**Editorial note for this self-study exercise:** Use these intended pattern families throughout: (a) constant first difference; (b) first differences increasing by a constant amount; (c) consecutive positive-integer squares; (d) products of consecutive positive integers; (e) separate arithmetic patterns in the odd and even positions. Enter all nine missing integers in part order (a) to (e), left to right within each part, separated by semicolons with no spaces.
On a Saturday afternoon, Armand sent m text messages each hour for 5 hours, and Tyrone sent p text messages each hour for 4 hours. Which of the following represents the total number of messages sent by Armand and Tyrone on this Saturday afternoon?
A. $9mp$
B. $20mp$
C. $5m + 4p$
D. $4m + 5p$
E. None of the above
**Editorial note for this self-study exercise:** Enter the letter of the correct option.
In a particular year, the birthdays of Alan, Benedict, Dennis and Edgar were Tuesday, Wednesday, Thursday and Friday (not in order). Their birthdays in that year were also special days: Labour Day, Teachers’ Day, Children’s Day and National Day (not in order). Furthermore, in that year:
i. Dennis’ birthday falls before Labour Day but later than Teachers’ Day.
ii. Benedict’s birthday does not fall on Teachers’ Day.
iii. Friday was either Alan’s birthday or Children’s Day (or both).
iv. Edgar’s birthday does not fall on Tuesday.
v. Dennis’ birthday does not fall on National day.
If they have different birthdays, determine each of their birthdays in that year.
A. Alan – Wednesday, Benedict – Tuesday, Dennis – Thursday, Edgar – Friday
B. Alan – Friday, Benedict – Wednesday, Dennis – Tuesday, Edgar - Thursday
C. Alan – Friday, Benedict – Tuesday, Dennis – Thursday, Edgar – Wednesday
D. Alan – Thursday, Benedict – Wednesday, Dennis – Tuesday, Edgar – Friday
E. None of the above
**Editorial note for this self-study exercise:** Use only the information supplied. No country, holiday dates or same-week assumption is provided. Explain whether a unique weekday assignment follows, and justify your conclusion; this response is marked manually. Do not import an unstated holiday calendar.
William puts some red, blue and white marbles into a box. The number of red marbles is 1/3 of the number of blue marbles. The number of white marbles is 1/4 of the number of red marbles. If there are 144 more blue marbles than red marbles, how many marbles are there in the box?
A student has to answer 10 questions, choosing at least 4 from each of Parts A and B. If there are 6 questions in Part A and 7 in Part B, in how many ways can the student choose 10 questions?
**Editorial note for this self-study exercise:** Questions are distinct; count each chosen set once, regardless of answering order.
A rectangular tank measuring 20cm by 15cm by 17cm is filled with water. When an iron bar is placed in the tank, the water level rises by 10cm. Find the volume of the iron bar.
**Editorial note for this self-study exercise:** For this self-study interpretation, the tank initially contains water but is not full to the brim. Its horizontal internal base is 20 cm by 15 cm and its height is 17 cm. Assume at least 10 cm of headroom initially, no overflow, and a fully submerged iron bar. Enter the bar volume in cubic centimeters as a number.
In a Science quiz, 35 questions were given. 3 points were given for each correct answer and 2 points were deducted for each incorrect answer. Tom’s score was 80. How many correct answers did he get?
**Editorial note for this self-study exercise:** Assume Tom answered all 35 questions, so every response was either correct or incorrect and none was blank.
The figure below is formed using five identical rectangles. The perimeter of the figure is 66cm. Find its area.
**Editorial note for this self-study exercise:** Use the exact edge-to-edge tiling shown, with no gaps or overlaps. Enter the area in square centimeters as a number.
A rectangle is divided into four smaller rectangles with areas as shown in the diagram below. Find the value of A.
**Editorial note for this self-study exercise:** A is the numerical area in square centimeters of the lower-left small rectangle. The dividing segments extend straight across the whole outer rectangle as shown.
Max had 140 more stamps than Donna. If Max gave 15 stamps to Donna, he would have thrice as many stamps as Donna. How many stamps did Max have at first?
There are four bus routes between A and B; and three bus routes between B and C. A man can travel round-trip in number of ways by bus from A to C via B. If he does not want to use a bus route more than once, in how many ways can he make round trip?
**Editorial note for this self-study exercise:** Each listed route can be used in either direction; reversing direction does not make it a new route. The trip is A to B to C, then C to B to A, with no detours.
A fraction is equivalent to $\frac35$. Its denominator and numerator add up to 56. What is the difference between the denominator and numerator of this fraction?
A. 21
B. 14
C. 2
D. 13
E. None of the above
**Editorial note for this self-study exercise:** Use positive integer numerator and denominator. Enter the numerical difference, rather than an option letter.
Samantha offers two different packages of yoga classes at her yoga studio. She offers two “hot yoga sessions” and three “zero gravity yoga sessions” at a total cost of $\$400$. She also offers four hot yoga sessions and two zero gravity sessions at a price of $\$440$. Samantha wants to offer a larger package for the long-time clients in which the cost must exceed $\$800$. If Samantha does not wish to include more than 13 sessions for the long-time client package, will she be able to create this package for her clients?
A. No, because the closest package that she can offer consists of three hot yoga and three zero gravity yoga sessions.
B. No, because the closest package that she can offer consists of four hot yoga and four zero gravity yoga sessions.
C. Yes, because she can offer five hot yoga and five zero gravity yoga sessions.
D. Yes, because she can offer six hot yoga and six zero gravity yoga sessions.
E. There are not enough data to reach any conclusion.
**Editorial note for this self-study exercise:** Assume each type of session has a fixed price used additively in every package, with no package-specific discounts. Choose the option whose complete statement is correct and enter its letter.
