{(1+a)(1+b)}{1+a+1+b} \gt \frac{1}{2}........2(1+a+b+ab)>2+a+b........2+2a+2b+2ab>2+a+b.......a+b+2ab>0\). Yes, as a and b are some positive values
Suff
(2) \(r > 2\) and \(s > 0\)
let r=2+a and s=0+b, then is \(\frac{(2+a)(0+b)}{2+a+0+b} \gt \frac{1}{2}........2(2b+ab)>2+a+b........4b+2ab>2+a+b.......3b+2ab>2+a\).
Say a = 0.1 and b=0.2..answer is NO
say b=10 and a = 0.1..answer is YES
Insuff
A
(1) \(r > 1\) and \(s > 1\)
let r=1+a and s=1+b, then is \(\frac{(1+a)(1+b)}{1+a+1+b} \gt \frac{1}{2}........2(1+a+b+ab)>2+a+b........2+2a+2b+2ab>2+a+b.......a+b+2ab>0\). Yes, as a and b are some positive values
Suff
(2) \(r > 2\) and \(s > 0\)
let r=2+a and s=0+b, then is \(\frac{(2+a)(0+b)}{2+a+0+b} \gt \frac{1}{2}........2(2b+ab)>2+a+b........4b+2ab>2+a+b.......3b+2ab>2+a\).
Say a = 0.1 and b=0.2..answer is NO
say b=10 and a = 0.1..answer is YES
Insuff
A
