Which of the following is greater than 2/3?

Like with many other questions, this question can be done in more than one way. I will tell my approach here:

Firstly, 2/3 is 0.6666(non-terminating decimal) or 0.67(approx.) by rounding off.

Next step would be to look at answer choices and eliminate the easiest ones.

13/27 can be eliminated right away since it is less than half(1/2). So, D is out.
C and E can be eliminated since they will come to 0.6 and 0.625.

A is slightly tricky because the value will come to 0.66. But this can be eliminated too since the decimal places terminate.

Hence, (B) is the answer.

While selecting A and B, alternative approach would be to equate the denominators and compare.

Which of the following is greater than 2/3?

A. 33/50
B. 8/11
C. 3/5
D. 13/27
E. 5/8

Sol: Which of the following is greater than 2/3 or 0.6666
A=0.66
C=0.6
D<0.5
E=0.625.
Ans B= 0.7272

2/3 corresponds to 0.67

A) Equal to 0.66 - Eliminated
B) 0.11 corresponds to 0.909 hence 8/11 corresponds 0.7272

I should stop here. Answer is B.

Find common denominator:

A: 33/50 & 2/3 => 99/150 & 100/150 NO
B: 8/11 & 2/3 => 24/33 & 22/33 YES Stop here. Solution is B.

Although Bunuel's approximation approach is a good way to solve this, an alternative is doing cross multiplication.
if 33/50 > 2/3, then 33*3 > 2*50 and so on. As soon as we check B we get our answer.

Some choices are obviously wrong. For the others, simply cross multiply and apply the product to the numerator.

\(\frac{8}{11}>\frac{2}{3}?\)

\((8*3=24)>2*11=22)\)

Relation between \(\frac{8}{11}\) and \(\frac{2}{3}\) may be found as follows.

Since, \(\frac{11}{8}\) \(<\) \(\frac{12}{8}\)

Or, \(\frac{8}{11}\) \(>\) \(\frac{8}{12}\)

Or, \(\frac{8}{11}\) \(>\) \(\frac{2}{3}\)

Multiple fractions with LCM of denominator to get the answer

This way we get rid off fractions / decimals & compare direct integers

Option A

\(\frac{2}{3} & \frac{33}{50}\)

LCM of 3 & 50 = 150

\(\frac{2}{3} * 150 = 100 ..................&................... \frac{33}{50} * 150 = 99\) ......... Ignore

Option B

\(\frac{2}{3} & \frac{8}{11}\)

LCM of 3 & 11 = 33

\(\frac{2}{3} * 33 = 22 ............... & ............. \frac{8}{11}* 33 = 24\) ................... Answer

Answer = B

I barely did any math for that question.

It is easy to remember that 2/3 is 0.6666...

Looking at the answer choices:
E:5/8 is almost 4/8 which is 0.5. --> eliminate
D:13/27 is almost 13/26 which is 0.5 --> eliminate
C: 3/5 is almost 3/6 which is 0.5, it is also easy to remember that it is 0.6 --> eliminate

What is left is A and B.
I calculated B first. 8/11 Turns out to be 0.7something --> Tick B

Hi here are my two cents for this question

I have one useful tip to share, fractions to % to decimal conversion table. I have attached the conversion table

\(\frac{1}{2}\) = (50%, .05) ,\(\frac{1}{3}\) = (33.3%, .3333) ,\(\frac{1}{4}\) = (25%, .25) ,\(\frac{1}{5}\) = (20%, .2) \(\frac{1}{6}\) = (16.66%, .1666) ,\(\frac{1}{7}\) =(14.28%, .1428) ,\(\frac{1}{8}\) =(12.5%, .125) ,\(\frac{1}{9}\) = (11.1%, .111) ,\(\frac{1}{10}\) = (10%,.1),\(\frac{1}{11}\) = (9.1%, .0909) ,\(\frac{1}{13}\) = (7.7%, .077) ,\(\frac{1}{17}\) = (5.9%, .059) ,\(\frac{1}{19}\) = (5.3%, .053) ,\(\frac{1}{23}\) = (4.3%, .0435) ,\(\frac{1}{29}\) = (3.40%, .0345) ,\(\frac{1}{31}\) = (3.2%, .0323)

How do we use it

So we have 2/3 is 66.67%

We know that , Since \(\frac{1}{5}\)= 20% then we can say \(\frac{1}{50}\)= 2% how ( \(\frac{1}{50}\) can be written as \(\frac{1}{5}\) * \(\frac{1}{10}\) = .2 * .1 = .02 which is 2% but i generally do it as 20 /10 = 2 % then \(\frac{33}{50}\) will be 66%

We know that, Since \(\frac{1}{11}\)= 9% approx then we can say \(\frac{8}{11}\)= 72% approx ( multiply 8*9=72) hence \(\frac{8}{11}\)= 72 %

We know that , Since \(\frac{1}{5}\)= 20% then we can say \(\frac{3}{5}\)= 60% ( multiply 20*3 = 60) hence \(\frac{3}{5}\)= 66 %]= 60 %

We know that \(\frac{13}{26}\)= 50 %,then \(\frac{13}{27}\)< \(\frac{13}{26}\) so we can say that \(\frac{13}{27}\) < 50 %

We know that Since \(\frac{1}{8}\)= 12.5% then we can say \(\frac{5}{8}\)= 62.5% ( multiply 12.5*5 = 62.5) hence \(\frac{5}{8}\)= 62.5 %,


So only value greater that 66.67 % is 72% which is option B

How is this method useful, is it worth spending some time on it ,
Many questions esp comparison, conversion and average will require your knowledge of conversion from fractions to decimals to percentage .

This will help in Ratios/ Interest/ Averages/ Time Distance/ Time Work

Which of the following is greater than 2/3?

A. 33/50
33/50 * 3/2 <99/100<1; 33/50 < 2/3
B. 8/11
8/11 * 3/2 = 24/22>1; 8/11 > 2/3
C. 3/5
3/5 * 3/2 = 9/10 < 1; 3/5 < 2/3
D. 13/27
13/27 * 3/2 = 39/54 < 1; 13/27< 2/3
E. 5/8
5/8 * 3/2 = 15/16 < 1; 5/8 < 2/3

IMO B

If we take\( \frac{2}{3}\) and \(\frac{8}{11}\) we see that if we multiply both fractions by 11/3 we get 22 in place of \(\frac{2}{3}\) and 24 in place of \(\frac{8}{11}\). Since 22 < 24 we can conclude that \( \frac{2}{3}\) < \(\frac{8}{11}\)


But I want to know more about a particular thought process that highlights more on the concept behind the above method.

Lets take 2 and 8. Now we know that 2 < 8. Now let's multiply LHS by 11 and RHS by 3 so we get
LHS - 2 * 11
RHS - 8 * 3

The inequality sign does not change. We had 2 < 8 and we still have 2 * 11 < 8 * 3. Now, let's multiply both sides by 3/11 we get \(\frac{2}{3}\) < \(\frac{8}{11}\)

So what I am observing is that when we have 2 (and despite of multiplying it by 11) and 8 (and despite of multiplying it by 3 which is way less than 11) are inequality sign does not change.

Bunuel could you like help me understand how these numbers are in play? Like how even after multiply one side by a larger value the inequality sign does not change OR when we divide one side by a larger number the sign still remains the same

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