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If b is an integer what is the value of (4b + 1)/(2b) when rounded to

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If b is an integer what is the value of (4b + 1)/(2b) when rounded to  [#permalink]

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New post 17 Sep 2017, 03:52
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Re: If b is an integer what is the value of (4b + 1)/(2b) when rounded to  [#permalink]

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New post 17 Sep 2017, 04:22
1
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
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Re: If b is an integer what is the value of (4b + 1)/(2b) when rounded to  [#permalink]

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New post 17 Sep 2017, 05:07
1
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.
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Re: If b is an integer what is the value of (4b + 1)/(2b) when rounded to  [#permalink]

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New post 17 Sep 2017, 05:20
1
Given that b is an integer
Further simplifying the given expression (4b+1)/2b ----> 2 + 1/2b

1. b>1
Least integer value is 2. Putting in above expression we get ---> 2 + 1/4 = 2.25 ---> Rounded to nearest integer, we get 2
Any value greater than 2 will make the term 1/2b smaller and rounding to the nearest integer will always give the value 2.
Sufficient

2. b>2
Again, any value greater than 2 will make the term 1/2b smaller thereby rounding the value to nearest integer will give 2. Sufficient.

Option D.

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Re: If b is an integer what is the value of (4b + 1)/(2b) when rounded to &nbs [#permalink] 17 Sep 2017, 05:20
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