Of the coins in a certain collection, 30 percent were issued more than ten years ago and 45 percent are foreign. Of the foreign coins, 20 percent were issued more than ten years ago. If there are 1,500 coins in the collection, how many are foreign coins that were issued ten years ago or less?

Rationale

There are 540 foreign coins that were issued ten years ago or less.

To determine the number of foreign coins issued ten years ago or less, we first find the total number of foreign coins in the collection. Given that 45 percent of the total 1,500 coins are foreign, we calculate 45% of 1,500, which equals 675 foreign coins. Next, since 20% of these foreign coins were issued more than ten years ago, we find that 20% of 675 is 135. Therefore, the remaining foreign coins, which were issued ten years ago or less, amount to 675 - 135 = 540.

A (75) YOUR ANSWER

This choice represents a significantly lower number of foreign coins than what is actually present in the collection. It does not take into account the total number of foreign coins or the percentage calculations provided in the question.

B (135) YOUR ANSWER

This choice inaccurately reflects the number of foreign coins issued more than ten years ago. It represents the 20% of the foreign coins, rather than those issued ten years ago or less, making it an incorrect answer.

C (315) YOUR ANSWER

This figure does not correspond to any of the calculated values. It fails to account for the correct percentages of foreign coins and their issuance timelines, leading to a miscalculation.

D (375) YOUR ANSWER

While this number is closer to the total of foreign coins, it still does not accurately reflect the calculation of those issued ten years ago or less. This answer also overlooks the necessity of subtracting the correctly calculated number of older foreign coins.

E (540) CORRECT

This choice correctly identifies the number of foreign coins that were issued ten years ago or less, as derived from the calculations based on the provided percentages.

Conclusion

In this collection of 1,500 coins, we find that the number of foreign coins issued ten years ago or less is 540. By accurately applying the given percentages to the total count of coins, we can effectively determine the specific quantity of coins that meet the criteria outlined in the question, confirming option E as the correct answer.

Of the coins in a certain collection, 30 percent were issued more than ten years ago and 45 percent are foreign. Of the foreign coins, 20 percent were issued more than ten years ago. If there are 1,500 coins in the collection, how many are foreign coins that were issued ten years ago or less?

There are 540 foreign coins that were issued ten years ago or less.

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