Counting numbers here are the positive integers starting at 1, for example 1, 2, 3, 4, … . What is the average of the sum of the first 4 counting numbers and the sum of the first 5 positive even numbers?
On Monday, only $\frac56$ of the students were present in a class. All the absent students were girls. If $\frac23$ of the students present were boys and 15 girls were present, how many students are in the class?
In the cryptarithm shown, different letters represent different digits and identical letters represent the same digit. What is the greatest value of the three-digit number GOO?
The addition is DUCK + DUCK = GOOSE. Leading digits D and G are nonzero.
Ashley has a paper rectangle measuring 8 cm by 12 cm. She folds it in half twice, first vertically and then horizontally. The new rectangle looks like the original but smaller. What is the area of the new smaller rectangle in $\mathrm{cm}^2$?
Azma took part in a gymnastics competition. When the ranking list arrived, no one had been disqualified. She was three places ahead of the first contestant in the lower half and three places behind the bronze medalist. First prize is gold, second is silver, and third is bronze. How many people competed?
Clarification for this edition: ranks have no ties; “three places” means a rank difference of 3; the upper and lower halves have equal numbers of contestants.
If all the numbers from 561 to 569 are added, what is their sum?
The source prints these choices: A. 5905; B. 5509; C. 5095; D. 5055; E. 5509. They are retained for source fidelity, but this edition uses numeric entry so that the computed sum can be entered even if no printed choice matches.
A boy sat an exam with 10 problems. He received 5 points for each correct answer and lost 2 points for each wrong or unanswered problem. His final score was 22. How many answers were correct?
