MYTS 2018 - Grade 4 - Round 2

A large parallelogram is divided into 8 congruent small parallelograms as shown. How many parallelograms are there in the entire diagram?

At present, the mother’s age plus the child’s age equals the father’s age. In 10 years the mother will be twice the child’s age and will have the father’s present age. Find everyone’s present age.

Five houses are numbered 1–5 as shown, each painted a different colour: blue, purple, yellow, grey or pink. The purple house is adjacent only to the blue house. The pink house lies between the grey and yellow houses. Find the sum of the numbers of the pink and blue houses.

Two rectangular plots have equal area. The tomato plot’s width is 1/5 of its length. One side of the cucumber plot is twice the tomato plot’s width. Their perimeters differ by 1 metre. Find each perimeter.

Four football teams M,Y,T,S play a single round robin. A win gives 3 points, a draw 1 and a loss 0. M finishes with at least as many points as T. T’s total goals for and against are 4–1; M’s are 1–4. What scores occurred in M’s three matches and in T’s three matches?

Lan wants to tile Figure 2 without overlap using 1 × 2 rectangles (Figure 3) and 2 × 2 squares (Figure 4). Is this possible, and if so what is the fewest pieces needed? Explain.