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

I have a very different method to solve this question (probably the fastest )

Approach: To be equal to \(\frac{1}{2}\) denominator has to be twice of the numerator
We can notice that in first four options denominator is one less that twice of numerator ( that means each fraction is greater than \(\frac{1}{2}\) )
So in these four option as the value of numerator will increase fraction will tend closer to \(\frac{1}{2}\) ( for example if there would be another option 50/99 it will be even closer to \(\frac{1}{2}\) )
Hence among first four D is the closest to \(\frac{1}{2}\). Between D and E, since D is smaller than E, hence it is closer to \(\frac{1}{2}\).

Video solution from Quant Reasoning:

Hi ScottTargetTestPrep

Could you explain the logic behind the strategy that you showed here? Will this work for any "closest to" questions?

Thanking you in advance!

In this question we can bring the idea of distance and measure the distance between the options and 1/2 as one of the strategies to answer the question.
So how should a SMART & LOGICAL GMAT aspirant think on this question?
The fraction closest to 1/2 will have the least distance from 1/2. Let me measure the distance of the answer options from ½.
A 4/7
Distance of 4/7 from 1/2 = 4/7 - 1/2
= 1/14

B 5/9
Distance of 5/9 from 1/2 = 5/9 - 1/2
= 1/18

C 6/11
Distance of 6/11 from 1/2 = 6/11 - 1/2
=1/22

D 7/13
Distance of from 7/13 from 1/2 = 7/13 - 1/2
= 1/26

E 9/16
Distance of 9/16 from 1/2 =9/16 - 1/2
= 1/16

All the fractions have the same numerator of 1 and hence the fraction with the largest denominator will carry the smallest value.
Thus 1/26 has the smallest value, is closest to 0 and hence 7/13 is the answer choice that is closest to 1/2 .
Mark D as the correct answer.

Devmitra Sen
GMAT Mentor
_________________

A- 0.57
b- 0.55
C- 0.54
D-0.53
E- O.56

The closest value to 1/2 i.e. 0.50 is D i.e. 0.53 or 7/13

I haven't looked at every solution listed, but all that I've seen are computationally heavy. Who wants to deal with that?!?
Instead, let's just look at how far each answer choice is from half.

A) \(\frac{4}{7}\) = \(\frac{8}{14}\), so \(\frac{1}{14}\) away
B) \(\frac{5}{9}\) = \(\frac{10}{18}\), so \(\frac{1}{18}\) away
C) \(\frac{6}{11}\) = \(\frac{12}{22}\), so \(\frac{1}{22}\) away
D) \(\frac{7}{13}\) = \(\frac{14}{26}\), so \(\frac{1}{26}\) away
E) \(\frac{9}{16}\), so \(\frac{1}{16}\) away

\(\frac{1}{26}\) < \(\frac{1}{22}\) < \(\frac{1}{18}\) < \(\frac{1}{16}\) < \(\frac{1}{14}\)

Answer is D

Alternatively, if you have relatively strong fraction skills, then you know that for answer choices with odd denominators (A-D), as the denominator gets larger, the choice gets closer to half. The outlier is \(\frac{9}{16}\) because it has an even denominator, so so you just need to compare \(\frac{7}{13}\) to \(\frac{9}{16}\).

D) \(\frac{7}{13}\) = \(\frac{14}{26}\), so \(\frac{1}{26}\) away
E) \(\frac{9}{16}\), so \(\frac{1}{16}\) away

\(\frac{1}{26}\) < \(\frac{1}{16}\)
Answer is D

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

Answer - D

A. 4/7 is 0.5/7 away from 1/2
B. 5/9 is 0.5/9 away from 1/2
C. 6/11 is 0.5/11 away from 1/2
D. 7/13 is 0.5/13 away from 1/2
E. 9/16 is 1/16 away from 1/2 = 0.5/8 away from 1/2

0.5/13 is the smallest of these numbers

Hence the answer is D

Posted from my mobile device
_________________

Hey ,
how much time did u take while solving this? Because I also used this very same method but it took me 4 minutes

If you are able to ace the conversions its a 1 minute problem.

For me, I multiplied each fraction by 2, something similar to the bow tie method.
This made all the differences between them and \(\frac{1}{2}\) which had become 1 all the more obvious.

A) \(\frac{4}{7}\) became \(\frac{8}{7}\)

B) \(\frac{5}{9}\) became \(\frac{10}{9}\)

C) \(\frac{6}{11}\) became \(\frac{12}{11}\)

D) \(\frac{7}{13}\) became \(\frac{14}{13}\)

E) \(\frac{9}{16}\) became \(\frac{18}{16}\)

Hence it became clear that D was the answer since the fraction \(\frac{14}{13}\) would be \(\frac{1}{13}\) greater than 1, as compared to the other fractions in options A, B, C, E.

Hope this helps!!

Hey try this method out- doing the reciprocal of each and seeing which one is closest to 2:

https://youtu.be/flXaClyurKI