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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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New post 15 Jun 2016, 01:01
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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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Re: Which of the following fractions is closest to 1/2?  [#permalink]

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New post 05 Dec 2016, 18:22
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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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New post 15 Jun 2016, 06:41
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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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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]

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New post 01 Aug 2016, 16:30
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1
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
6
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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Re: Which of the following fractions is closest to 1/2?  [#permalink]

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New post 21 Aug 2016, 03:10
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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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New post 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) \(\frac{9}{16}\)


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

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New post 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) \(\frac{9}{16}\)


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
3
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
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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 14 Nov 2017, 20:25
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


Could you please clarify how you deal with A/C E using the first method you proposed?

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

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New post 16 Nov 2017, 23:08
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
0

How do we know those closest to zero. Can you illustrate with a diagram please? Thanks


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

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New post 17 Nov 2017, 04:09
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There are 4 ways to solve the problem (Which is also basically a summary to above explanations):
1. Calculate the decimal and find the answer: This should be used when the numbers are small or calculation is easy.
2. Subtract the number (1/2 in this case) one by one with all the options to find the distance between those numbers, the smallest value would mean the closest number. (My favorite)
3. Use algebra to solve the arithmetic: To be used cautiously after identifying the pattern enabling algebraic equation formation.
4. Divide the options with the given number to see which number is closest to 1 (1 because we will also be dividing the given number, 1/2 in this case, to the same number)
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Re: Which of the following fractions is closest to 1/2?  [#permalink]

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New post 10 Jan 2018, 12:49
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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


Let's check the answer choices...

A) 4/7
3.5/7 = 1/2. So, 4/7 is 0.5/7 away from 1/2
Since 0.5/7 = 1/14, we can say that 4/7 is 1/14 away from 1/2

B) 5/9
4.5/9 = 1/2. So, 5/9 is 0.5/9 away from 1/2
Since 0.5/9 = 1/18, we can say that 5/9 is 1/18 away from 1/2

C) 6/11
Using the same logic, we can say that 6/11 is 1/22 away from 1/2

D) 7/13
Likewise, 7/13 is 1/26 away from 1/2

E) 9/16
And 9/16 is 1/16 away from 1/2

Of the BLUE fractions, 1/26 is the SMALLEST
So, the correct answer is D

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

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New post 22 Mar 2018, 06:51
sahilvijay wrote:
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.

Thank you!
I guess this is the best way to do it without wasting time
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Which of the following fractions is closest to 1/2?  [#permalink]

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New post 18 Aug 2018, 23:01
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



Hi chetan2u,
would like your feedback on this question and approach
\(\frac{4}{7}\) > \(\frac{4}{8}\)
\(\frac{5}{9}\) > \(\frac{5}{10}\)
\(\frac{6}{11}\) > \(\frac{6}{12}\)
\(\frac{7}{13}\) > \(\frac{7}{14}\)
\(\frac{9}{16}\) > \(\frac{9}{18}\)

Now if we see in \(\frac{4}{7}\) & \(\frac{4}{8}\) denominator increases by 14%
Similarly
In \(\frac{5}{9}\) & \(\frac{5}{10}\) denominator increases by 11%
In \(\frac{6}{11}\) & \(\frac{6}{12}\) denominator increases by 9%
In \(\frac{7}{13}\) & \(\frac{7}{14}\) denominator increases by 7%
In \(\frac{9}{16}\) & \(\frac{9}{18}\) denominator increases by 12.5%

Since we know as if numerator is same, denominator increases the fraction decreases further. So by this we can say Option D is much closer to \(\frac{1}{2}\)

Awaiting for new learning.
Probus
_________________
Probus

~You Just Can't beat the person who never gives up~ Babe Ruth
GMAT Club Bot
Which of the following fractions is closest to 1/2?   [#permalink] 18 Aug 2018, 23:01

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

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