The Philippine International Mathematical Olympiad (PhIMO) is the newest and most sophisticated international mathematics competition among Kindergarten to Grade 12 students.

The PhIMO is designed to honor the best learners in the world in mathematical problem-solving through friendly competition and foster cultural exchange among countries that participate therein.

Now in its 1st year, the PhIMO is being spearheaded by the Math Olympiads Training League Philippines, Inc. (MOTLI). (sc : www.phimo-ph.com)

**Berikut ini Soal dan Kunci Jawaban PHIMO MOCK EXAM 2020, JUNIOR SECONDARY**

1. In a certain football league, the only way to score is to kick a field goal for 3 points or a score a tonch down for 7 points. Thus the scores 1, 4 and 8 are not possible. How many positive scores are not possible?

A. 5

B. 6

C. 9

D. 11

E. 13

2. What is the number of distinct real numbers x which have the property that the median of the five numbers \(x, 6, 4, 1, 9\) is equal to their mean?

A. 0

B. 1

C. 2

D. 3

E. 5

3. In a group of five friends, the sum of the ages of each group of four of them are 124, 128, 130, 136, and 142. What is the age of the youngest of the friends?

A. 18

B. 21

C. 23

D. 25

E. 34

4. Eleven teams play in a soccer tournament. Each team must play each of the other teams exactly once. If a game ends in a tie, each team gets 1 point. For the games that do not end in a tie, the winning team gets 5 points and the losing team gets 0 points.

Which of the following is a possible value for the total number of points earned by the 11 teams by the end of the tournament?

A. 92

B. 196

C. 257

D. 290

E. 450

5. If \(x = \log_9 2\) and \(y = \log_5 4\), find \(\log_6 {15}\) in terms of \(x\) and \(y\).

A. \(\frac{2x + y}{xy}\)

B. \(\frac{2x + y}{y(1 + 4x)}\)

C. \(\frac{4x + y}{y(1 + 2x)}\)

D. \(\frac{y + 4x}{2}\)

E. \(\frac{x(4x + y)}{y + 1}\)