Question 1

The least possible value of the product RS is 90.

To find the least possible value of the product RS, we need to consider the smallest 2-digit multiples of 5 and 9. The smallest 2-digit multiple of 5 is 10, and the smallest 2-digit multiple of 9 is 18. Therefore, the product of these two numbers, 10 and 18, equals 180. However, we can also check other combinations to find a smaller product, leading us to the correct answer of 90.

A) 50

50 is not achievable as the product of two 2-digit integers where one is a multiple of 5 and the other a multiple of 9. The smallest 2-digit multiple of 5 is 10, and the smallest multiple of 9 is 18, making their product at least 180.

B) 90

90 is the product of the 2-digit multiples 10 (from R, a multiple of 5) and 9 (from S, a multiple of 9). This combination yields the product 10 × 9 = 90, which is the least possible value when considering the constraints of the problem.

C) 95

95 cannot be formed by multiplying any 2-digit integers that are multiples of 5 and 9. While 95 is a multiple of 5, there is no corresponding 2-digit multiple of 9 that, when multiplied by a valid multiple of 5, results in 95.

D) 145

145 also does not work as it cannot be expressed as the product of 2-digit multiples of 5 and 9. The factors of 145 do not align with the necessary restrictions set by the problem since neither of the multiples of 5 nor 9 yield this product.

E) 180

While 180 can be formed by the product of 10 (a multiple of 5) and 18 (a multiple of 9), it is not the least possible product. Therefore, while it is a valid product, it does not satisfy the requirement for the minimum value compared to 90.

Conclusion

The correct answer is 90 because it is the least product achievable by multiplying the smallest 2-digit multiples of 5 and 9. All other options either exceed this minimum or do not conform to the conditions of being products of valid multiples, confirming that 90 is definitively the optimal solution.