Mapa Institute of Technology - GED 102

1)I have two more sisters than brothers. Each of my sisters has two more sisters than brothers. How many more sisters than brothers does my youngest brother have?

2. If 8 people greet each other at a meeting by shaking hands with one another, how many handshakes will take place? (assume that a person will shake hands only once with one person)

3. The number of ducks and pigs in a farm totals of 35. The total number of legs among them is 98. Assuming that each duck has exactly 2 legs and each pig has 4 legs, how many ducks are in the farm?
4. Determine the sixth number in the sequence 17, 15, 25, 53, 105.
5. This is a type of reasoning where a statement is reached by examining specific examples.
6. How many triangles are in the figure?

7. A Golden Rectangle has a width measuring 2.1 cm. What is the best estimate of its length?

8. Which of the following best defines the Golden Ratio?

9. Which is the closest approximation of the Golden Ratio?
10. In Fibonacci’s Rabbit experiment, which assumptions were applied?
    1. A female rabbit always produces a pair of rabbits, one male and one female.
    2. A female rabbit is able to produce offspring one month after it was born.
    3. The gestation period for a female rabbit is one month.
11. Let Fn denotes the nth Fibonacci number where F1=F2=1. If F22=17,711 and F24=46,368, then what is F23?
12. Let Fn denotes the nth Fibonacci number where F1=F2=1. Find F19.
13. Let Fn denotes the nth Fibonacci number where F1=F2=1. Find the sum F2+F3+F4+F5.
14. Consider the following the statements: p: You have high fever.

q: You have COVID-19 virus.

Write the following statement in symbolic form: You have COVID-199 virus but you don’t have high fever.

q?  p

15. Which of the following is a mathematical statement?
16. Consider the following conditional statement:

You can visit another city in Metro Manila only if you have a quarantine pass. What is the contrapositive of the statement?

17. Using a truth table, identify which of the statements given below is equivalent to the compound statement: p v (q  ? p ).
18. Under which conditions is the following compound statement “FALSE”? ( p ?r ¿ v (q ? r )
19. Which of the following pairs of statements are logically equivalent?
    1. Statement 1: It is not true that either I watch “Crash Landing on You” or you watch “Money Heist”.

Statement 2: I did not watch “Crash Landing on You” and you watched “Money Heist”.

19. 2. Statement 1: Joe tells you that he is an engineer and he studied in Mapua. Statement 2: If Joe is lying, then Joe is not an engineer, or he did not study in Mapua.
20. The following are symmetries of an equilateral triangle EXCEPT…
21. In a square ABCD, where does the vertex A go if a reflection with respect to the diagonal BD is applied?
22. In a 12-hour clock, what time is 64 hours past 7 o’clock?
23. Determine the check digit of the ISBN: 978-0-7432-5820.
24. Six different groups of children would like to visit the zoo and feed different animals. (assume each group will visit the zoo in only one day.)

Group 1 would like to feed the bears, dolphins, and gorillas. Group 2 would like to feed the bears, elephants, and hippos. Group 3 would like to feed the dolphins and elephants.

Group 4 would like to feed the dolphins, zebras, and hippos. Group 5 would like to feed the bears, and hippos.

Group 6 would like to feed the gorillas, hippos, and zebras.

Use a graph coloring to find the minimum number of days that are required so that all groups can feed the animals they would like to feed but no animals will be fed twice on the same day.

25. Which design wins if majority rule is applied?

26. Every planar graph is
27. A Euler circuit is possible to trace in graph where
28. A graph with at least one vertex and with no edges is called
29. On May 6, 2007, Dianne borrowed P6,000 and promised to pay the principal and interest at 16% compounded quarterly on Aug. 6,2014. How much did she repay then (approx..)?
30. Ed deposits P1,500 in a bank with 12% compounded quarterly. How much will he have in his account at the end of 2 years (approx.)?
31. What type of weighted voting system is described in W=(22:6,4,5,4,3)?
32. What type of voting system eliminates the candidates with the fewest number of first-place votes?
33. In a normal distribution, what percentage of the data lie within 2 standard deviations from the mean?
34. Consider the bivariate data: X: 10, 12, 14, 15, 16

Y: 8, 7, 5, 4, 1

Formulate the linear regression formula and estimate the value of y when x=5.

35. Which of the following does not apply to the normal distribution?
36. Consider the LP Problem: Maximize P=2x+3y Subject to : x + y ≤ 6

X    ≤3

X    ≥ 0, y ≥ 0

What is the value of y in the optimal solution?

37. In 2017, July 4 fell on a Tuesday. What day of the week is July 4, 2022?
38. Find the sum: 11010+10011 in the binary system.
39. An amount of Php 4,500 is deposited in a new account earning a simple interest at 5% rate for 7 years. What is the total interest earned at the end of 7 years?
40. A walk with no repeated vertex is called a ____
41. Determine the area under the normal curve that is between z=-1.97 and z=0.86.
42. The university is introducing…Which design wins if pairwise comparison is applied?
43. In a square ABCD, where does the vertex A go if a reflection with respect to the diagonal AC is applied?
44. Which type of symmetry is impossible to exist in a finite design?
45. The conditional statement ‘p arrow to the right q’ is logically equivalent to -–
46. What is the domain of the function f(x)=|x|?
47. What is the contrapositive of the statement: If x is not equal to y then x^2 Is not equal to y^2.
48. Consider the following conditional statement: you can visit another city in metro manila only if you have a q pass.

What is the converse of the statement?