NUMERICAL ABILITY

ACE ACADEMY IES ESE HANDWRITTEN CLASSROOM NOTES

ENGINEERING SERVICES GOVT JOBS EXAMINATION NOTES

FREE DOWNLOAD PDF

Numerical Ability Engineering Services IES ESE Ace Academy Notes PDF Free Download at CivilEnggForAll.com

PLEASE NOTE : MOST OF THE PDF’S AVAILABLE IN THE INTERNET WITH THE NAME OF IES ACE ACADEMY NOTES ARE FAKE. FOR THE SAKE OF INCREASING THEIR WEBSITE POPULARITY/TRAFFIC, FEW WEBSITES ARE ALLEGEDLY PROVIDING SOME USELESS MATERIALS WITH THE NAME OF IES ACE ACADEMY NOTES WHICH IN RETURN MIGHT RUIN STUDENT’S VALUABLE MARKS. TO HELP THE STUDENTS WHO ARE WORKING THEIR LEVEL BEST TO CRACK THE RANKS, WE ARE PROVIDING ONLY VERIFIED ACE ACADEMY IES NOTES HERE. BUT HOWEVER THERE MIGHT BE SOME MANUAL ERRORS IN THE CONTENT OF THIS BOOK.

Numerical Ability Engineering Services IES ESE Ace Academy Notes PDF

TOPICS COVERED IN THIS BOOK

Boats and Streams
Mixtures and Alligations
Progressions
Data Interpretation
Clocks
Blood Relations
Indices and Surds
Syllogism
Directions
Cubes and Dice
Puzzles
Number Systems
Letter System
Ratio and Proportions
Problems on Age
Percentages
Profit and Loss
Averages
Time, Men and Work
Pipes and Cisterns
Time, Speed and Distance

TESTS OF DIVISIBILITY

Divisibility By 2 : A number is divisible by 2, if its unit’s digit is any of 0, 2, 4, 6, 8 Ex. 84932 is divisible by 2 while 65935 is not.
Divisibility By 8 : Anumber is divisible by 3, if the sum of its digits is divisible by 3 Ex. 592482 is divisible by 3, since sum of its digits (5+9+2+4+8+2) 30, which is divisible by 3 But, 864329 is not divisible by 3, since sum of its digits (8+6+4+3+2+9) 32, which is not divisible by 3
Divisibility By 4 : A number is divisible by 4, if the number formed by the last two digits is divisible by 4. Ex. 892648 is divisible by 4, since the number formed by the last two digits is 48, which is divisible by 4 But, 749282 is not divisible by 4, since the number formed by the last two digits is 82, which is not divisible by 4
Divisibility By 6 : A number is divisible by 5, if its unit’s digit is either o or 5 Thus, 20820 and 50345 are divisible by 5, while 30934 and 40946 are not.
Divisibility By 6 : A number is divisible by 6, if it is divisible by both 2 and 3. Ex The number 35256 is elearly divisible by 2 Sum of its digits (3+5+2+5+6) 21, which is divisible by 3 Thus, 35256 is divisible by 2 as well as 3. Hence, 35256 is divisible by 6
Divisibility by 8 : A number is divisible by 8 if the number formed by the last three digits of the given number is divisible by 8.
Ex : 953360 is divisible by 8, since the number formed by last three digits is 360, ehich is divisible by 8.
But, 529418 is not divisible by 8, since the number formed by last three digits is 418, which is not divisible by 8
Divisibility By 9 : A number is divisible by 9, if the sum of its digits is divisible by 9 Ex. 60732 is divisible by 9, since sum of digits (6+0+7+3+2) 18, which is divisible by 9 But, 68956 is not divisible by 9, since sum of digits (6+8+9+6+6) 34, which is not divisible by 9
Divisibility By 10 : A number is divisible by 10, if it ends with 0 Ex. 95410, 10480 are divisible by 10, while 96375 is not
Divisibility By 11 : A number is divisible by 11, if the difference of the sum of its digits at odd places and the sum of its digits at even places, is either 0 or a number divisible by 11 Ex. The number 4832718 is divisible by 11, since (sum of digits at odd places) (sum of digits at even places) (8+7+3+4)-(1+2+8)=11, which is divisible by 11.
Divisibility By 12 : A number is divisible by 12, if it is divisible by both 4 and Ex. consider the number 34632 (i) The number formed by last two digits is 32, which is divisible by 4 (ii) Sum of digits (3+4+6+3+2)=18, which is divisible by 3 Thus, 34632 is divisible by 4 as well as 3. Hence, 34632 is divisible by 12
Divisibility By 14 : A number is divisible by 14, if it is divisible by 2 as well as 7
Divisibility By 15 : A number is divisible by 15, if it is divisible by both 3 and itself
Divisibility By 16 : A number is divisible by 16, if the number formed by the last digits is divisible by 16 Ex. 7957536 is divisible by 16, since the number formed by the last four digits is 7536, which is divisible by 16
Divisibility By 24 : A given number is divisible by 24, if it is divisible by both 3 and 8
Divisibility By 40 : A given number is divisible by 40, if it is divisible by both 5 and 8
Divisibility By 80 : A given number is divisible by 80, if it is divisible by both 5 and 16 Note If a number is divisible by p as well as q, where p and g are co-primes, then the given number is divisible by pq If p and g are not co-primes, then the given number need not be divisible by pa, even when it is divisible by both p and g Ext. 36 is divisible by both 4 and 6, but it is not divisible by (4 x 6) 24, since 4 and 6 are not co-primes

PROGRESSION :

A succession of numbers formed and arranged in a definite order according to certain definite rule is called a progression.

Arithmetic Progression (A.P): If each term of a progression differs from its preceding constant, such a progression is called an arithmetical progression. This constant difference is called the common difference of the A.P An A.P with first term a and common difference d is given by a, (a+d), (a+2d), (a+3d),…
The nth term of this AP is given by Tn = a(n-1)d.
The sum of n terms of this A.P Sn = n(First term+Last Term)/2
Geometrical Progression (G.P): A progression of numbers in which every term bears a constant ratio with its preceding term, is called a geometrical progression The constant ratio is called the common ratio of the G.P