Aptitude - Decimal Fraction - Discussion

@Shahid your cross multiplication method is great.

The fraction whose numerator after cross multiplication gives the greater value is greater.

Here take the 1st two 6/7 and 5/6
6*6>5*7.

From given options option D only satisfy this...So ans is D.

Take LCM for the Decimals: 3, 5, 7, 5, 6, 7.
The LCM is 3*5*6*7.

Now multiply each number with (2*3*5*7)/(3*5*6*7).

We will get the numerator values as 70, 84, 90, 168, 175, 180.

No the decreasing order is : 6/7, 5/6, 4/5,3/7,2/5, 1/3.

By carefully watching this particular problem, we can observe that the option A,B & C numerators are in ascending order whereas the option D numerator are given in descending order.

Another simple method:

Lets option A that is:
1/3 , 2/5 , 3/7 , 4/5 , 5/6 ,6/7

Take the LCM of all the denominators which is
3,5,7,5,6,7

LCM is 210
make the denominator 210. The fraction which is
70/210 , 84/210 , 90/210 ,168/210 , 175/210 ,180/210

now we can easily compare the values because all the denominator is same.
So the decending order is:

180/210 , 175/210 ,168/210 ,90/210 ,84/210 , 70/210.

i.e.

6/7 , 5/6 , 4/5 , 3/7 , 2/5 , 1/3.

This is the answer, it is very short to solve, hope now you will got it.

We can directly opt the first big fraction.

Another shortcut to solve this que is to multiply numerator by 100 and simply dividing it with denominator like this:

100/3=33.3.
200/5=40.
300/7=42.8.
400/5=80.
500/6=83.3.
600/7=85.6.

Then we have the answer.

85.6>83.3>80>42.8>40>33.3.

Answer is 6/7 > 5/6 >4/5 > 3/7 > 2/5 > 1/3.

1/3 = 5/15.
2/5 = 6/15.

So option 1,2 & 3 will be wrong because of 5/15<6/15(not in descending order).

And for 4th one:

6/7=36/42.
5/6=35/42(so 6/7>5/6).

5/6=25/30.
4/5=24/30(so 5/6>4/5).

4/5=28/35.
3/7=15/35(so 4/5>3/7).

3/7=15/35.
2/5=14/35(so 3/7>2/5).

2/5=6/15.
1/3=5/15(so 2/5>1/3).

1/3 = 0.33
2/5 = 0.40
3/7 = 0.42
4/5 = 0.80
5/6 = 0.83
6/7 = 0.85

Convert all into like fractions by taking their lCM, their LCM comes out to be 210 and then convert them according to their LCM and then we get the answer.