Problems And Answers PHIMO MOCK 2020 SECONDARY 3

6. Find the number of integers \(n\) such that \(\frac{5n + 26}{2n + 3}\) is an integer.

A. 1
B. 2
C. 3
D. 4
E. 5

7. Now is December. Which month will it be after \(43^{689}\) months?

A. April
B. May
C. June
D. July
E. August

8. What is the measure of the acute angle between the hour and minute hands of a correctly working clock at 4:18?

A. 12°
B. 15°
C. 18°
D. 21°
E. 24°

9. If a unit sphere (r = 1) circumscribes a cube, what is the surface area of the said cube?

A. 8 sq. units
B. 6 sq. units
C. 4 sq. units
D. 2 sq. units
E. 1 sq. unit

10. Find all ordered pairs \((x, y)\) such that \((x – 2y)^2 + (y – 1)^2 = 0\).

A. (1,2)
B. (-1,2)
C. (-2,1)
D. (2,1)
E. (2,-1)