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17 Sep 2017, 03:52
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D
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Difficulty:
35%
(medium)
Question Stats:
66% (01:24) correct
34%
(01:39)
wrong
based on 70
sessions
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If b is an integer what is the value of (4b + 1)/(2b) when rounded to the nearest integer?
(1) b > 1
(2) b > 2
(1) b > 1
(2) b > 2
17 Sep 2017, 04:22
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b is an integer
value of : \(\frac{4b + 1}{2b}\) when rounded to the nearest integer
\(\frac{4b + 1}{2b} = 2+\frac{1}{2b}\)
=>for b =+ve integer => maximum value of \(\frac{1}{2b}\)will be for b=1 => \(2 + \frac{1}{2} = 2+0.5 = 2.5 = 3\) rounded to nearest integer
=> for \(b >1\) value of \(\frac{1}{2b}\) will be less than 0.5 => \(2 + \frac{1}{2*2} = 2+0.25 =2.25 = 2\) rounded to nearest integer
so for all values of b > 1 nearest integer value for \(\frac{4b + 1}{2b}\) = 2
=> for b=0 value is not defined.
=> for b=-ve integer => minimum value of \(\frac{1}{2b}\) will be for \(b=-1\) => \(2 + \frac{1}{-2} = 2-0.5 = 1.5 = 2\) rounded to nearest integer
=> for \(b <-1\) value of \(\frac{1}{2b}\) will be less than 0.5 => \(2 + \frac{1}{-2*2} = 2-0.25 = 1.75 = 2\) rounded to nearest integer
so for all values of \(b =<-1\) nearest integer value for \(\frac{4b + 1}{2b}\) = 2
(1) b > 1
As per above discussion for b >1 => \(\frac{4b + 1}{2b}\) = 2
Sufficient
(2) b > 2
As per above discussion for b >2 => \(\frac{4b + 1}{2b}\) = 2
Sufficient
Answer: D
value of : \(\frac{4b + 1}{2b}\) when rounded to the nearest integer
\(\frac{4b + 1}{2b} = 2+\frac{1}{2b}\)
=>for b =+ve integer => maximum value of \(\frac{1}{2b}\)will be for b=1 => \(2 + \frac{1}{2} = 2+0.5 = 2.5 = 3\) rounded to nearest integer
=> for \(b >1\) value of \(\frac{1}{2b}\) will be less than 0.5 => \(2 + \frac{1}{2*2} = 2+0.25 =2.25 = 2\) rounded to nearest integer
so for all values of b > 1 nearest integer value for \(\frac{4b + 1}{2b}\) = 2
=> for b=0 value is not defined.
=> for b=-ve integer => minimum value of \(\frac{1}{2b}\) will be for \(b=-1\) => \(2 + \frac{1}{-2} = 2-0.5 = 1.5 = 2\) rounded to nearest integer
=> for \(b <-1\) value of \(\frac{1}{2b}\) will be less than 0.5 => \(2 + \frac{1}{-2*2} = 2-0.25 = 1.75 = 2\) rounded to nearest integer
so for all values of \(b =<-1\) nearest integer value for \(\frac{4b + 1}{2b}\) = 2
(1) b > 1
As per above discussion for b >1 => \(\frac{4b + 1}{2b}\) = 2
Sufficient
(2) b > 2
As per above discussion for b >2 => \(\frac{4b + 1}{2b}\) = 2
Sufficient
Answer: D
17 Sep 2017, 05:07
Kudos
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solving the equation, (4b+1)/2b, 2+(1/2b), so now analyzing the statements,
Statement 1 - b>1, means that 1/2b can be .25,.16 and would further keep on reducing as the denominator would keep on increasing, hence after rounding off, the answer shall be 2 and hence statement 1 is sufficient.
Statement 2 - b>2 would mean the same that the value of 1/2b would be nearing zero only on rounding off and hence after rounding off, the answer would be 2 only. hence statement 2 is also sufficient.
so answer is D as both statement are sufficient individually.
Statement 1 - b>1, means that 1/2b can be .25,.16 and would further keep on reducing as the denominator would keep on increasing, hence after rounding off, the answer shall be 2 and hence statement 1 is sufficient.
Statement 2 - b>2 would mean the same that the value of 1/2b would be nearing zero only on rounding off and hence after rounding off, the answer would be 2 only. hence statement 2 is also sufficient.
so answer is D as both statement are sufficient individually.
