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www.talentsprint.com TalentSprint©2016
Number system
1.
When sum and difference of two numbers (X and Y) are given, then X = (sum + difference)/2 Y = (sum + difference)/2 2.
Difference between two digits of two digit number is = (Difference in srcinal and interchanged number)/9 3.
Sum of first n odd numbers is n
2
4.
Sum of first n even numbers n(n+1) 5.
Sum of squares of first n natural numbers is n(n+1)(2n+1)/6 6.
Sum of cubes of first n natural numbers is [n(n+1)/2]
2
Algebra
1.
(a+b)
2
= a
2
+ 2ab + b
2
2.
(a-b)
2
= a
2
- 2ab + b
2
3.
(a+b)
2
= (a-b)
2
+ 4ab 4.
(a-b)
2
= (a+b)
2
- 4ab 5.
(a+b)
3
= a
3
+b
3
+3ab(a+b) = a
3
+b
3
+3a
2
b+3ab
2
6.
(a-b)
3
= a
3
- b
3
-3ab(a-b) = a
3
- b
3
- 3a
2
b + 3ab
2
7.
a
3
+b
3
=(a+b)
3
- 3ab(a+b) 8.
a
3
- b
3
=(a-b)
3
+ 3ab(a-b)
www.talentsprint.com TalentSprint©2016
9.
a
2
-b
2
= (a-b)(a+b) 10.a
3
+b
3
= (a+b)(a
2
-ab+b
2
) 11.a
3
- b
3
= (a-b)(a
2
+ab+b
2
) 12.a
m
x a
n
= a
m+n
13.a
m
/ a
n
= a
m
–
n
14.(a/b)
(m / n)
=(b/a)
-(m / n)
15.a
m
/ b
–
n
= a
m
x b
n
Ratio and Proportion
1.
If four quantities are in proportion, then Product of Means = Product of Extremes. In the proportion a:b::c:d, we have bc = ad 2.
If a:b::c:x, x is called the fourth proportional of a, b, c. a/b = c/x or, x = bc/a. 3.
If two numbers are in a:b ratio and the sum of these numbers is x, then numbers will be ax/(a+b) and bx/(a+b) respectively 4.
If three numbers are in the ratio a:b:c and the sum of these numbers is x, then these numbers will be ax/(a+b+c), bx/(a+b+c) and cx/(a+b+c) respectively 5.
The ratio of two numbers is a : b. If n is added to each of these numbers, the ratio becomes c : d. The two numbers will be given as an(c-d)/(ad-bc) and bn(c-d)/(ad-bc) respectively
www.talentsprint.com TalentSprint©2016
6.
The ratio of two numbers is a : b. If n is subtracted from each of these numbers, the ratio becomes c : d. The two numbers are given as an(d-c)/(ad-bc) and bn(d-c)/(ad- bc) respectively 7.
If the ratio of two numbers is a: b, then the numbers that should be added to each of the numbers in order to make this ratio c:d is given by (ad-bc)/(c-d) 8.
If the ratio of two numbers is a:b, then the number that should be subtracted from each of the numbers in order to make this ratio c:d is given by (bc-ad)/(c-d) 9.
The CP of the item that is cheaper is CP
cheaper
and the CP of the item that is costlier (dearer) is CP
Dearer
. The CP of unit quantity of the final mixture is called the Mean Price and is given by
=
ℎ
−
−
ℎ
Percentage
1.
a % of b = a x b/100 2.
If A is x% more than B, then B is less than A by
%100100
x x
3.
If A is x% less than B, then B is more than A by
%100100
x x
4.
If A is x% of C and B is y% of C, then A = x/y
B
www.talentsprint.com TalentSprint©2016
5.
If two numbers are respectively x% and y% more than a third number, then first number is
%100100100
y x
of the second number and the second number is
%100100100
x y
of the first number 6.
If two numbers are respectively x% and y% less than a third number, then the first number is
%100100100
y x
of the second number and the second number is
%100100100
x y
of the first number 7.
If the price of a commodity decreases by P %, then the increase in consumption so that the expenditure remains same is
%100100
P P
8.
If the price of a commodity increases by P%, then the reduction in consumption so that the expenditure remains same is
%100100
P P
9.
If a number is changed (increased/decreased) successively by x% and y%, then net% change is given by [x+y+(xy/100)]%, which represents increase or decrease in value according as the sign is positive or negative 10.If two parameters A and B are multiplied to get a product and if A is changed by x% and another parameter B is changed by y%, then the net% change in the product (A
B) is given [x+y+(xy/100)]% 11.In an examination, the minimum pass percentage is x%. If a student secures y marks and fails by z marks, then the maximum marks in the examination is 100(y+z)/x

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