48 Views

Question : How many natural numbers less than 1000 are divisible by 5 or 7 but not by 35?

Option 1: 243

Option 2: 341

Option 3: 285

Option 4: 313


Team Careers360 20th Jan, 2024
Answer (1)
Team Careers360 24th Jan, 2024

Correct Answer: 285


Solution : The number of natural numbers less than 1000 that are divisible by 5.
$⇒\left\lfloor\frac{999}{5}\right\rfloor = 199$
The number of natural numbers less than 1000 that are divisible by 7.
$⇒\left\lfloor\frac{1000}{7}\right\rfloor = 142$
However, we've double-counted numbers that are divisible by both 5 and 7, i.e., numbers that are divisible by 35.
There are $\left\lfloor\frac{1000}{35}\right\rfloor = 28$ such numbers.
The total number of natural numbers less than 1000 that are divisible by 5 or 7 but not by 35 is $199+ 142 - 2\times28 = 285$
Hence, the correct answer is 285.

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books