Aptitude - Decimal Fraction - Discussion

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).

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.

We can directly opt the first big fraction.

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.

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.

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.

Please explain answer.