Given below are
Shortcut Formulae frequently used in solving Aptitude Question Papers
1.
1+2+3+4…. +n = n (n+1) / 2
2.
12+22+32…. +n2
= n (n+1)(2n+1) / 6
3.
13+23…+n3 = [n2(n+1)2]
/ 4
4.
1+3+5…. 2n-1= n2
5.
Every prime number greater than 3 can be written
using the formula (6k+1) or (6k-1)
6.
Number of factors present in a number is given as
(p+1)(q+1)(r+1)…Where N=(ap)+(bq)+(cr)…
Where a, b,
c are prime numbers and p, q, r are positive numbers
In the same way sum of all factors=[(a(p+1) / (a-1)][(b(q+1)
/ (b-1)]…
7.
If there is P volume of pure
liquid initially in each operation and Q volume is taken out and replaced by Q
volume of water then at the end of n such operations, the concentration k is
given as K = [(P-Q) / P]n
8.
If successive increase in percentage is given p%,
q%, r% then effective % increase is given as
[(100+p)/100][(100+q)/100][(100+r)/100]-1}*100
9.
If an article is sold such that a article has a
profit of p% on one and loss of p% on other then we have the net result to be
loss and the loss percent is (p2) / 100
10.In a party each members shakes
hand with other member. If total number of Hand shakes were N then Number of
members in Party = Larger nearest whole squared number to N. E.g.: N=210,
Larger nearest Square to 210 is 225. So Members = (225)1/2 = 15.
11.
If a person goes at X km/hr in forward direction and
returns back at Y km/hr then the average speed is 2XY / (X+Y)
12.
If a person traveling between two points reaches p
hours late traveling at u kmph and reaches early traveling at v kmph, the distance
between two points is [vu(p-q)] / (v-u)
13.
If we have a term of this sort “Apple” the number of
possible arrangements possible are
5! /2!
14.
Number of ways of selecting one or more items from n
given items is (2n)-1
15.
If we are given problems based on number of squares
possible all together then we have a generalized short cut method of doing it
Eg:
given a chess board (8*8) how many squares can be formed the solution is (82)
+ (72) + (62) + (12)
19.
If a problem is given with some sequence (2, 4, 6...)And
(3, 6, 9..) along with just 2 operations possible the answer is the number of
Square terms.
20.
In calendars the first day of the year after the
leap year will be in this manner. If Jan 1 of 2006 was on Sunday then Jan 1 of
2005 will be on Saturday and that of Jan 1 of 2004 will be on Thursday this is
because 2004 is a leap year so there is an extra gap of one.
21.
Given a circular track and both the riders ride in
the same direction then the first time they meet is given as L / (a-b) for
opposite direction it is L / (a+b)
Where L is the
length of the track and a, b the speed of riders.
22.
If A can complete a work in a days and B can
complete it in b days then A and B working together can complete it in ab /
(a+b)
23.
If A can complete a work in a days and B can complete
it in b days and C can complete it in c days then all working together can
complete it in abc / (ab+bc+ca)
24.
If two trains start at the same time from two points
A and B towards each other and after crossing they take x and y hrs to reach B
and A respectively then (A speed): (B speed)=[(x)1/2] : [(y)1/2]
25.
If Length of a rectangle is increased by I1% and
Breadth is increased by I2% then The Percentage increase in Area is I1+I2+[(I1*I2) / 100]
26.
If Length of a rectangle is increased by I% and
Breadth is decreased by D% then Percentage increase or decrease in Area is
I-D-[(I*D) / 100]
27.
If Length of a rectangle is decreased by D1% and
Breadth is decreased by D2% then Percentage increase or decrease in Area
is D1-D2+[(D1*D2) / 100]
28.
If A is R% more than B, the Percentage B less than A
is (100*R)/(100+R)
29.
If A is R% less than B, the Percentage B more than A
is (100*R)/(100-R)
34.
How many numbers are divisible by n between A and B.
Solution is (A / n) – (B / n)
30.Let the present population of a
town be P with an annual increase of R% then:
Population
after n years = P (1+R/100)n
Population n
years ago = P / (1+R/100)n
30.
