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A company has the following reserves:
- Share premium: $60,000
- Revaluation reserve: $75,000
- General reserve: $10,000
- Retained earnings: $21,500
What is the maximum number of $1 bonus shares the company can issue?
A bonus issue can be made from any reserve, including capital reserves (Share Premium, Revaluation) and revenue reserves (General, Retained). Total = $60,000 + $75,000 + $10,000 + $21,500 = $166,500.
$n$ is an even integer and a multiple of 3.
Compare:
Column A: The remainder when $n$ is divided by 12
Column B: 6
Since $n$ is even and a multiple of 3, $n$ must be a multiple of $\text{lcm}(2, 3) = 6$.
So $n = 6k$ for some integer $k$.
When we divide $n = 6k$ by 12:
- If $k$ is even (say $k = 2m$): $n = 12m$, remainder = 0
- If $k$ is odd (say $k = 2m + 1$): $n = 6(2m + 1) = 12m + 6$, remainder = 6
So the remainder when $n$ is divided by 12 can be either 0 or 6.
Since Column A could be 0 (less than 6) or 6 (equal to 6), the relationship cannot be determined.
Identify the cause-and-effect relationship: i. Sara's productivity at work has significantly decreased. ii. Sara has been experiencing frequent interruptions due to ongoing construction work near her office.
The most logical cause-and-effect relationship is that the construction work (cause) leads to interruptions, which then lead to decreased productivity (effect). The other options reverse the causality or deny a relationship.
Find the count of natural numbers less than $7000$ that can be formed using the digits $0, 1, 3, 7, 9$ with repetition allowed.
1-digit: $1, 3, 7, 9$ (excluding 0) $= 4$
2-digit: First digit: 4 choices (1,3,7,9); second: 5 choices $= 4 \times 5 = 20$
3-digit: First digit: 4 choices; others: 5 each $= 4 \times 5 \times 5 = 100$
4-digit $< 7000$: First digit must be $1$ or $3$ (2 choices, since 7000 and above excluded โ first digit can be 1, 3 only for $< 7000$; digits 7 and 9 give $\geq 7000$): $2 \times 5 \times 5 \times 5 = 250$
Total $= 4 + 20 + 100 + 250 = \mathbf{374}$
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