Question 20

There are 11 positive integers less than 25 that can be expressed as the sum of a positive multiple of 4 and a positive multiple of 5.

The integers less than 25 that can be represented as the sum of a positive multiple of 4 and a positive multiple of 5 total 11.

A) 2

This option is incorrect as there are more than two positive integers less than 25 that can be expressed as the sum of a positive multiple of 4 and a positive multiple of 5. A thorough examination reveals various combinations that yield multiple valid sums.

B) 5

Option B is also incorrect. While five may appear to be a plausible count, a detailed enumeration of the sums reveals that the actual number of valid integers is significantly higher, thus disproving this option.

C) 10

This choice underestimates the total. Although ten is closer than the previous options, it still fails to capture all valid integers that can be formed from the sums of multiples of 4 and 5. The correct total exceeds this count.

D) 11

This option accurately reflects the count of positive integers less than 25 that can be expressed as the sum of a positive multiple of 4 and a positive multiple of 5. A systematic assessment confirms this number, making it the correct choice.

E) 22

This option is incorrect as it exceeds the limit of integers less than 25. There cannot be 22 positive integers below 25, making this option invalid.

Conclusion

The correct answer is 11 because it precisely identifies the valid sums of positive multiples of 4 and 5 within the given range. Other options fail to account for the actual combinations or exceed the integer limits imposed by the question, confirming that 11 is the only accurate count.