SITES TO LEARN APTITUDE online :->
NUMBER
SYSTEM
1. Natural
number: 1,2,3,4……….
2. Whole
number: 0,1,2,3………
3. VBODMAS
: Vinculum, Bracket, Of, Division, Multiplication, Addition, Subtraction
4. (a+b)(a-b)
= a2-b2
5. (a+b)2=a2+b2+2ab
6. (a-b)2=
a2+b2-2ab
7. (a+b)3=a3+b3+3ab(a+b)
8. (a-b)3=a3-b3-3ab(a-b)
9. Ascending
and descending order :->
a) When
numerator and denominator of the fractions increase by a constant value, the
last fraction is the biggest.
b) The
fraction whose numerator after cross-multiplication gives the greater value is
greatest.
10. Rules
on counting number :
a) Sum
of all the first n natural number : n(n+1)/2
b) Sum
of first n odd number : n2
c) Sum
of first n even number = n(n+1)
d) Sum
of squares of first n natural number = n(n+1)(2n+1)6
e) Sum
of cubes of first n natural number = [n(n+1)/2]2
11. The
difference between the square of two consecutive number is always an odd
number.
12. The
difference between the square of two consecutive number is the sum of the two
consecutive numbers.
13. For
Odd numbers :
When there is an odd digit in the unit
place (except 5), multiply the number by itself until you get 1 in the unit
place
For Even numbers:
When there is an even digit in the unit
place, multiply the number by itself until you get 6 in the unit place.
If there is 1,5 and 6 in the unit place
of the given number, then after any times of its multiplication, it will have
the same digit in the unit place.
14. Product
of two number is equal to the product of their HCF and LCM
15. The
HCF of two/more function is the highest fraction which is exactly divisible by
each of the fraction. Then HCF= HCF of numerator/LCM of denominator
16. LCM
of fraction = LCM of numerator/HCF of denominator
17. When
two numbers, after being divided by a third number, leave the same remainder,
the difference, of those two numbers must be perfectly divisible by the third
number.
(A) 6 : 30
(B) 6 : 00
(C) 6 : 15
(D) 4 : 20
2. If the numbers divisible by 3 between 14 and 55 (both inclusive) and the numbers with 3 at unit’s place of them are removed then how may numbers will remain?
(A) 24
(B) 23
(C) 22
(D) 25
3. If x means -, ÷ means +, + means ÷, – means x then find the value of 13 – 12 ÷ 400 + 20 x 100
(A) 1/760
(B) 76
(C) 176
(D) 186
Example :->
1. A trader told his servant Shambhu that he left for his home from the shop after every 2 : 40 hours. I left for home 55 minutes earlier and for the next time I will leave for home from my shop at 8 : 15 p.m. At which time did I inform my servant?(A) 6 : 30
(B) 6 : 00
(C) 6 : 15
(D) 4 : 20
2. If the numbers divisible by 3 between 14 and 55 (both inclusive) and the numbers with 3 at unit’s place of them are removed then how may numbers will remain?
(A) 24
(B) 23
(C) 22
(D) 25
3. If x means -, ÷ means +, + means ÷, – means x then find the value of 13 – 12 ÷ 400 + 20 x 100
(A) 1/760
(B) 76
(C) 176
(D) 186
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