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, SECONDARY 3**

1. On a certain test, the average score for the women in the class is 83, while the average score for the men in the class is 71. If the average score of all the stuents in the class is 80, then what percentage of the students are women?

A. 60%

B. 65%

C. 70%

D. 75%

E. 80%

2. An odd integer between 600 and 800 is divisible by 7 and also divisible by 9. What is the sum of its digits?

A. 27

B. 21

C. 18

D. 12

E. 7

3. If \(9^{-x} = 7\), then what is the value of \(27^{2x+1}\)?

A. \(\frac{27}{7\sqrt 7}\)

B. \(189\sqrt 7\)

C. \(\frac{343}{27}\)

D. \(\frac{7\sqrt 7}{27}\)

E. \(\frac{27}{343}\)

4. If \(x@y =\frac{x^3 – y^3}{x – y}\), for how many real values of \(x\) does \(x@1 = 0\)?

A. 0

B. 1

C. 2

D. 3

E. 4

5. If the squares of two consecutive odd numbers difer by 1000, what is the sum of the two odd numbers?

A. 500

B. 520

C. 540

D. 530

E. 540