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

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Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132619 [0], given: 12326

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

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17 Sep 2017, 03:52
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45% (medium)

Question Stats:

72% (01:05) correct 28% (01:24) wrong based on 36 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
[Reveal] Spoiler: OA

_________________

Kudos [?]: 132619 [0], given: 12326

Senior Manager
Joined: 02 Jul 2017
Posts: 269

Kudos [?]: 79 [1], given: 65

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

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17 Sep 2017, 04:22
1
KUDOS
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

Kudos [?]: 79 [1], given: 65

Intern
Joined: 19 Sep 2016
Posts: 35

Kudos [?]: 2 [1], given: 3

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

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17 Sep 2017, 05:07
1
KUDOS
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.

Kudos [?]: 2 [1], given: 3

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Location: India
WE: Information Technology (Computer Software)
Re: If b is an integer what is the value of (4b + 1)/(2b) when rounded to [#permalink]

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17 Sep 2017, 05:20
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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Kudos [?]: 9 [0], given: 33

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