Question:medium

‘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

Updated On: Jan 13, 2026
  • Statement (1) alone is sufficient to answer the question
  • Statement (2) alone is sufficient to answer the question
  • Both the statements together are needed to answer the question
  • Either statement (1) alone or statement (2) alone is sufficient to answer the question
  • Neither statement (1) nor statement (2) suffices to answer the question
Show Solution

The Correct Option is A

Solution and Explanation

The correct answer is option (A):
Statement (1) alone is sufficient to answer the question

Here's the breakdown of why the correct answer is "Statement (1) alone is sufficient to answer the question":

The core of the problem is determining the tens digit of a positive integer 'a'.

Understanding the Statements

* Statement 1: When a is divided by 100, leaves a remainder 20.

This statement provides direct information about the last two digits of 'a'. If a number leaves a remainder of 20 when divided by 100, it means the last two digits of the number are 20. Therefore, the tens digit of 'a' must be 2.

* Statement 2: When a is divided by 105, leaves a remainder 20.

This statement gives us information about 'a' but doesn't immediately reveal the tens digit. It tells us that a = 105k + 20, where 'k' is an integer. Let's look at a few possibilities:

* If k = 0, a = 20. The tens digit is 2.
* If k = 1, a = 125. The tens digit is 2.
* If k = 2, a = 230. The tens digit is 3.

We can see that the tens digit varies depending on the value of 'k'. Therefore, this statement alone is not sufficient to determine the tens digit of 'a'.

Analyzing the Options

* We need to find an answer that correctly identifies the relationship between the statements and answering the question.

* Statement 1 alone is sufficient, as it directly tells us the tens digit is 2.

* Statement 2 alone is not sufficient, as it doesn't give us the tens digit.

* Combining statements isn't necessary, since statement 1 alone gives us the answer.

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