Question

How many numbers between 500 to 900 (both inclusive) are divisible by either 7, or 9?

Answer 1

Numbers between 500 and 900 that are divisible by 7 are 504, 511, 518, …, 889, 896.

Here, a= 504, d= 7 an= 896

AP formula

an= a+(n-1)d


896 = 504 + (n-1)7

896 - 504 = 7 (n-1)

7(n-1) = 392

n-1 = (392/7)

n-1 = 56

n = 56+1

n = 57

Hence, 57 numbers are between 500 and 900 that are divisible by 7.



Numbers between 500 and 900 that are divisible by 9 are 504, 513, …891, 900.

Here, a= 504 , d= 9, an= 900

AP formula

an= a+(n-1)d

900 = 504 + (n-1)9

900- 504 = 9(n-1)

396 = 9(n-1)

396/9= n-1

44= n-1

44+1= n

n = 45


Hence ,45 numbers are between 500 and 900 divisible by 9.

we need to eliminate numbers which are divisible by (7*9) = 63.


Such numbers that are divisible by 63 are
504, 567,…819, 882.

Here , a= 504, d= 63, an= 882

AP formula

an= a+(n-1)d


882 = 504 + (n-1)63

882-504 = 63 (n-1)

378= 63 (n-1)

6 = n-1

6+1= n

n = 7


Hence, 7 numbers between 500 and 900 divisible by 63.

The total numbers between 500 and 900 divisible by either 7 or 9

= 57 + 45 - 7
= 95

Hence, The total numbers between 500 and 900 divisible by either 7 or 9 are 95.

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