Question

If \( abcd \neq 0 \) and \( 0 < c < b < a < 1 \), is \( \frac{a^4bc}{d^2} < 1 \)? Statement (I): \( a = \sqrt{d} \)
Statement (II): \( d > 0 \)

• A. Statement (I) alone is sufficient.
• B. Statement (II) alone is sufficient.
• C. Both statements (I) and (II) are sufficient.
• D. Neither statement is sufficient.

Hint:

For numbers between 0 and 1, multiplication decreases the value, while division by a small number can increase it significantly.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The task is to translate the base-10 decimal value 25 into its corresponding base-2 binary format.


Step 2: Key Formula or Approach:
Decimal to binary conversion involves continuously dividing the number by 2 and noting the remainders. The final binary string is formed by reading these remainders in reverse order (from the last quotient to the first).


Step 3: Detailed Explanation:
Executing the repeated division by 2 for 25 yields:
\[ 25 \div 2 = 12 \text{ (Remainder } 1) \] \[ 12 \div 2 = 6 \text{ (Remainder } 0) \] \[ 6 \div 2 = 3 \text{ (Remainder } 0) \] \[ 3 \div 2 = 1 \text{ (Remainder } 1) \] \[ 1 \div 2 = 0 \text{ (Remainder } 1) \] Collecting the remainders from the bottom up gives the sequence \(11001\).
Hence, the binary form of \(25_{10}\) is \(11001_{2}\).


Step 4: Final Answer:
The correct choice is (A).