Monday, May 29, 2017

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
                               c2 = 25
                     c = square root of 25
                     c = 5 hours

3. John bought a car for P 500,000.00 It depreciates as follows:
          1st year = 10%
          2nd year = 15%
          3rd year = 20%
          4th year = 25%
          5th year = 30%
If John decides to sell the car for P 175,000.00 at the end of the 5th 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 5th 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