BISC Quantum Quest (Round 2)

Amir bought 3 identical notebooks and 2 identical pens. The total cost of the notebooks and pens was $26. The cost of each notebook is $4 more than the cost of each pen. Let the cost of each pen be p. what is the cost of each pen?

Options:

• cost of each pen is approximately $3

• cost of each pen is approximately $2

• cost of each pen is approximately $4

• cost of each pen is approximately $5

A rectangle's length is 5 units more than twice its width. If the perimeter of the rectangle is 58 units, what is the width of the rectangle?

• width is 9 units

• width is 8 units

• width is 7 units

• width is 6 units

A large square of side-length 10 em contains a smaller square of side-length 4 em. as shown in the diagram. The corresponding sides of the two squares are parallel. What percentage of the large square is shaded?

• 25%

• 30%

• 40%

• 42%

The large rectangle in the diagram is divided into 30 equal squares. as shown. The perimeter of the shaded region is 240 em. What is the area of the rectangle?

• 480 cm2

• 750 cm2

• 1080 cm2

• 1920 cm2
  

After having played 200 games of chess. my winning rate is exactly 49%. What is the smallest number of extra games I need to play to increase my winning rate to exactly 50%?

• 1

• 2

• 3

• 4

15. Pentagon ABCDE is divided into four triangLes with equaL perimeter. TriangLe ABC is equiLateraL and AEF, DFE and CDF are three identicaL isosceLes triangLes. What is the ratio of the perimeter of the pentagon ABCDE to the perimeter of triangLe ABC?

• 3/2

• 4/3

• 5/3

• 5/2

A square of numbers is taken out from a multiplication table. Only one number is visible. The integers x and y are both positive and x is greater than y. What is the value of x?

• 6

• 7

• 8

• 10

The large square in the diagram is dissected into four smaller squares. The circle touches the right hand side of the square at its midpoint. What is the side-length of the large square? Note that the diagram is not drawn to scale.

• 18 cm

• 20 cm

• 24 cm

• 28 cm

Two equilateral triangles are put together to form a hexagon with their opposite sides parallel. We know the length of four sides of this hexagon.
as shown in the diagram. What is the perimeter of the
hexagon?

• 66

• 68

• 70

• 72

Triangle ABC is isosceles with LABC =40°. The two marked angles. LEAB and LDCA. are equaL. What is the size of the angle LCFE?

• 55°

• 60°

• 65°

• 70°