If p and q are positive integers, what is the remainder when (27)12p + (3)6q is divided by 5?(1) p is an odd prime number(2) q is divisible by 10a)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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If p and q are positive integers, what is the remainder when (27)^12p + (3)^6q is divided by 5?

(1) p is an odd prime number

(2) q is divisible by 10

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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If p and q are positive integers, what is the remainder when (27)12p +...

Steps 1 & 2: Understand Question and Draw Inferences

Given: Positive integers p and q

To find:

The remainder when (27)^12p + (3)^6q is divided by 5
The remainder when an expression is divided by 5 is determined by the units digit of the expression

The units digit of the expression is obtained from the sum of the units digits of (27)^12pand (3)^6q
1. Units digit of 27^12p = Units digit of 7^12p = Units digit of (7⁴)^3p = Units digit of 1^3p = 1
2. Units digit of (3)^6q = Units digit of (3²)^3q = Units digit of (9)^3q
  - If q is even, units digit of (9)^3q = units digit of 9^even = 1
  - If q is odd, units digit of (9)^3q = units digit of 9^odd = 9

Thus, the units digit of the expression is equal to
1. 1 + 1 = 2 (if q is even)
2. 1 + 9 = 0 (if q is odd)

Correspondingly, the remainder when the expression is divided by 5 is equal to
1. 2 (if q is even)
2. 0 (if q is odd)

So, to answer the question, we need to know if q is even or odd.

Step 3: Analyze Statement 1 independently

(1) p is an odd prime number

Statement 1 gives no information about q’s even-odd nature.

So it’s not sufficient to answer the question

Step 4: Analyze Statement 2 independently

(2) q is divisible by 10?

So, q is of the form 10k, where k is a positive integer
Thus, q is even

Since we now know the even-odd nature of q, we can answer the question. Statement 2 alone is sufficient.

Step 5: Analyze Both Statements Together (if needed)

Since we’ve already arrived at a unique answer in Step 4, this step is not required

Answer: Option B

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If p and q are positive integers, what is the remainder when (27)12p + (3)6q is divided by 5?(1) p is an odd prime number(2) q is divisible by 10a)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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If p and q are positive integers, what is the remainder when (27)12p + (3)6q is divided by 5?(1) p is an odd prime number(2) q is divisible by 10a)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 If p and q are positive integers, what is the remainder when (27)12p + (3)6q is divided by 5?(1) p is an odd prime number(2) q is divisible by 10a)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 If p and q are positive integers, what is the remainder when (27)12p + (3)6q is divided by 5?(1) p is an odd prime number(2) q is divisible by 10a)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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