Divisibility Rule of 4 and 9

Question of The Day28-06-2021

If the 7-digit number 456x45y is divisible by 36, then find the value of (x + y) for the smallest value of y.

Answer

Correct Answer : c ) 3

Explanation :

According to the question

456x45y is divisible by 36

The prime factorization of 36 - 2² x 3³

⇒ The number should be divisible by the factors of 36

⇒ Factors of 36 = 4 and 9

⇒ 456x45y is divisible by 4 and 9

Divisibility rule of 4

If the last 2 digits are divisible by 4 then the number is divisible by 4

Last 2 digit of the number = 5y

The values of y for which 5y is divisible are 2 and 6. Let's consider the smallest value 2.

⇒52 is divisible by 4

⇒ y = 2

⇒ Number becomes 456x452

Divisibility rule for 9

If the sum of the digit is divisible by 9 then the number is divisible by 9

⇒ Sum of the digits of the number = 4 + 5 + 6 + x + 4 + 5 + 2

⇒ 26 + x

Since 26 + 1 = 27 is divisible by 9

⇒ x = 1

⇒ Value of (x + y) = 1 + 2

⇒ 3

Hence, (c) is the correct answer.

0 LIKES

COMMENTS

Comments

Share QOTD

Current-Affairs

Attempt Daily Current
Affairs Quiz

Attempt Quiz

May 20

Word Of The Day

Detractor

A person who criticizes someone or something.

A person who tries to degrade the value or reputation of someone or something.

"He considers his political opponents as detractors and doesn't value their comments."

Popular Blog

MPPSC Mains 2020 Admit Card out now | MPPSC Prelims Admit Card 2022 will be out soon!!!

RRB NTPC CBT-2 Exam Schedule is out now!!!

Russia expelled from UNHRC

UPPCS Mains Question Papers 2021 - Essay, General Hindi, GS Paper 1, GS Paper 2, GS Paper 3, GS Paper 4

Daily Current Affairs and GK | 21 May 2022

Daily Current Affairs and GK | 20 May 2022

Daily Current Affairs and GK | 19 May 2022

Daily Current Affairs and GK | 18 May 2022

Daily Current Affairs and GK | 17 May 2022

Banking Economic Financial Awareness | 18, 19 and 20 May 2022

Banking Economic Financial Awareness | 15, 16 and 17 May 2022

Banking Economic Financial Awareness | 13 and 14 May 2022

Banking Economic Financial Awareness | 11 and 12 May 2022

Banking Economic Financial Awareness | 8, 9 and 10 May 2022