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Which of the following fractions is closest to 1/2?

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Which of the following fractions is closest to 1/2? [#permalink]

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Which of the following fractions is closest to \(\frac{1}{2}\)?
A) \(\frac{4}{7}\)
B) \(\frac{5}{9}\)
C) \(\frac{6}{11}\)
D) \(\frac{7}{13}\)
E) \(\frac{9}{16}\)


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[Reveal] Spoiler: OA

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Re: Which of the following fractions is closest to 1/2? [#permalink]

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AbdurRakib wrote:
Which of the following fractions is closest to \(\frac{1}{2}\)?
A) \(\frac{4}{7}\)
B) \(\frac{5}{9}\)
C) \(\frac{6}{11}\)
D) \(\frac{7}{13}\)
E) \(\frac{9}{16}\)


OG 2017 New Question

Please Explain


Hi,

Do not waste time in calculating..
look at the similarity in all choices- they all EXCEPT E are of type \(\frac{x}{2x-1}\)...
and \(\frac{x}{2x-1}\) for an integer x is always >1/2 and will become lesser in value , that is will keep getting closer to 1/2 with higher VALUE of x..

you can check in two ways-
1) for x as 1 or 2 or 3..
x=1, \(\frac{x}{2x-1}\) = 1..
x=2, \(\frac{x}{2x-1}\) = 2/3..
x=3, \(\frac{x}{2x-1}\) = 3/5..
so each successive value is smaller than previous one..

2) simplify the term..- IMPORTANT
\(\frac{x}{2x-1}\)=\(\frac{1}{(2x-1)/x}\) = \(\frac{1}{(2x/x-1/x)}\) = \(\frac{1}{(2-1/x)}\)
so the denominator should be closer to 2 so \(2-\frac{1}{x}\) should be close to 2, and therefore x should be MAX to make \(\frac{1}{x}\) less

Therefore, here 7 is the highest value in the four choices so D is the closest to 1/2.

lets see E... It is the TYPE \(\frac{x}{2(x-1)}\)... clearly since 7 and 9 are close to each other but denominator in E is reduced by a larger number,
D is the answer
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Re: Which of the following fractions is closest to 1/2? [#permalink]

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chetan2u wrote:
AbdurRakib wrote:
Which of the following fractions is closest to \(\frac{1}{2}\)?
A) \(\frac{4}{7}\)
B) \(\frac{5}{9}\)
C) \(\frac{6}{11}\)
D) \(\frac{7}{13}\)
E) \(\frac{9}{16}\)


OG 2017 New Question

Please Explain


Hi,

Do not waste time in calculating..
look at the similarity in all choices- they all EXCEPT E are of type \(\frac{x}{2x-1}\)...
and \(\frac{x}{2x-1}\) for an integer x is always >1/2 and will become lesser in value , that is will keep getting closer to 1/2 with higher VALUE of x..

you can check in two ways-
1) for x as 1 or 2 or 3..
x=1, \(\frac{x}{2x-1}\) = 1..
x=2, \(\frac{x}{2x-1}\) = 2/3..
x=3, \(\frac{x}{2x-1}\) = 3/5..
so each successive value is smaller than previous one..

2) simplify the term..- IMPORTANT
\(\frac{x}{2x-1}\)=\(\frac{1}{(2x-1)/x}\) = \(\frac{1}{(2x/x-1/x)}\) = \(\frac{1}{(2-1/x)}\)
so the denominator should be closer to 2 so \(2-\frac{1}{x}\) should be close to 2, and therefore x should be MAX to make \(\frac{1}{x}\) less

Therefore, here 7 is the highest value in the four choices so D is the closest to 1/2.

lets see E... It is the TYPE \(\frac{x}{2(x-1)}\)... clearly since 7 and 9 are close to each other but denominator in E is reduced by a larger number,
D is the answer


Fantastic Explanation. I wish I could give you 2 Kudos.
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Re: Which of the following fractions is closest to 1/2? [#permalink]

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New post 03 Aug 2016, 07:49
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RichaChampion wrote:
chetan2u wrote:
AbdurRakib wrote:
Which of the following fractions is closest to \(\frac{1}{2}\)?
A) \(\frac{4}{7}\)
B) \(\frac{5}{9}\)
C) \(\frac{6}{11}\)
D) \(\frac{7}{13}\)
E) \(\frac{9}{16}\)


OG 2017 New Question

Please Explain


Hi,

Do not waste time in calculating..
look at the similarity in all choices- they all EXCEPT E are of type \(\frac{x}{2x-1}\)...
and \(\frac{x}{2x-1}\) for an integer x is always >1/2 and will become lesser in value , that is will keep getting closer to 1/2 with higher VALUE of x..

you can check in two ways-
1) for x as 1 or 2 or 3..
x=1, \(\frac{x}{2x-1}\) = 1..
x=2, \(\frac{x}{2x-1}\) = 2/3..
x=3, \(\frac{x}{2x-1}\) = 3/5..
so each successive value is smaller than previous one..

