Question

How many 5-digit numbers are there that are divisible by either 60 or 70 but are not divisible by 120?

Answer 1

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;

$\frac{99999}{60} = 1666\frac{13}{20}$ and $\frac{10000}{60} = 166\frac{2}{3}$

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;

$\frac{99999}{70} = 1428\frac{39}{70}$ and $\frac{10000}{70} = 142\frac{6}{7}$

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;

$\frac{99999}{120} = 833\frac{13}{40}$ and $\frac{10000}{120} = 83\frac{1}{3}$ 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.

Answer 2

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