Target Exam

CUET

Subject

General Aptitude Test

Chapter

Numerical Ability

Topic

Number System

Question:

Given below are two statements:

Statement (I): 2469385422 is divisible by 18.
Statement (II): 3475824638 is divisible by 11.

In light of the above statements, choose the most appropriate answer from the options given below.

Options:

Both Statements are true.

Both Statements are false.

Statement (I) is true but Statement (II) is false.

Statement (I) is false but Statement (II) is true.

Correct Answer:

Both Statements are true.

Explanation:

The correct answer is Option (1) → Both Statements are true.

We will check each statement using divisibility rules.

Statement (I): 2469385422 divisible by 18

  • A number is divisible by 18 if it is divisible by 2 and 9.

Step 1: Divisible by 2 → last digit = 2 → divisible

Step 2: Divisible by 9 → sum of digits divisible by 9

Digits: 2 + 4 + 6 + 9 + 3 + 8 + 5 + 4 + 2 + 2 = 45
45 ÷ 9 = 5 → divisible

Statement (I) is true

Statement (II): 3475824638 divisible by 11

  • Rule: Difference between sum of odd-position digits and even-position digits divisible by 11

Positions: 1 2 3 4 5 6 7 8 9 10
Digits: 3 4 7 5 8 2 4 6 3 8

  • Sum of digits at odd positions (1,3,5,7,9) = 3+7+8+4+3 = 25
  • Sum of digits at even positions (2,4,6,8,10) = 4+5+2+6+8 = 25

Difference = 25 - 25 = 0 → divisible by 11

Statement (II) is true