Question : If the digits of a two-digit number are reversed, then the number is decreased by 36. Which of the following is correct regarding the number?
I. The difference between the digits is 4.
II. The value of the number can be 84.
III. Number is always a composite number.
Option 1: I, II, and III
Option 2: II and III
Option 3: I and III
Option 4: I and II
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Correct Answer: I and II
Solution :
Given: If the digits of a two-digit number are reversed, then the number is decreased by 36.
Let the original number be ab which is written as (10a + b). After interchanging the digits the number will be (10b + a).
Difference = 9a - 9b = 36
So, a - b = 4
Check the following statements one by one and find the correct ones.
I. The difference between the digits = a – b = 4. It is the correct statement.
II. The value of the number can be 84. Yes, it is possible. So, it is the correct statement.
III. Number is always a composite number. It is an incorrect statement because the possible numbers are 15, 26, 37, 48, 59, 62, 73, 84, 95. In this we have both prime numbers as well as composite numbers.
Hence, the correct answer is I and II.
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