# Mathematics Part 2

WORD PROBLEMS
1. A DVD player is on sale ar a price of P 2,000. If he discount is 20% what is the original price of the DVD player?
A. P 2,500
B. P 2,400
C.  P 2.250
D. P 2,300
E. P 2, 450

ANS: A
EXPLANATION: 100% - 20% = 80%, 2000 + 0.8 = 2500

2. The Manila Metrostars scored 120 points twice nd 105 points three times in the fove games versus Hotdogs. What is Manila Metrostars’ average score?
A. 110 points
B. 117.5 points
C. 112.5 points
D. 115 points
E. 111 points

ANS: E
EXPLANATION: (2 X 120 + 3 X 105) = 555,555/5 = 111.

3. Mr. Baladjay received a a commission of P. 40,000 for selling real estate in Sta. Elena worth P 2,000,000. What is the rate of commission?
A. 5%
B. 2%
C.  4%
D. 1%
E. 8 %

ANS: B
EXPLANATION: 40,000 ÷ 2,000,000 = 0.02 = 2%

4. Penny deposite money at a bank at 10% interest compounder annually. If his money became P 137,00 at the end of one year, how much is his orginal deposit?
A. P 115,000
B. P 110,000
C. P 100,000
D. P 130,000

ANS: B
EXPLANATION: 100% + 10% = 110% = 1.1 137,500 ÷  1.1 = 125,000.

5. Miss Akasya types at a rate of 75 words per minute, At this rate, how long will take her to type a manuscript of 3600 words?
A. 48 minutes

B. 45 minutes
C. 54 minutes
D. 50 minutes
E. 60 minutes

ANS:  A
EXPLANATION: 3600 ÷ 75 =48.

6. A rectangular lot has a perimeter of 140 meters. If the length of thelot is 20 meters more than its width, what is its area?
A.  3,200 sq. meters
B. 2,500 sq. metes
C. 1,125 sq.  meters
D. 4,075 sq. meters
E.  none of the above

ANS:  C
EXPLANATION: Let w= width. 140 = 2 w + 2 (w + 20) 2w + 2w + 40 + 140 4w = 100 w = 25, w + 20 = 45, area = 25 x 45 = 1125

7. The gas tank of Mr. Ford’s car is 5/8 full. If he used 2/5 of this travelling from his house to his province, what part of the tank now has gas?
A. 7/40
B. 3/8
C. 7/15
D. 7/13
E. 1/12

ANS:  B
EXPLANATION: 5/8 x 2/5 = 1/4  = 5/8 – 2/8 = 3/8

8. 56. Men can build a small building in 20 days. At this rate, how many days can 35 men build a small building?
A. 12 1/2
B. 25
C. 48
D. 32
E. 24

ANS:  D
EXPLANATION: 56 x 20 ÷ 35 = 32

9. In Mehan’s garden, there are three roses for every two daisies. If there are three roses for every two daisies. If there a total of 45 roses and daisies, how many roses are there?
A. 15
B. 18
C. 27
D. 21
E. 24

ANS: C
EXPLANATION: 3  + 2 = 5 45 ÷ 5 = 9, 3 x 9 = 27

10. The difference between the squares of two consecutive positive integers is 17. What is the larger number?

A. 8
B. 9
C. 11
D. 7
E. 12

ANS:  D
EXPLANATION: x² (x – 1)² = 17 → x² - (x² - 2x + 1) = 17 → x² - x² + 2x – 1 = 17 → 2x – 1 = 17 ² 2x = 18 → x = 9.

11. In one day, the robots in Sta. Rosa factory can make 10 cars each. Two robots did not functioning, requiring the rest to make two more cars a day? How many robots were there originally?
A. 32
B. 24
C. 16
D. 12
E. 8

ANS:  D
EXPLANATION: 10 x 12 (x-2) 10x =12x – 2x = 24 x =12.

12. Biboy received his pension of P 10,000 on April 1 and spent it for his daily needs at a strict budget of 300 pesos a day. On what date will he have P 4,000 left?
A. April  10
B. April 27
C. April 20
D. April 12

ANS:  D
EXPLANATION: 10,000 – 4,000 = 6,000. 6,000 ÷ 300 = 20

13. Johnny English invested \$20,000 at rural bank at an annual rate of 10%. How much will investment be after two years?
A. \$22,000
B. \$24,200
C. \$23,800
D. \$24,000
E. \$22,000

ANS:  B
EXPLANATION: 20,000 x (1.10)² = 20,000 x 1.21 = 24,200.

14. The annual budget of a certain department amounts to P 2 billion. From his amount, the budget of the three bureaus are in the ratio 5:3:2.How much does the bureau with the smallest budget receive?
A. P 400 million
B. P 600 million
C. P 200 million
D. P1 billion
E. P 800 million

ANS:  A
EXPLANATION: 5 + 3 + 2 = 10 2,000,000,000 ÷ (2/10) = 400,000,000.

15. The sum of two integers is 74. If their difference is 26 what is the bigger number?
A. 24
B. 38
C. 48
D. 46
E. 50

ANS:  E
EXPLANATION:  74 – 26 = 48 ,48 /2 = 24,24 + 26 = 50

16. Brad Warden spent 30% of his love allowance on snacks, 40% on a book and had 45m pesos left. How much is his allowance?
A. 150
B. 180
C. 120
D. 200
E . 100

ANS:  A
EXPLANATION: 30% + 40% = 70%, 100% - 70% = 30% , 45 + 30% = 150.

17. Pipe A can fill a swimming pool in three hours while Pipe B can fill the same pool in two hours. If Pipe A and B are both open, how long will they fill the swimming pool?
A. 1 hour
B. 72 minutes
C. 2.5 hours
D. 5 hours
E. 50 minutes

ANS:  B
EXPLANATION:  x/3  +  x/2  =  1 → 5x /6 = 1 → x= 6/5 → 6/5 x 60 minutes = 72 minutes

18. Alonzo walks from his house to his office at a rate of six kilometers per hour. If it takes him 20 minutes for his trip how far is it from his house to his office?
A. 1 km
B. 1.5 km
C. 2 km
D. 2.5 km
E. 3 km

ANS:  C
EXPLANATION: 20min/60min = 1/3 6 x 1/3 = 2

19. An office canteen needs X kilos of rice for each customers a month. If there are Y customers in the canteen, for how long many months will Z kilos of rice last?
A. Y/XY
B. XY/Z
C. XYZ
D. Z/XY
E. XZ/Y

ANS:  D
EXPLANATION: X times Y represents the kilos of rice needed for Y customers. To get the number  of months , divide Z by XY.

20. Mr. Francisco bought garments at Divisoria for P.  22,000. If he sold them all and grossed P 29,700, how much profit did he make?
A. 35%
B. 25%
C. 15%
D. 30%
E. 20%

ANS: A
EXPLANATION: 29,700 ÷ 22,000 = 1.35 – 1 = 0.35 =  35%