Question

How many integers in between -200 to 500 (both inclusive) are multiple of 3 or 5?​

Answer 1

The correct answer is 326.

Given: Range of Integers -200 to 500.

To Find: The total number of integers which divisible by 3 or 5.

Solution:

The number of Integers divisible by 3 = (number of integers divisible in range -200 to 0) + (number of integers divisible in range 0 to 500).

= (Quotient of $\frac{200}{3}$) + (Quotient of $\frac{500}{3}$)

= 66 + 166

= 232

The number of Integers divisible by 5 = (number of integers divisible in range -200 to 0) + (number of integers divisible in range 0 to 500).

= (Quotient of $\frac{200}{5}$) + (Quotient of $\frac{500}{5}$)

= 40 + 100

= 140

Now, as the multiple of both 3 and 5 are counted two times so we need to subtract those numbers.

Therefore, we will find the numbers which are divisible by 15 (LCM of 3 & 5).

The number of Integers divisible by 15 = (number of integers divisible in range -200 to 0) + (number of integers divisible in range 0 to 500).

= (Quotient of $\frac{200}{15}$) + (Quotient of $\frac{500}{15}$)

= 13 + 33

= 46

Total numbers = (Divisible by 3 + Divisible by 5) - Common factors

= (232 + 140) - 46

= 326

Hence, the integers in between -200 to 500 (both inclusive) multiple of 3 or 5 are 326.

#SPJ2

Answer 2

The final answer is 321

Given,

Integers' range is between -200 to 500

To Find,

The number of integers between the range.

Solution,

you want to count the multiple of 3 between the range of -200 to 500

-198 is the first number divisible by 3

-198 = -60*3

and the last one is 498

498= 3*166

so their number is

166- (-60)+1

=166+60+1

=227

now we can count multiples of 5in the range

The first one is -200

-200= -40*5

last one is 500

500=100*5

so their number is

100-(-40)+1

=100+40+1

=141

in order to solve the problem of double-counting the numbers, we can find the multiples of 15

15=3*5

The first one in the range is -195

-195= -13*5

the last one in the range is  495

495= 33*5

so their number is

33- (-13)+1

=33+13+1

=47

so the number of multiple of 3 or 5 is

227+141-47 =321

Hence there are 321 integers between -200to 500 which are multiple by both 3 or 5