Answer:
1820
Step-by-step explanation:
As long as the 5-digit numbers are divisible by 60 they are also divisible by 120. See solution for the number of 5 digits number divisible by 60 and the solution of 5 digits divisible by 120.
The number of 5 digit number divisible by 60 and 70 is 215
The total 5-digit numbers that are divisible by either 60 or 70 = 1499+1286-215 = 2570
The total 5-digit numbers that are divisible by either 60 or 70 but are not divisible by 120:
(5 digit number divisible by 60 or 70) -
(5 digit number divisible by 120)
2570 - 750 = 1820
Find attached for solution
Answer:
The number of 5-digit numbers divisible by either 60 or 70 but are not divisible by 120 is 2035, 5-digit numbers
Step-by-step explanation:
Here, to find the number of 5-digit numbers divisible by 60 and 70 but not divisible by 120 we have
The 5-digit numbers are between 10000 and 99999
Therefore, we have;
[tex]\frac{99999}{60} = 1666\frac{13}{20}[/tex] and [tex]\frac{10000}{60} = 166\frac{2}{3}[/tex]
Thus we have multiples of 60 from 167×60 to 1666×60 which are 5-digit numbers
Hence we have, 1666 - 167 = 1499 numbers which are 5-digits and divisible by 60
Similarly for 70, we have;
[tex]\frac{99999}{70} = 1428\frac{39}{70}[/tex] and [tex]\frac{10000}{70} = 142\frac{6}{7}[/tex]
Therefore the total number of 5-digit numbers divisible by 70 is 1428 - 143 = 1285 5-digit numbers
Hence, the number of 5-digit numbers divisible by both 60 or 70 = 1499 + 1285 = 2784 5 digit numbers
The number of 5-digit numbers divisible by 120 is found similarly as follows;
[tex]\frac{99999}{120} = 833\frac{13}{40}[/tex] and [tex]\frac{10000}{120} = 83\frac{1}{3}[/tex] which is 833 - 84 = 749, 5 digit numbers
Therefore, the number of 5-digit numbers divisible by either 60 or 70 but are not divisible by 120 since any 5-digit number divisible by 120 is divisible by 60 = 2784 - 749 = 2035, 5-digit numbers.
