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MATHEMATICS EXERCISE I

MATHEMATICS
EXERCISE I
Direction: Study carefully each problem is solved. Learn the formula used in each exercise.
Problem 1. Mary Ann must reach her destination by six in the evening. The total distance from point of origin to her destination is 300 kms. If she is to travel at the rate of 60 kms. Per hour, what time should she leave in order to her destination by 6 pm?
a.     2 pm.
b.     3 pm.
c.      1 pm.
d.     12 noon
e.     9 am
Problem 2. What is the average speed in miles per hour of a plane that covers             120 mile in one (1) hour and 20 minutes?
a.     30 mph (miles per hour)
b.     60 mph
c.      90 mph
d.     100 mph
e.     None
Problem 3. If a wheel rotates 12 times each minute, how many degrees does it             rotate in 5 seconds?
a.     60̊˚
b.     150 ˚
c.      240 ˚
d.     360 ˚
e.     90 ˚
Problem 4. Find how many pieces of oslo paper can be bought for P 17.00 at the      rate of 2 for P4.25?
a.     8
b.     15
c.      16
d.     75
e.     None of these
Problem 5. In a company with 270 employees, 2 out of every 9 are required to             work each Sunday. How many employees are required to work each             Sunday?
a.     135
b.     60
c.      3
d.     18
e.     None of these
Problem 6. Mrs. Salve made a down payment on a lot and had a balance of P7,             200. She pays for this over a period of 2 years by making equal payments             every other month. How much is the monthly installment?
a.     P600
b.     P300
c.      P36
d.     P3
e.     None of these
Problem 7. Mr. Ejercita borrowed P200 at 6% per annum for one (1) month in             order to pay a bill of P200 on which he was allowed a discount of 2 ½%.             The net result of these two transaction was:
a.     A gain of P4
b.     A gain of P5
c.      A gain of P8
d.     A gain of P7
e.     None of these
Problem 8. A staff of Basic and Co. of 20 clerks can finish a certain job in 6 days. How many more clerks should be put on the job in order to complete it in 4 working days.;
a.     7
b.     13
c.      27
d.     30
e.     None of these
Problem 9. On January 1, 2000, Anthony invested P200, 000.00 for 2 years at the      rate of 16.5% per annum compounded annually. By April 1, 2001, how             much interested would he have earned?
a.     P45,650.00
b.     P50,000.00
c.      P40,000.00
d.     P242,611.25
e.     P42,6611.25
Problem 10. Mr. Santarosa paid a total of P36, 000.00 in net income tax for             income earned in 2000. His tax rate is 28 ¼% of his annual net income.             What is his monthly net income?
a.     P10,000.00
b.     P10,619.46
c.      P11,000.00
d.     P12,000.00
e.     P127,433.60
Problem 11. How will it cost to lay 20 square meter of tiles if each square ft. of             tiles cost P8.50?
Problem 12. Find the denominator of an equivalent fraction to 5/6, when the             numerator is 350.
a.     416
b.     417
c.      418
d.     419
e.     None of these
Problem 13. What is the numerator of an equivalent fraction to 7/8 when the             denominators is 256?
a.     220
b.     221
c.      222
d.     224
e.     None of these

MATHEMATICS
EXERCISE II
ANSWERS AND SOLUTION
Problem 1.
            Answer: c. 1pm.
            Distance = rate x time
            In order to find out the total traveling time of Mary Ann from point of             origin to her destination, based on the formula above:
            T = Distance/rate thus, 300 km. / 60 km./hr. = 5 hours total travelling time
            Therefore, Mary Ann must leave by 1pm to reach her destination by 6 pm.

Problem 2.
            Answer: c. 90 miles per hour
            Distance = rate x time
            120 miles per hour = 1 hour and 20 minutes
            120 mph/80 = 80 minutes/80
            Rate = 1.5 miles per minute
                         1.5 miles x 60 minutes
                         90 miles per hour

Problem 3.
            Answer: d. 360˚ in 5 seconds
            360 ˚ = 1 complete rotation
            360 ˚ x 12 times = 4,320 degrees in one minute
            4,320 /60 seconds = 72 ˚ in one second
            72 ˚ x 5 seconds = 360 ˚ in 5 seconds

Problem 4.
            Answer: a. 8
            P17.00 / P4.25 = 4 x 2 = 8

Problem 5.
            Answer: b. 60
            270/9 = 30 No. of 9’s
            30 x 2 = 60

Problem 6.
            Answer: a. P600
            24 months / 2 = 12
            P7, 200 / 12 = P600

Problem 7.
            Answer: a. a gain of P4
            P200 x 0.06 = P12
            P12 – 12 = P1 interest for 1 month
            P200 x 2 ½% = P5
            P200 – P1 = P199 borrowed
            P200 – P5 = 195 amount par
            P4 gained

Problem 8.
            Answer: e. none of these
            Let x = No. of men to finish in 4 days
            20 : x = 4 : 6
            4x = 120
            X = 30 men to finish in 4 days
            30 – 20 = 10 men to be added

Problem 9.
            Answer: e. P42, 611.25
            For 2000 : P 200,000.00 x 165% = P33,000.00
            For 2001 : P starting balance = P200,000.00 + P33,000.00
                                                                   = P233, 000.00
            Monthly interest rate = 16.5% / 12
                        = 1.375% monthly
            Monthly interest for 2001 = P233, 000.00 x 1.375%
                        =P3,203.75 monthly
            1st quarter 2001 interest : P3,2013.75 x 3 months
                        =P9, 611.25
            Total interest earned:
                        = P33, 000.00 + P9,611.25
                        =P42, 611.25

Problem 10.
            Answer: b. P10, 619.46 monthly net income
            Tax paid = income tax rate x annual net income
            Tax rate = 28 ¼% = .2825
                        P36, 000.00 / .2825 = P127, 433.60
            Monthly income = P127, 433.60
                        =P10, 619.46 monthly income

Problem 11.
            Answer: P1, 829.88
            1 sq. m = 10.764 sq. ft.
            20sq. (10.764)
            215.28 sq. ft.
           
            20 sq. of m = 215.28 sq. ft.
            P 8.50 / sq. ft x 215.28 sq. ft.
            P 1,829.88  

Problem 12.
            Answer: e. none of these
            5/6 = 350/d or 5 : 6 = 350 : d
                        5d = 6 x 350
                        d = (6 x 350)/5 = 420

Problem 13.
            Answer: d. 224
            7 = N or 7 : 8 = N : 26
            8 256             8N = 7 x 256
                        N = (7 x 256)/8 = 224

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