n is a positive integer that lies between 100 and 200, exclusive, and has no digits repeated. Is the units digit of n equal to 5? (1) n is divisible by 9 and the 2-digit number formed by inverting the units and tens digit of n is a prime number. (2) The difference between the units digit and the tens digit of n is the same as the difference between the tens digit and the hundreds digit of n and is equal to 2.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'B'. Can you explain this answer?

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n is a positive integer that lies between 100 and 200, exclusive, and has no digits repeated. Is the units digit of n equal to 5?

(1) n is divisible by 9 and the 2-digit number formed by inverting the units and tens digit of n is a prime number.

(2) The difference between the units digit and the tens digit of n is the same as the difference between the tens digit and the hundreds digit of n and is equal to 2.

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Correct answer is option 'B'. Can you explain this answer?

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Test: Unit Digit- 2

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n is a positive integer that lies between 100 and 200, exclusive, and ...

Steps 1 & 2: Understand Question and Draw Inferences

n is an integer with no repeated digits such that 100 < n < 200
- From the above inequality, it is clear that Hundreds digit(n) = 1
- Let the number n = 1bc, where b and c are the tens and units digits of n respectively.

To Find: Is Units Digit(n) = 5?

That is, is c = 5?

Step 3: Analyze Statement 1 independently

n is divisible by 9 and the 2-digit number formed by inverting the units and tens digit of n is a prime number.

The number cb is a prime number
Also, since n is divisible by 9, the sum of the digits of n must be divisible by 9
- Therefore, 1 + b + c must be divisible by 9
- So, 1 + b + c = { 9, 18}.
  - It cannot be equal to 27 or more as the maximum possible sum of b + c = 9 +8 = 17 (Remember that the digits of n are distinct. So, if one digit is 9, the maximum value of the other digit can be 8).
- So, following cases are possible:
  - Either b + c = 8. Possible combinations of two distinct positive integers adding up to 8 can be:

(b, c) = (2, 6). In this case cb = 62, which is not a prime number. So, this case is not possible.
(b, c) = (3, 5). In this case, cb = 53, which is a prime number. So, this is a possible case.
(b, c) = (5, 3). In this case cb = 35, which is not a prime number. So, this case is not possible
(b, c) = (6, 2). In this case cb = 26, which is not a prime number. So, this case is not possible.

Or b + c = 17. In this case, (b, c) = (8, 9) in any order. Following cases are possible:

If (b, c) = (8, 9), then cb = 98, which is not a prime number. So, this case is not possible
If (b, c) = (9, 8), then cb = 89, which is a prime number. So, this is a possible case.

Hence, the possible values of n = { 135, 198}. So, the units digit of n = {5, 8}

As we do not have a unique value of units digit(n), the statement is insufficient to answer.

Step 4: Analyze Statement 2 independently

2. The difference between the units digit and the tens digit of n is the same as the difference between the tens digit and the hundreds digit of n and is equal to 2.

We’ve already inferred in Steps 1 and 2 that Hundreds digit(n) = 1
So, Tens Digit(n) = 1 + 2 = 3
And, Units Digit(n) = 3 + 2 = 5

Thus, the units digit(n) = 5

As we have a unique value of units digit(n) , this statement is sufficient to answer.

Step 5: Analyze Both Statements Together (if needed)

As we have a unique value from step 4, this step is not required.

Answer: B

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n is a positive integer that lies between 100 and 200, exclusive, and has no digits repeated. Is the units digit of n equal to 5? (1) n is divisible by 9 and the 2-digit number formed by inverting the units and tens digit of n is a prime number. (2) The difference between the units digit and the tens digit of n is the same as the difference between the tens digit and the hundreds digit of n and is equal to 2.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'B'. Can you explain this answer?

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n is a positive integer that lies between 100 and 200, exclusive, and has no digits repeated. Is the units digit of n equal to 5? (1) n is divisible by 9 and the 2-digit number formed by inverting the units and tens digit of n is a prime number. (2) The difference between the units digit and the tens digit of n is the same as the difference between the tens digit and the hundreds digit of n and is equal to 2.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'B'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about n is a positive integer that lies between 100 and 200, exclusive, and has no digits repeated. Is the units digit of n equal to 5? (1) n is divisible by 9 and the 2-digit number formed by inverting the units and tens digit of n is a prime number. (2) The difference between the units digit and the tens digit of n is the same as the difference between the tens digit and the hundreds digit of n and is equal to 2.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for n is a positive integer that lies between 100 and 200, exclusive, and has no digits repeated. Is the units digit of n equal to 5? (1) n is divisible by 9 and the 2-digit number formed by inverting the units and tens digit of n is a prime number. (2) The difference between the units digit and the tens digit of n is the same as the difference between the tens digit and the hundreds digit of n and is equal to 2.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'B'. Can you explain this answer?.

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