Answers - Sample Test in Problem-Solving & Critical Thinking

B. Part 2

1.  Which is the smallest?

          a. 1/3

          b. 14%

          c. 0.2²

               d.  square root of 4

Detalye:       1/3 = 0.33

                    14% = 0.14

                    0.2² = 0.2 x 0.2 = 0.04

                    Square root of 4 = 2

2.  From his house, Jose drove West to his mother’s house for 4 hours. Then went North to visit his girlfriend for a 3-hour drive. From there, he decided to take a short cut South East to his house. Assuming that all conditions are the same, how long will it take Jose to reach his house?

          a. 3.5 hours

          b. 4 hours

          c. 5 hours

          d. 6 hours

Detalye:       Remember Pythagorean Theorem (Right Triangle)

                     a²  + b²  = c²

                               4²  + 3²  = c²

                              (4x4) + (3x3) = c²

                              16 + 9 = c²

                               c^{2 =} 25

                     c = square root of 25

                     c = 5 hours

3. John bought a car for P 500,000.00 It depreciates as follows:

          1^st year = 10%

          2^nd year = 15%

          3^rd year = 20%

          4^th year = 25%

          5^th year = 30%

If John decides to sell the car for P 175,000.00 at the end of the 5^th year, he will get a… (without considering taxes).

          a. loss of P14,350

          b. profit of P 14,350

          c. no profit or loss

          d. cannot determine loss or profit

Detalye:        Value of car after 1st year = 500,000 – (500,000 x 10%) = 500,000 – 50,000 = 450,000

                    Value of car after 2nd year = 450,000 – (450,000 x 15%) = 450,000 – 67,500 = 382,500

                    Value of car after 3rd year = 382,500 – (382,500 x 20%) = 382,500 – 76,500 = 306,000

                    Value of car after 4th year = 306,000 – (306,000 x 25%) = 306,000 – 76,500 = 229,500

                   

                    Value of car after 5th year = 229,500 – (229,500 x 30%) = 229,500 – 68,850 = 160,650

                    175,000 – 160,650 = 14,350 Profit                  

4. If two fair dice are rolled together, what is the probability that the outcome is 1 & 1?

          a. 1/6

          b. 1/12

          c. 1/3

          d. 1/36

Detalye:       Ang isang dice ay may 6 anim na mukha na may nakasulat na  tuldok na may bilang buhat 1 hanggang 6. Kapag inihagis ang isang dice, ang bilang ng tuldok na lalabas ay maaring 1, 2, 3, 4, 5 o 6. Kung gayon, ang probabilidad na  lalabas ang isang tuldok o 1 ay 1/6. Ang pangalawang dice ay gayon din ang probabilidad na lalabas ang 1 o 1/6.

          Kung gayon, kapag inihagis nang sabay ang 2 dice, ang probabilidad na 1 at 1 ang lalabas ay 1/6 + 1/6 = 2/6 o 1/3. MALI!

          Sa halip na i-add, dapat ay i-multiply ang dalawang probabilidad. Kaya, 1/6 x 1/6 = 1/36 ang tamang sagot. Subukang ilista ang mga combination na lalabas para makitang tama ang sagot. Halimbawa = 1,1 ; 1,2; 1,3; 1,4; atbp.

5. Nena’s grades in 5 subjects are 80, 83, 86, 81 & 88 while Josefa got 78, 82, 89 & 85 in 4 subjects. To have the same average grade, Josefa should get  ____ in her 5^th subject:

          a. 82

          b. 79

          c. 83.70

          d. 84

Detalye:       Average na Grado ni Nena = 80, 83, 86, 81 & 88 = 418/5 = 83.60

                    Average na Grado ni Josefa = 78, 82, 89, 85 & X =  (334 + X)/5 = 83.60

                    334 + X = 5(83.60)

                    X = 418 – 334

                    X = 84