G102 [special]

Manila. Having their locations in coastal areas, PAGASA has identified them as key floodgates, Gate 1, Gate 2, Gate 3, Gate 4, and

Gate 5. This year, the recorded average volume of flood are 12 inches, 27 inches, 32 inches, 44 inches and 65 inches.

The city at Gate 4 got the least floods; the city in Gate 2 has the most floods

- Navotas is in Gate 1

- Caloocan got more floods than Valenzuela

- Marikina got more flood than Manila, but lesser than Navotas

-Valenzuela recorded an average of 44 inches flood

- The city in Gate 1 got 32 inches of floods, the city in Gate 3 got 27 inches of flood.

Which city has the highest recorded flood?

Caloocan

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In Metro Manila, five cities were identified to be most flood-prone areas, namely Caloocan, Marikina, Navotas, Valenzuela and

Manila. Having their locations in coastal areas, PAGASA has identified them as key floodgates, Gate 1, Gate 2, Gate 3, Gate 4, and

Gate 5. This year, the recorded average volume of flood are 12 inches, 27 inches, 32 inches, 44 inches and 65 inches.

- The city at Gate 4 got the least floods; the city in Gate 2 has the most floods

- Navotas is in Gate 1

- Caloocan got more floods than Valenzuela

- Marikina got more flood than Manila, but lesser than Navotas

-Valenzuela recorded an average of 44 inches flood

- The city in Gate 1 got 32 inches of floods, the city in Gate 3 got 27 inches of flood.

Where is Valenzuela located?

Gate 5

Determine the next two numbers in the sequence: 1, 10, 7, 20, 13, 30, 19, ?, ?

40, 25

Find a pair of numbers that provides a counterexample to show that the given statement is false.

If the sum of two counting numbers is an even counting number, then the product of the two counting numbers is an even counting number.

3, 5

Determine the next two numbers in the given sequence: 28, 25, 5, 21, 18, 5, 14, ?, ?

11, 5

Use inductive reasoning to predict the most probable next number in each list.

3, 7, 15, 27, 43, 63, ?

87

Determine the next number in the given sequence: 31, 29, 24, 22, 17, ?

15

Determine the next two numbers in the sequence: 3, 5, 35, 10, 12, 35, 17, ?, ?

19, 35

Determine the next two numbers in the sequence: 17, 17, 34, 20, 20, 31, 23, ?, ?

23, 28

Determine the next two numbers in the sequence: 42, 40, 38, 35, 33, 31, 28, ?, ?

26, 22

Determine the next two numbers in the sequence: 6, 20, 8, 14, 10, 8, 12, ?, ?

14, 14

Determine the next number in the given sequence: 14, 28, 20, 40, 32, 64, ?

56

Given n(L) = 710, n(M) = 270 and n(L n M) = 30, find n(L u M).

n = number of elements

950

Given n(A) = 1200, n(A u B) = 2270, and n(A n B) = 310, find n(B).

n = number of elements

1380

Given n(J) = 210, n(K) = 188 and n(J u K) = 388, find n(J n K).

n = number of elements

10

Find the domain of VTTTT 9 - x² [this means square root]

[-3, 3]

Let f(x) = 3x² + x - 5. Evaluate f(-2).

5

The vertical line test states that ____.

A curve in the coordinate plane is the graph of a function if and only if no vertical line intersects the curve more than once.

Let f(x) = x² and g(x) = x - 3. Find f(g(x)).

(x - 3)²

Find the domain of f(x) = 1 / (x² -x).

All real numbers except x=0,-1.

Let m and n be two real numbers such that m > n. Which of the following is equivalent to a Golden Ratio?

m + n / m

Let M be the Golden Ratio, which has an approximate value of 1.618. Which of the following is a property of M?

A) M = 1 + 1 / M

B) M= VTTT 1 - M

A only

In formal writing and communication, the common size of bond paper are the following:

Foolscap ---- 216 mm by 343 mm

A4 —— 210 mm by 297 mm

B4 —— 250 mm by 353 mm

A3 —— 297 mm by 420 mm

Which paper type is nearest to the Golden Ratio in terms of width to length ratio?

Foolscap

Question 25

Let Fn denote the nth Fibonacci number, where F1 = F2 =1. Find the sum F2 + F3 + F4 + F5.

11

Let Fn denotes the nth Fibonacci number, where F1 = F2 =1. Find F30.

832,040

A Fibonacci prime is a Fibonacci number that is also a prime number. Examples are F3=2, F4=3, F5=5, and F7=13. Which of the following is a Fibonacci prime?

233

This 21st-century mathematician is well known for his work on atmospheric phenomena. His many contributions to modeling naturally occurring patterns include cloud formations, rainbows, river meanders, honeycombs, and snowflakes.

John Adams

Let Fn denotes the nth Fibonacci number, where F1 = F2 =1. Find F19.

4,181

Let A be the statement "Alden is Asian" and B be the statement "Bernie is American". Which of the following best symbolizes the

statement "Alden is Asian while Bernie is American"?

A ʌ B

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Let A be the statement "Alden is Asian" and B be the statement "Bernie is American". Which of the following is the simplest

equivalent symbolism for the statement "Either Alden is Asian and Bernie is American, or neither Alden is Asian nor Bernie is

American"?

A ←→ B

Logically, "not both" and "both not" mean the same.

False

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Let A be the statement "Alden is Asian" and B be the statement "Bernie is American". Which of the following is the simplest

equivalent symbolism of the statement "Alden is Asian or if Alden is not Asian then Bernie is American"?

A v B

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How will you write the statement "It is not true that either I am wise or you are a fool" into a logically equivalent statement?

I am not wise and you are not a fool.

Joe tells you that he is an actor and went to India last summer. You know that he is lying to you, what compound statement about Joe is true?

I. Joe is an actor or he went to India last summer.

Il. Either Joe is not an actor or he did not go to India las summer.

II only

Consider a propositional language where

P: Paola is happy.

Q: Paola paints a picture.

R: Renzo is happy.

Formalize into symbols the following sentence: "If Paola is happy and paints a picture then Renzo isn't happy".

(P ∧ Q) → ¬R

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Consider a propositional language where

P: Paola is happy.

Q: Paola paints a picture.

R: Renzo is happy.

Formalize into symbols the following sentence: "If Paola is happy only if she paints a picture".

P —> Q

The statement "The number 1 is neither an odd nor an even" is a disjunction.

False

What is the truth value of the statement "If 2 is even then every prime number is odd"?

False