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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) $$\frac{9}{16}$$

OG 2017 New Question
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Re: Which of the following fractions is closest to 1/2?  [#permalink]

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66
37
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.

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

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33
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

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

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66
14

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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2
1
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

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,

Fantastic Explanation. I wish I could give you 2 Kudos.
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Posts: 8336
Re: Which of the following fractions is closest to 1/2?  [#permalink]

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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

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,

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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3
0.5/7, 0.5/9, 0.5/11, 0.5/13, 0.5/8 .. are the differences.
Pick 0.5/13 Board of Directors D
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Re: Which of the following fractions is closest to 1/2?  [#permalink]

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14
1
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

$$\frac{1}{2}$$ = 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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2
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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Re: Which of the following fractions is closest to 1/2?  [#permalink]

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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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1
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

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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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

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,

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

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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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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

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,

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

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

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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.

0

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

Sent from my SAMSUNG-SM-G920A using GMAT Club Forum mobile app
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Re: Which of the following fractions is closest to 1/2?  [#permalink]

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2
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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8
Top Contributor
2
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

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

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1
sahilvijay wrote:

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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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

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,

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
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