19 Views

Question : If the 9-digit number 97x4562y8 is divisible by 88, what is the value of $\left(x^2+y^2\right)$ for the smallest value of y, given that x and y are natural numbers?

Option 1: 64

Option 2: 68

Option 3: 76

Option 4: 80


Team Careers360 24th Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

Correct Answer: 80


Solution :

Factors of 88 = 8 × 11
If a number is divisible by 88 then it will be divisible by 8 and 11 also.
The given number is 97x4562y8.
For the smallest possible value of y considering that y is a natural number,
2y8 will be divisible by 8
So, y will be 4 for 248, which is divisible by 8.
As y = 4,
Sum of even places in number = 8 + 2 + 5 + x + 9 = 24 + x
Sum of odd places in number = 7 + 4 + 6 + 4 = 21
Difference between sums = 24 + x – 21 = 3 + x
For 3 + x to be divisible by 11, x = 11 – 3 = 8
Value of $x^2 + y^2$
= $4^2 + 8^2$
= 16 + 64
= 80
Hence, the correct answer is 80.

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