Question

If 5,000 invested for one year at p percent simple annual interest yields $500, what amount must be invested at k percent simple annual interest for one year to yield the same number of dollars?
(1) k = 0.8p
(2) k = 8

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• D. EACH statement ALONE is sufficient.
• E. Statements (1) and (2) TOGETHER are not sufficient

Hint:

For simple interest problems, use the formula \( \text{Interest} = \frac{P \times r \times t}{100} \) to solve for unknowns.

Answer 1

The Correct Option is A

Step 1: Analyze statement (1).
We are given that 5,000 invested at p percent yields $500. The formula for simple interest is:
Interest = (P × r × t) / 100
Substituting the values:
500 = (5000 × p × 1) / 100 ⇒ p = 10
So, the interest rate is 10%. Now, to find the amount A that must be invested at k percent for one year to yield the same interest:
500 = (A × k × 1) / 100 ⇒ A = (500 × 100) / k
From statement (1), we have k = 0.8p = 0.8 × 10 = 8. Substituting k = 8 into the equation:
A = (500 × 100) / 8 = 6250
Thus, the amount to be invested is $6250.
Step 2: Analyze statement (2).
Statement (2) tells us that k = 8, but we still need to know the amount to invest. Since statement (2) alone does not give us sufficient information to determine the amount, it is not sufficient on its own.
Conclusion:
A = $6250