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# What is the value, rounded to the nearest integer, of 3a + 4 divided

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Joined: 02 Sep 2009
Posts: 43828
What is the value, rounded to the nearest integer, of 3a + 4 divided [#permalink]

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11 Jan 2017, 02:26
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Difficulty:

65% (hard)

Question Stats:

55% (00:56) correct 45% (01:25) wrong based on 54 sessions

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What is the value, rounded to the nearest integer, of 3a + 4 divided by a ?

(1) a > 8
(2) 10 > a > 7
[Reveal] Spoiler: OA

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Joined: 01 Jul 2014
Posts: 7
Location: United States
Concentration: Operations, General Management
WE: Operations (Manufacturing)
What is the value, rounded to the nearest integer, of 3a + 4 divided [#permalink]

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11 Jan 2017, 02:35
Bunuel wrote:
What is the value, rounded to the nearest integer, of 3a + 4 divided by a ?

(1) a > 8
(2) 10 > a > 7

[A]
FROM statement 1:
1/a < 1/8
4/a<4/8
3+ 4/a < 3+ 4/8
irrespective of the value of a the nearest integer will be 3
sufficient
from statement 2
a = 7.5
3+4/7.5 > 3.5
so the nearest integer is 4
a= 8
3+4/8
nearest integer is 3
hence, statement 2 is not sufficient

Last edited by anurag790 on 11 Jan 2017, 07:45, edited 1 time in total.
Intern
Joined: 24 Oct 2016
Posts: 1
Re: What is the value, rounded to the nearest integer, of 3a + 4 divided [#permalink]

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11 Jan 2017, 03:12
The answer is D,

Since a or b leads to 3
Manager
Joined: 08 Nov 2015
Posts: 68
GMAT 1: 460 Q32 V22
Re: What is the value, rounded to the nearest integer, of 3a + 4 divided [#permalink]

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11 Jan 2017, 05:21
Bunuel wrote:
What is the value, rounded to the nearest integer, of 3a + 4 divided by a ?

(1) a > 8
(2) 10 > a > 7

From the question stem it follows that 3a+4/a = 3 + 4/a ?

1. a can be any value greater than 8 ie. 9,10,11 etc. Not sufficient
2. 10 >a >7
a=8,9. This again not sufficient.

From 1 and 2, it again appears that 8 < a < 10, and it is not mentioned that a is an integer. Hence we cannot have specific value.

Hence the correct answer to me seems to be E.
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What is the value, rounded to the nearest integer, of 3a + 4 divided [#permalink]

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11 Jan 2017, 05:35
Bunuel wrote:
What is the value, rounded to the nearest integer, of 3a + 4 divided by a ?

(1) a > 8
(2) 10 > a > 7

The question asks what is the value, rounded to the nearest integer, of $$\frac{3a+4}{a}=3+\frac{4}{a}$$

(1) $$a>8 \implies \frac{4}{a}<\frac{4}{8}=0.5$$. Hence $$3+\frac{4}{a} \approx 3 + 0 = 3$$. Sufficient.

(2) $$7 < a < 10$$

If $$a=7.5$$ then $$3+\frac{4}{7.5} > 3 + \frac{4}{8}=3.5$$. Hence $$3+\frac{4}{a} \approx 4$$
If $$a=9$$ then $$3+\frac{4}{9} < 3 + \frac{4}{8}=3.5$$. Hence $$3+\frac{4}{a} \approx 3$$

Insufficient.

The answer is A.
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Posts: 646
Re: What is the value, rounded to the nearest integer, of 3a + 4 divided [#permalink]

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11 Jan 2017, 06:11
Bunuel wrote:
What is the value, rounded to the nearest integer, of 3a + 4 divided by a ?

(1) a > 8
(2) 10 > a > 7

we can rewrite it as 3a/a +4/a

a. a > 8 = max value of 3 + 4/9 ~ 3.4 , so value is 3
if we take a= 10 3 + 4/10 ~ 3.4, so value is 3
for 11 3+ 4/11 --it will also give 3 ...
so for any value of a, the integral value will be 3.
suff

b . we will get 3.5 for a= 8..we can either write 4 or 3
a=9 ..integral value will be 3
so insuff

Answer =A
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Joined: 03 Sep 2016
Posts: 3
Re: What is the value, rounded to the nearest integer, of 3a + 4 divided [#permalink]

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12 Jan 2017, 04:13
3+4/a
1.) Any value that a takes should be greater than 8 (i.e.) 9,10 and so on which will definitely give values for 3+4/a as lesser than 3.5 and hence the resulting number can be rounded to the nearest integer as 3.-> Sufficient

2.) a can take any value from 7.1 to 9.9 meaning the nearest rounded integer can either be 3 or 4 and hence -> not sufficient.

Answer is A
Manager
Joined: 26 Jun 2014
Posts: 79
Re: What is the value, rounded to the nearest integer, of 3a + 4 divided [#permalink]

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05 Feb 2017, 07:56
[quote="ntdung@inbox.com"]The answer is D,

Since a or b leads to 3[/quote

Can you please explain how you got the answer?
Manager
Joined: 26 Jun 2014
Posts: 79
Re: What is the value, rounded to the nearest integer, of 3a + 4 divided [#permalink]

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08 Feb 2017, 21:53
Edit:
anurag790 wrote:
Bunuel wrote:
What is the value, rounded to the nearest integer, of 3a + 4 divided by a ?

(1) a > 8
(2) 10 > a > 7

[A]
FROM statement 1:
1/a < 1/8
4/a<4/8
3+ 4/a < 3+ 4/8
irrespective of the value of a the nearest integer will be 3
sufficient
from statement 2
a = 7.5
3+4/7.5 > 3.5
so the nearest integer is 4
a= 8
3+4/8
nearest integer is 3
hence, statement 2 is not sufficient

When a= 8
3+4/8
Now the value is 3.5. The nearest integer can be 4 as well i guess. how did you decide?
Re: What is the value, rounded to the nearest integer, of 3a + 4 divided   [#permalink] 08 Feb 2017, 21:53
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# What is the value, rounded to the nearest integer, of 3a + 4 divided

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