9 Views

Question : If the 7-digit number 678p37q is divisible by 75 and p is not a composite, then the values of p and q are:

Option 1: p = 5, q = 5

Option 2: p = 3, q = 0

Option 3: p = 3, q = 5

Option 4: p = 2, q = 5


Team Careers360 4th Jan, 2024
Answer (1)
Team Careers360 10th Jan, 2024

Correct Answer: p = 3, q = 5


Solution : 75 = 5 × 5 × 3
Since 7-digit number 678p37q is divisible by 75,
678p37q is divisible by 3 and 5 simultaneously.
By the divisibility rule of 5, q should be 0 or 5.
q = 0 or 5 -------------(i)
By the divisibility rule of 3,
6 + 7 + 8 + p + 3 + 7 + q is a multiple of 3.
⇒ 31 + p + q = 33 or 36 or 39 or ......
When q = 0,
p = 2 or 5 or 8
When q = 5,
p = 0 or 3
Hence, the correct answer is p = 3, q = 5.

SSC CGL Complete Guide

Candidates can download this ebook to know all about SSC CGL.

Download EBook

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