If the price of a commodity increases by R% then the
reduction in consumption so as not to increase the expenditure is (100*R) /
(100+R)
31.
If the price of a commodity decreases by R% then the
increase in consumption so as not to decrease the expenditure is (100*R) /
(100+R)
32.
Let the present value of a machine be P. Suppose
depreciates at the rate of R% per annum. Then
Value of Machine
after n years = P(1-R/100)n
Value of Machine n years
ago = P / (1-R/100)n
35.
In a examination A% registered Candidates are absent
and B% failed out of those who are present. If successful Candidates are X
then.
Number of
Registered Candidates = (100*100*X ) / [(100-A)(100-B)]
36.
If a number divisible by D1 leaves a remainder R1, Then the same number when
divided by D2 the remainder
will be the remainder got in scomputing R 1 / D2.
37.
A reduction of A% in the price of a commodity
enables the purchaser to obtain C kgs more for Rs. B. Then the price per kg of
the commodity before reduction is (A*B) / [(100-A)*C]
38.
When the price of a commodity decreased by A%, the
sale increased by B%. The effect on Sale
39.
A number should be subtracted from numbers a, b, c,
d so that the remainders may be proportional. Then the number is (AD-BC) /
[(A+D)-(B+C)]
40.
If N men takes X days to complete a work if M men
left the team they complete the work in Y days. Then the number of men Left the
team is M = [N(Y-X)] / Y.
41.
If the Average age of N members is A. If M members
are added to the team the Average becomes less by a value B. Then the Average
age of Newcomers is A – [(N/M + 1) * B]
42.
If A number of men or B number of women can complete
a work in X days. Then time taken to complete the same work by a number of men
and b number of women is X / (a/A + b/B)
43.
If P1 number of pipes working H1 number of hours can fill a tank in D1 days. Then number of hours
H2 needed for P2 number of pipes to fill same
tank in D2 number of days
is H2 = (P1 * H1 * D1) / (P2 * D2)
44.
A and B together can do a piece of work in X days. A
can do it alone in Y days.Then number of days needed by B to finish the work
alone is XY/(Y-X)
45.
Two pipes can fill a tank in X hours and Y hours
respectively. The third pipe can empty it in Z hours. Then the number of hours
needed to fill the tank if all pipes are opened simultaneously is XYZ / (YZ +
ZX –XY)
46.
A train with a speed of X kmph starts from a place.
Another train starts from the same place after t hours with a speed of Y kmph .
Then
The time in which they meet is (X*t)
/ (Y-X)
The distance taken to meet is Y(X*t) /
(Y-X)
47.
If a train passes the station of length X metres in
T1 seconds but a
person in T seconds. Then the length of the Train is (X*T1) / (T1-T)
48.
If the Cost price of X articles is equal to the
Selling price of Y articles. Then the Gain Percent is [100(X-Y)] / X
49.
By selling B items one gains the selling price of A
items. Then the Gain percent is (A*100) / (B-A)
50.
Selling price of an item is X.The Profit percent is
equal to the Cost Price. Then the Cost Price is –50+[10*(25+X)1/2]
51.
A certain sum of money at Simple interest amounts to
Rs.A in a years and Rs.B in b years. Then Rate percent = [(B-A)*100] / [Ab-Ba].
Also Principal =
(Ab-aB) / b-a
52.
If a certain sum at simple interest is becoming m
times in t years then it will become n times in [(n-1)*t] / [m-1] years
53.
If a certain sum at C becomes n times with rate
percent R% then the number of years required is [(n-1)*100] / R years
54.
If a sum at simple interest becomes n times in T
years then Rate percent is [(n-1)*100]/T
55.
The difference between S.I and C.I on a sum of money
at R% per annum for n years is Rs.X. Then the principal is X[(100/R)n]
56.
The Compound interest value on a certain sum is C.I
for n years for R% then the simple interest will be for same R% and n years is
S.I = n * C.I / (n+R/100)
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