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Wednesday, April 11, 2018

Quantitative Analysis and numerical Reasoning Part 6



Problem – Solving

1. Josef purchased a lawn mower which was sold at 20% discount. He paid Php 14,800.00 for the lawn mower. How much was the original price of the law mower?
1.   Php 18,250
2.   Php 18,565
3.   Php 18,500
4.   18,575

Let  X = original price of the lawn mower
20%  = discount given   Php 14,800.00 = net price paid
X - .20X = Php 14,800.00
      .80X   = Php 14,800
      .80                  .80
             x  = Php 18,500.00
P 18,500 - .20 ( P 18.500 ) = P14,800
P 18,500 – P 33,700 = P14,800
          P14,800 = P14,800

Ans: 3

2. Ruth is paid P 17,000 for  regular 40hr. week. Up to 40 hours, she is paid at the regular hourly rate. For overtime of more than 40 hrs, she receives 11 ½ times as much as the regular hourly rate. How many hours did she work during a particular week when she earned about P 24,650.00 ?
1.   48 hrs
2.   52 hrs
3.   55 hrs
4.   54 hrs

Ruth’s regular rate per hour. = P17,000 / 40 hrs = P 425.00 per hr.
Ruth’s overtime rate per hour: Regular x 1.5 = P 425.00 x 1.5 = P 637.50
Ruth’s overtime pay: P 24,650 - P 7,650
Ruth’s overtime pay per hour: P 7,650 / P 637.50 = 12 hrs
Regular work week + overtime : 40 hrs = 52 hrs.

Ans: 2

3. A stationery pad that sells for P 18.50 can be bought for for P 150 when a dozen pads are purchased at one time. What is the savings per pad, in pesos, when the pads are purchased by the dozen?
1.   P 6.95
2.   P 6.50
3.   P 6.75
4.   P 6.00

P 150.00 / 12 = p 12.50 per pad
P 18.50 – P 12.50 = P 6.00

Ans: 4

4. On the day of the school concert, 500 tickets were sold. The students paid P150 each while non-students paid P200 each. If the total of P85,000 was collected, how many non-students attended?
1.   250
2.   230
3.   260
4.   200

Money collected = P85,000           # of tickets sold = 500 tickets
Let X = number of students           Let Y = number of non-students
              X + Y = 500
150X + 200Y = P 85,000
( X     +    Y     =    500 ) 150                     check: X + 200 = 500
 150X     +   200Y =    85.000                                   X  = 500 – 200

150X      +  150 Y =  75.000                                     X        =       300
150X      -   200 Y =  85.000
-                   50 Y = 10.000
          Y =  200

Ans: 4

5. A faucet filled a 315 gallon tank in 9 hrs. Later, the tank suffered a crack at the bottom and started leaking at the rate of 6 gallons/hr. How long will it takes the faucet to refill the emptied tank?
1.   11 hrs and 29 mins
2.   11 hrs
3.   10 hrs and 48 mins
4.   13 hrs

315b/9t – 6/1
                                                35 T - 6T = 31
                                                29T / 29 = 315 / 29
                                                          T = 10 hrs and 89 mins
                                                             = 10 hrs and 1 hr and 29 mins
                                                             = 11 hrs and 29 mins

Ans: 1

6 . Josef Raymund divided his estate among his three children: Joe, Ray and Sef in the ratio of 3: 2 : 2. If Sef received the amount of P 2.85M, what was the total estate ?
1.   P 10M
2.   P 9.975M
3.   P 9.5M
4.   P9.9M

P 2,850,000 / 2 = P 1,425        Joe : 3 ( P1,425,000 ) = P 4,275,000
           Ray : 2 ( P1,425,000 ) = p 2,850,000
            Sef : 2 ( P 1,425,000 )
                                     Total = P 9,975,000

