Arithmetic1

In all competitive exams questions on clock are common . At what time the hands of a clock be together?. The explanation for this question is Given in below table shows "  How many times will the hands of a clock coincide in a day? " . Sl No Hours Fraction part Fraction part simplified Time when the hands of a clock meet together 1 1-2 60/11 5    5/11 5    5/11 min past 1 2 2-3 120/11 10  10/11 10  10/11 min past2 3 3-4 180/11 16   4/11 16   4/11 min past 3 4 4-5 240/11 21  9/11 21   9/11 min past 4 5 5-6 300/11 27  3/11 27   3/11 min past 5 6 6-7 360/11 32  8/11 32   8/11 min past 6 7 7-8 420/11 38  2/11 38   2/11 min past 7 8 8-9 480/11 43  7/11 43   7/11 min past  8 9 9-10 540/11 49  1/11 49   1/1...

In all competitive exams questions on clock are common . At what time the hands of a clock be together?. The explanation for this question is Given in below table shows "  How many times will the hands of a clock coincide in a day? " . Sl No Hours Fraction part Fraction part simplified Time when the hands of a clock meet together 1 1-2 60/11 5    5/11 5    5/11 min past 1 2 2-3 120/11 10  10/11 10  10/11 min past2 3 3-4 180/11 16   4/11 16   4/11 min past 3 4 4-5 240/11 21  9/11 21   9/11 min past 4 5 5-6 300/11 27  3/11 27   3/11 min past 5 6 6-7 360/11 32  8/11 32   8/11 min past 6 7 7-8 420/11 38  2/11 38   2/11 min past 7 8 8-9 480/11 43  7/11 43   7/11 min past  8 9 9-10 540/11 49  1/11 49   1/1...

by seeing the prime number table we know that 25 prime numbers are existing in between 1 to 100 the following table explains Prime numbers 1-25 2,3,5,7,11,13,17,19,23 9 26-50 29,31,37,41,43,47 6 51-75 53,59,71,73,61,67 6 75-100 79,83,89,97 4  in the above table shows that from 1 to 25 numbers there are 9 prime numbers similarly from 25 to 50 there are 6 prime numbers are there.like wise from 51-75 there are 6 prime numbers and from 75 to 100 there are 4 prime numbers there. since the prime numbers between  50 and 100 is 53,59,71,73,61,67,79,83,89,97. so there are 10 prime numbers are there between 50 and 100 see also: sum of prime numbers from 1 to 100

The following table shows the sum of prime numbers Prime numbers sum 1-25 2+3+5+7+11+13+17+19+23 100 26-50 29+31+37+41+43+47 228 51-75 53+59+71+73+61+67 384 75-100 79+83+89+97 348 so sum of the prime numbers from 1 to 25 = 100.  the sum of prime numbers from 26 to  50  =  228 since the sum of prime numbers from 1 to 50 =328 The sum of prime numbers from 1 to 50 is 328 see also: sum of prime numbers from 1 to 100

The following table shows the sum of prime numbers Prime numbers sum 1-25 2+3+5+7+11+13+17+19+23 100 26-50 29+31+37+41+43+47 228 51-75 53+59+71+73+61+67 384 75-100 79+83+89+97 348 so sum of the prime numbers from 1 to 25 = 100.  the sum of prime numbers from 26 to  50  =  228  the sum of prime numbers from  51 to 75  = 384  the sum of prime numbers from  76 to 100= 348 since the sum of prime numbers from 1 to 100 = 100+228+384+348                                                                            =1060 sum of the prime numbers from 1 to 100 = 1060 see also: prime number-2

Even numbers are 2,4,6,8,10,…. Now we will see the sum of elements: Sum of first 2 even numbers: 2+4= 6= 2(2+1) Sum of first 3 even numbers: 2+4+6= 12= 3(3+1) Sum of first 4 even  numbers: 2+4+6+8=20= 4(4+1) Sum of first 5 even numbers: 2+4+6+8+10 = 30 = 5(5+1) Sum of first n even numbers: 2+4+6+8+10+. . . . .  n numbers= n(n+1) since the sum of first n even numbers is n(n+1) see also: Average of first n even numbers

Odd  numbers are 1,3,5,7,9,…. Now we will see the sum of elements: Sum of first 2 odd  numbers: 1+3= 4= 2 2 Sum of first 3 odd  numbers: 1+3+5= 9= 3 2 Sum of first 4 odd  numbers: 1+3+5+7=16= 4 2 Sum of first 5 odd  numbers: 1+3+5+7+9 = 25 = 5 2 Sum of first n odd  numbers: 1+3+5+7+9+. . . . .  n numbers= n 2    since the sum of first n odd numbers is    n 2