2) simplify the term..- IMPORTANT
\(\frac{x}{2x-1}\)=\(\frac{1}{(2x-1)/x}\) = \(\frac{1}{(2x/x-1/x)}\) = \(\frac{1}{(2-1/x)}\)
so the denominator should be closer to 2 so \(2-\frac{1}{x}\) should be close to 2, and therefore x should be MAX to make \(\frac{1}{x}\) less

Therefore, here 7 is the highest value in the four choices so D is the closest to 1/2.

lets see E... It is the TYPE \(\frac{x}{2(x-1)}\)... clearly since 7 and 9 are close to each other but denominator in E is reduced by a larger number,
D is the answer


Fantastic Explanation. I wish I could give you 2 Kudos.


thank you :) :)
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Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: Which of the following fractions is closest to 1/2? [#permalink]

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0.5/7, 0.5/9, 0.5/11, 0.5/13, 0.5/8 .. are the differences.
Pick 0.5/13 :)

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Re: Which of the following fractions is closest to 1/2? [#permalink]

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AbdurRakib wrote:
Which of the following fractions is closest to \(\frac{1}{2}\)?
A) \(\frac{4}{7}\)
B) \(\frac{5}{9}\)
C) \(\frac{6}{11}\)
D) \(\frac{7}{13}\)
E) \(\frac{9}{16}\)


To determine which answer choice is closest to 1/2, we can subtract 1/2 from each answer choice. The difference that is closest to zero will indicate the fraction that is closest to 1/2.

A) 4/7

4/7 - 1/2 = 8/14 - 7/14 = 1/14

B) 5/9

5/9 - 1/2 = 10/18 - 9/18 = 1/18

C) 6/11

6/11 - 1/2 = 12/22 - 11/22 = 1/22

D) 7/13

7/13 - 1/2 = 14/26 - 13/26 = 1/26

E) 9/16

9/16 - 1/2 = 9/16 - 8/16 = 1/16

Since 1/26 is closest to zero, 7/13 is closest to 1/2.

Answer: D
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Re: Which of the following fractions is closest to 1/2? [#permalink]

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AbdurRakib wrote:
Which of the following fractions is closest to \(\frac{1}{2}\)?
A) \(\frac{4}{7}\)
B) \(\frac{5}{9}\)
C) \(\frac{6}{11}\)
D) \(\frac{7}{13}\)
E) \(\frac{9}{16}\)


OG 2017 New Question

Please Explain


\(\frac{1}{2}\) = 50%

Now, Check the options...

A) \(\frac{4}{7}\) = 57.14 %
B) \(\frac{5}{9}\) = 55.56 %
C) \(\frac{6}{11}\) = 54.54 %
D) \(\frac{7}{13}\) = 53.85 %
E) \(\frac{9}{16}\) = 56.25 %

Since the closest answer is (D) , that will be our answer...


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Re: Which of the following fractions is closest to 1/2? [#permalink]

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Any simple and quick method to calculate?

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Re: Which of the following fractions is closest to 1/2? [#permalink]

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New post 22 Feb 2017, 10:32
ScottTargetTestPrep wrote:
AbdurRakib wrote:
Which of the following fractions is closest to \(\frac{1}{2}\)?
A) \(\frac{4}{7}\)
B) \(\frac{5}{9}\)
C) \(\frac{6}{11}\)
D) \(\frac{7}{13}\)
E) \(\frac{9}{16}\)


To determine which answer choice is closest to 1/2, we can subtract 1/2 from each answer choice. The difference that is closest to zero will indicate the fraction that is closest to 1/2.

A) 4/7

4/7 - 1/2 = 8/14 - 7/14 = 1/14

B) 5/9

5/9 - 1/2 = 10/18 - 9/18 = 1/18

C) 6/11

6/11 - 1/2 = 12/22 - 11/22 = 1/22

D) 7/13

7/13 - 1/2 = 14/26 - 13/26 = 1/26

E) 9/16

9/16 - 1/2 = 9/16 - 8/16 = 1/16

Since 1/26 is closest to zero, 7/13 is closest to 1/2.

Answer: D


amazing explanation. thank you.

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I simply thought of fractions as pieces of pie.
I want 1/2 of pie. What is the closest to that? I estimate that most of the fractions are close to 1/2.
If I divide pie in 7 parts and take 4 I will get less then if I divide pie in 13 parts and take 7. So I picked D.

