Question

‘a’ is a positive integer. What is the tens digit of a?
Statement 1: When a is divided by 100, leaves a remainder 20
Statement 2: When a is divided by 105, leaves a remainder 20

• A. Statement (1) alone is sufficient to answer the question
• B. Statement (2) alone is sufficient to answer the question
• C. Both the statements together are needed to answer the question
• D. Either statement (1) alone or statement (2) alone is sufficient to answer the question
• E. Neither statement (1) nor statement (2) suffices to answer the question

Answer 1

The Correct Option is A

Let's solve the problem step-by-step using the given statements:

Objective: Find the tens digit of a positive integer 'a'.

Statement 1: When 'a' is divided by 100, the remainder is 20.

• This implies that 'a' can be expressed in the form: a = 100k + 20, where k is an integer.
• From the expression a = 100k + 20, it's clear that the number a ends in 20.
• Therefore, the tens digit of a is clearly 2.
• Thus, Statement 1 alone is sufficient to determine the tens digit of a.

Statement 2: When 'a' is divided by 105, the remainder is 20.

• This implies that 'a' can be expressed in the form: a = 105m + 20, where m is an integer.
• However, knowing just this doesn't help us determine the exact digits of a, specifically the tens digit.
• The expression doesn't tell us anything about the last two digits of a.
• Therefore, Statement 2 alone is not sufficient to determine the tens digit of a.

Conclusion: Based on the analysis above, Statement 1 alone is sufficient to find the tens digit of 'a'. Therefore, the correct answer is:

Statement (1) alone is sufficient to answer the question.