roughworks

UCEED 2018

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Q16.Shown in the figure is a pyramid with a square base, formed by vertices EFGH and a top vertex I. The diagonally opposite vertices, EG and FH are connected to form the vertex J at their intersection. The vertices I and J are also connected as shown. How many triangles are formed by all these vertices?

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Q18.Meethapur works on a barter system. Each person there loves different sweets. Mukund is willing to exchange 2 toffees for a lollypop and 3 ice creams for a toffee. Ranjana is willing to exchange one ice cream for 2 lollypops and 3 toffees for a lollypop. Mukund and Ranjana don't know each other, but both of them know Sita who loves toffees. Sita has one lollypop. She can meet Ranjana and Mukund only once (not necessarily in that order). What is the maximum number of toffees that Sita can get?

UCEED2018Q17·nat·Hard64 attempts

The length and breadth of the white rectangle are 6 and 4 respectively. The proportions of the outer black, middle red and inner white rectangles are the same. What is the length of the hypotenuse of triangle ABC?

Keyboards off — use the numpad, just like on exam day.