Six cards are laid out on a table as shown in the figure below. Each of the cards has a number on one side and a letter on the other side. What is the minimum number of cards you need to flip and see to make sure the rule, “cards that have a vowel on one side always have an even number on the other side” is TRUE? Cards: 3, M, 7, E, 8, R

A family of four—grandfather, father, son and daughter—are caught in a heavy rain and are stranded at a bus stop close to their home. However they have only one umbrella with them. The umbrella can take a maximum of two people without either of them getting wet. The four members…

X1 is a 3D form generated from the shape X, using certain 3D operations. It has 14 surfaces in total. If the same operations are carried out on shape Y, how many surfaces would the resulting 3D form have? [Figure: see page 7 of source PDF]

How many distinct motifs appear in the figure on the right? Flips and rotations are to be counted separately, for example the motifs P and Q are distinct. [Figure: see page 6 of source PDF]

In 2018, a person spent half the time working, a third in sleeping and one-eighth in cooking. He spent the rest of the time exercising. How many total hours did he spend exercising?

At most how many triangles can appear by adding two straight lines to the figure? [Figure: see page 6 of source PDF]

If the given shape in the figure is used to tile the grid on the right without any overlaps, what is the minimum number of units that will be left uncovered? Flips and rotations are allowed. [Figure: see page 7 of source PDF]

A cube is created by stacking 27 smaller cubes as shown in the figure. A plane, going through vertices A, B and C, cuts the cube as shown in the figure. How many smaller cubes will get cut? [Figure: see page 5 of source PDF]

A rectangular wooden plank has another smaller rectangular hole cut into it as shown in the figure given below. What is the minimum number of cutting planes that can divide the wooden plank into four parts of equal volume? [Figure: see page 8 of source PDF]