Given $\overline{XYZ}+\overline{ZYX}=\overline{ABAA}$, where $A,B,X,Y,Z$ are five different positive single-digit numbers, how many ordered pairs $(X,Z)$ satisfy the equation? Swapping $X$ and $Z$ counts as a different pair.
A sports club offers soccer, basketball and baseball. Every member plays at least one sport. A member may play any one, any two or all three sports, with no restrictions on combinations. Which diagram can represent all these possible membership combinations? The area outside the circles contains no club members.
A cricket climbs a staircase by jumping either 1 step or 2 steps each time. In how many different ways can it climb a 7-step staircase? For example, 3 steps can be climbed in exactly three ways: 1+1+1, 1+2, or 2+1. The order of jumps matters.
How many fractions in the list $\frac18,\frac19,\frac1{10},\frac1{11},\ldots,\frac1{64},\frac1{65},\frac1{66}$ have terminating decimal representations?
Assume all sections within each shape have equal area. Consider only the flower, circle or other shape itself, excluding its surroundings. Which shape has the smallest fraction shaded? Use the grey-filled regions in the original illustration.
A rectangular park measures 100 m by 50 m. It is fenced with a stone wall, except for a steel gate 2 m wide along the perimeter. The wall and gate are both 3 m high. Stone costs 23 dollars per square metre and steel costs 17 dollars per square metre. Find the total cost in dollars, using the area of the fencing material once (not both faces).
For fidelity, the original options were A: 10384; B: 6900; C: 20700; D: 456; E: 20615. This edition asks for the calculated amount rather than an option letter.
Mr and Mrs Hansen and their three children sit at a circular table. In how many different ways can they sit if the parents are adjacent? The five people are distinct. Rotations count as the same arrangement; reflections count as different. In the original example below, Cases 1 and 2 are rotations of each other, while Case 3 differs.
$\overline{XYX}$ and $\overline{YXY}$ are three-digit integers with distinct nonzero digits $X,Y$. How many different values can the sum $\overline{XYX}+\overline{YXY}$ have?
Two identical rectangular cards partially overlap. Their overlap is a square of area $4\text{ cm}^2$. The total area of the non-overlapping portions of the two cards is $12\text{ cm}^2$. What is the area of one card, in square centimetres?
Several people were surveyed about their preference among four drinks A,B,C,D. Each person chose one drink, and everyone surveyed is represented in the graph. If the fraction preferring A is $m/n$ in lowest terms, find $m+n$.
The interest on 1200 dollars exceeds the interest on 1000 dollars by 30 dollars over 3 years. Find the annual interest rate. Both deposits use the same rate and interest model, but the question does not specify simple interest or compounding. For this question, do not assume an unstated model; decide whether the information determines a unique annual rate.
