The average mass of Mona, Amanda, Jack and Brian is 68kg. The mass of Mona and Amanda is 36kg less than the mass of Jack and Brian. If Mona’s mass is 56kg, find the mass of Amanda.
**Editorial note for this self-study exercise:** The comparison is between the two combined masses. Enter Amanda’s mass in kilograms as a number.
There are 65% of the students at Raffle Junior High School play piano, 40% of the students play basketball and 25% of the students both play piano and basketball. What is the percentage of the number of students who do neither play piano nor play basketball at Raffle Junior High School?
**Editorial note for this self-study exercise:** Enter the percentage number without the percent sign.
The LCM of three numbers P, Q and R is $2^5\times3^6\times5^2\times7^2$. Given that $P=2^4\times3^5\times7^2$ and $Q=2^5\times3^2\times5\times7$. Find the smallest value of R, in index notation.
**Editorial note for this self-study exercise:** P, Q and R are positive integers. For automatic checking, use prime factors in increasing order, ^ for each exponent and * between powers, with no spaces. Omit factors whose exponent is zero. Example of the format only: 2^3*7^2.
It is given that the 4-digit number $\overline{abab}$ has 6 factors. What is the smallest possible value of $\overline{abab}$?
**Editorial note for this self-study exercise:** The overline denotes the four decimal digits a, b, a, b; a is nonzero. Count positive integer divisors.
The diagram shows parts of a city where the lines are roads. Charles walks from point X to point Y along the roads without ‘backtracking’ (i.e. he can only walk downwards or to the right in the diagram below). How many ways can he walk from X to Y?
A. 54
B. 55
C. 56
D. 57
E. None of the above
**Editorial note for this self-study exercise:** Enter the number of routes, rather than an option letter.
6 arrows land on the target shown below. Each arrow is in one of the regions of the target. Which of the following total scores is possible: 16, 19, 26, 31, 41, 44?
**Editorial note for this self-study exercise:** Each arrow scores 3, 5 or 7 according to its region; more than one arrow may land in the same region.
The speed of sound in air is 1100 feet per second. The speed of sound in steel is 16500 feet per second. Robin, one ear pressed against the railroad track, hears a sound through the rail six seconds before hearing the same sound through the air. To the nearest foot, how far away is the source of that sound?
**Editorial note for this self-study exercise:** Assume the same straight-line travel distance through air and steel, from the same emitted sound. Enter the distance in feet, rounded to the nearest integer, without units.
In the figure below, PSR, RTQ and PAQ are three semicircles of diameters 10 cm, 3 cm and 7 cm respectively. Find the area of the shaded region.
**Editorial note for this self-study exercise:** Keep the area exact: write it as $c\pi$ cm² and enter only the coefficient c, using a number or a fraction a/b. Use a decimal point if entering a decimal. Do not replace pi by a decimal approximation.
The boys and girls soccer clubs are trying to raise money for new uniforms. The boys’ soccer club is selling candy bars for $\$2$ a piece and the club is selling candy bars for $\$2$ a piece and the girls’ soccer club is selling candles for $\$4$. They must raise at least $\$800$. If the girls sold 100 candles, how many candy bars must be the boys sell?
**Editorial note for this self-study exercise:** Find the minimum number of candy bars the boys must sell. Count sales revenue only; no costs are supplied. The repeated candy-bar clause in the original wording refers to the same sales, not an additional club. Enter a number of bars, not a money amount.
How many 4-cm cubes can a cuboid measuring 2.5m by 1.2m by 53cm hold?
**Editorial note for this self-study exercise:** Find the maximum number of whole cubes in edge-parallel rows and layers: cube edges are parallel to the corresponding box edges. Use internal box dimensions, with no wall thickness or gaps required; do not cut or rotate cubes into tilted packings.
In the following number sequence,
..., 245, 234, 223, 212, 201, ...,
234 is the 55th term.
a) Find the first term.
b) Find the 70th term.
**Editorial note for this self-study exercise:** Continue the constant difference shown throughout the sequence. Enter (a) then (b) as two integers separated by a semicolon with no spaces.
1/2 of John’s money is $\$45$ more than 1/3 of Kim’s money. They have a total of $\$800$. How much money does each of them have?
**Editorial note for this self-study exercise:** Enter John’s amount first, then Kim’s amount, in whole dollars, separated by a semicolon with no spaces. Do not include currency symbols.
The diagram shows a regular pentagon PQRST. The lines QS and RT meet at U. Find the angle $\angle PUR$?
**Editorial note for this self-study exercise:** Find the ordinary angle between the rays UP and UR, between 0° and 180°. Enter its measure in degrees as a number.