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I approached it in this way:
1/2, each of the answer choices is 1/2 + something, so: 0,5/7, 0,5/9, 0,5/11, 0,5/13, 1/16=0,5/8, the smallest is 0,5/13
Hence D

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Re: Which of the following fractions is closest to 1/2? [#permalink]

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AbdurRakib wrote:
Which of the following fractions is closest to \(\frac{1}{2}\)?
A) \(\frac{4}{7}\)
B) \(\frac{5}{9}\)
C) \(\frac{6}{11}\)
D) \(\frac{7}{13}\)
E) \(\frac{9}{16}\)


OG 2017 New Question

Please Explain



there is one property:
If factor (suppose a/b) is between zero and one then, (a/b)<((a+1)/b+1))<((a+2)/b+2))<........<1
Means if we add one in numerator and denominator it will tend toward 1.

Now come to questiom
if we divide 1/2 by all answer choices one by one, The no. which will be closer to 1/2, will give no. closer to 1 once divided by option choices.

1.) 7/8
2.)9/10
3.)11/12
4.) 13/14
5.)16/18=8/9

So 13/14 is relatively closer to 1, hence, answer will be option (d)

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Re: Which of the following fractions is closest to 1/2? [#permalink]

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New post 21 Mar 2017, 09:31
RichaChampion wrote:
chetan2u wrote:
AbdurRakib wrote:
Which of the following fractions is closest to \(\frac{1}{2}\)?
A) \(\frac{4}{7}\)
B) \(\frac{5}{9}\)
C) \(\frac{6}{11}\)
D) \(\frac{7}{13}\)
E) \(\frac{9}{16}\)


OG 2017 New Question

Please Explain


Hi,

Do not waste time in calculating..
look at the similarity in all choices- they all EXCEPT E are of type \(\frac{x}{2x-1}\)...
and \(\frac{x}{2x-1}\) for an integer x is always >1/2 and will become lesser in value , that is will keep getting closer to 1/2 with higher VALUE of x..

you can check in two ways-
1) for x as 1 or 2 or 3..
x=1, \(\frac{x}{2x-1}\) = 1..
x=2, \(\frac{x}{2x-1}\) = 2/3..
x=3, \(\frac{x}{2x-1}\) = 3/5..
so each successive value is smaller than previous one..

2) simplify the term..- IMPORTANT
\(\frac{x}{2x-1}\)=\(\frac{1}{(2x-1)/x}\) = \(\frac{1}{(2x/x-1/x)}\) = \(\frac{1}{(2-1/x)}\)
so the denominator should be closer to 2 so \(2-\frac{1}{x}\) should be close to 2, and therefore x should be MAX to make \(\frac{1}{x}\) less

Therefore, here 7 is the highest value in the four choices so D is the closest to 1/2.

lets see E... It is the TYPE \(\frac{x}{2(x-1)}\)... clearly since 7 and 9 are close to each other but denominator in E is reduced by a larger number,
D is the answer


Fantastic Explanation. I wish I could give you 2 Kudos.



Kudos for your concept! You made me write my first comment in gmatclub!!
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Re: Which of the following fractions is closest to 1/2? [#permalink]

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New post 21 Mar 2017, 23:35
Sometimes it is easier to go directly with calculation instead of try with equations.

(1/2) - each option. In less than 2 minutes you will find that the smallest difference is (1/2) - (7/13)
Answer is D
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Re: Which of the following fractions is closest to 1/2? [#permalink]

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New post 15 Jun 2017, 21:32
Swat824 wrote:
Any simple and quick method to calculate?




How I picked the correct answer in 1 min is :

Qn> 1/2

Ans>
1. 1/1/75
2. 1/1.8
3. 1/1.83
4. 1/1.85
5. 1/1.7

Among all 1.85 is closest to 1/2 hence D is answer .

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Re: Which of the following fractions is closest to 1/2? [#permalink]

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New post 17 Aug 2017, 11:03
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ANSWER IS D

i have 1 very nice way to solve
multiply all by 2 and write in form of 1+ something

like 4/7 x 2 = 8/7 = 1+1/7
now consider only latter part like 1/7

now for all when u do same you will get

1+1/7
1+1/9
1+1/11
1+1/13
1+2/16 = 1+1/8

now here 13 is max so we have selected it

if the number had been 1/2 exact then multiplying by 2 would have yielded 1 exactly and writing in same form 1+0

now see 0 part for the number whose denominator is max will be closer to zero

hence we have selected 13.

Give Kudos If you like this method, i have seen no body has used this.

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Re: Which of the following fractions is closest to 1/2?   [#permalink] 17 Aug 2017, 11:03
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Which of the following fractions is closest to 1/2?

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