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

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15 Jun 2016, 01:01

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D

E

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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) \(\frac{9}{16}\)

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) \(\frac{9}{16}\)

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
_________________

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

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01 Aug 2016, 16:30

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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) \(\frac{9}{16}\)

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.
_________________

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) \(\frac{9}{16}\)

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.

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
_________________

Scott Woodbury-Stewart Founder and CEO

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

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06 Dec 2016, 08:34

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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) \(\frac{9}{16}\)

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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Abhishek....

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

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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.

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

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24 Feb 2017, 12:13

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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.

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

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11 Mar 2017, 13:16

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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

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

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13 Mar 2017, 10:02

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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) \(\frac{9}{16}\)

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)

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

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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) \(\frac{9}{16}\)

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!!
_________________

------------------------------ "Trust the timing of your life"

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

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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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