Data Interpretation Formulas
We use some aptitude formulas in solving DI questions. Most Common questions are asking in this format from Percentages
1) X is what % of y that means x/y * 100.
Eg: 72 is what % of 360 = [72/360]×100 =20%
2) What percentage is x of y? I.e. x/y * 100.
3) X is what percent more than y = xy/y * 100
4) X is what percent less than y = yx/y * 100
5) Percentage change between two particular values = [final – initial/ initial] * 100
Memorize some fractional values and percentage values.


 1/2 = 50%
 1/3 = 33.33%
 ¼ = 25%
 1/5 = 20%
 1/6 =16.66%
 1/7 = 14.28%
 1/8 = 12.5%
 1/9 = 11.11%
 1/10 = 10%
 1/11 =9.09 %
 1/12 = 8.33%
 1/13 = 7.69%
 1/14 = 7%
 1/15 = 6.66%
 1/16 = 6.25%
 1/17 = 5.88%
 1/18 =5.55%
 1/19 = 5.26%
 1/20= 5%
 5%= 1/20 = 0.05
 10% =1/10 =0.1
 15% =3/20
 20% = 1/5
 25% = ¼
 30% =3/10
 40% =2/5
 50% =1/2
 55%=11/20
 60% = 3/5
 70% = 7/10
 75% = 3/4
 80% = 4/5
 90% = 9/10
 100%=1
 6 ¼ % = 1/6
 12 ½ % = 1/8
 16 2/3 % = 1/6
 33 1/3 % = 1/3
 66 2/3 % =2/3
 125% =5/4
 150% = 3/2

Comparison of two fractions:
Eg: Compare, 3/4, and 1/4.
By seeing itself, we can say 3/4 is big. Implement here our logic of cross multiplication of two fractions.
¾ ¼ we get, 12 and 4 we know 12 > 4 so we can say ¾ >1/4
Apply the same logic big fractions it’s very simple and takes less time.
Formulas on Averages:
 Average = sum of elements/ no. of elements (or) (a1 + a2 + a3 + a4 +………… an)/n
 Sum of first n odd numbers: 1 + 3 + 5 + ………… + (2n1)= n^{2}
 Sum of first n even numbers: 2 + 4 + 6 + …………+ 2n = n (n+1).
 Sum of first n natural numbers: 1+2+3 +4 + ……..+n = n(n+1)/2.
 Sum of squares of first n natural numbers: 1^{2} + 2^{2} + 3^{2} + 4^{2} + 5^{2} + 6^{2} + …………+n^{2 }= [n (n+1)(2n+1)]/6.
 Sum of cubes of first n natural numbers: 1^{3} + 2^{3}+3^{3} + 4^{3} + …… + n^{3 }= [n(n+1)/2]^{2}