Ans: 2

7. The Del Rosario family’s monthly income is P 25,000. The family spends 30% for food, 20% FOR rentals, 10% for clothing ans 16% for miscellaneous. How much is saved in peso value?
1.   P6,520
2.   P6,250
3.   P6,000
4.   P6,400

solution: 30% + 20% + 10% + 16% = 76%
             P25,000 x 76 / 100 = P1,900,000 / 100 = P 19,000
             P25,000 - P19,000 = 6,000

Ans: 3

8. A motorcycle covers 225kms in 2 ½ hrs. How far can he go in 1 ¾ hrs?
1.   158 kms
2.   157.5 kms
3.   150 kms
4.   165 kms

solution: 225 kms = 2.5 hrs     2.5hrs. N    = 225 (1.75)
                  N           1.75 hrs    2.5hrsN    = 393.75
                                                    2.5          2.5
                                          N   = 157.5 kms

Ans: 2

9. One way fare from Manila to Davao is P5,200. How many round trip tickets can be purchased with the amount of P104.000?
1.   11
2.   10
3.   12
4.   9

solution:  P5,200 x 2 = P10,400 round trip fare
             P104,000 / p10,400 = 10 round trip tickets

Ans: 2

10. Mr. Sison left his house at 7:00am and drove his car at 50kph. He rested for half an hour. What time he reach his destination which is 600kms away?
1.   7:30pm
2.   7:00pm
3.   8:00pm
4.   8:30pm

solution: speed = distance / time       ST = D
                                                        S      S
          T = D / S     T = 600 / 50 T = 12 hrs + 30 mins (rest time)
                             T = 7: 30 PM

Ans: 1

11. Ruth bought 55 copies of Phil. History and paid a total of p3,850.00. if she buys 3 copies more of the same book, how uch will she pay in all?
1.    P4,060
2.   P4,260
3.   P4,160
4.   P4,150

Solution: P3,850 / 55 copies = p70.00 per copy.
             P 70.00 x 3 more copies = P210.00
             P 3,850  210.00 = P4,060 total cost for 58 books

Ans: 1

12. A manufacturer finds that 150 pieces of pens are defective and unsuitable for sale. If the defective pens are equivalent to three percent of the production, how many pens are being produced?
1.   5,100
2.    
3.   5,000
4.   5,150

solution: Let X = no. of pens produced
               3% = percentage of defective pens in proportion to production
               150 = no. of defective pens

          3%X = 150 ; 3% X = or 150/3% or 150/.03
                             X = 5,000

Ans: 3

13. Timmie owns 40% of the stock in millennium Traders, Inc. Jsef owns 15,000
 shares. Bernice owns all the shares not owned by Timmie nor Josef. How many shares does Timmie own if Bernice has 25% more shares than Timmie?
1.   45,000 shares
2.   50, 000 shares
3.   60,00 shares
4.   75,000 shares

Solution: Timmie = 40% Millenium Traders
              Bernice = owns 25% more than Timmie’s share in the Company
              Josef = owns shares neither owned by Timmie’s nor Bernice
         = 100% - 40% - 50% - 10%

I f Josef owns 10% of Millennium  equivalents to 15,000 shares,
then Let X = 15,000 /.10
             X = 150,000       thus : Timmie owns : 40% X 150,000
                                                           = 60.000

Ans: 3

14. Mang Lorenzo, a gardener, can now a lawn in 3hrs. After 2 hrs, it raned and he stopped moving the lawn. In the afternoon. Aling Tina, completed the rest of the word in one hour and 30 minutes. How long would it takes Aling Tina to mow the lawn by herself?
1.   1 hr and 30 mins.
2.   2 hrs and 22 mins.
3.   2 hrs
4.   2 hrs and 30 mins.

solution: Part of work done =  time actually spent working
                                        time required to accomplish work    

Let X # of hours it would take Aling Tina to mow the lawn by herself.
Mang Lorenzop  = 2/3 of the work done in hrs.
Aling Tina = 1 ½ hrs to finish the rest of the work. 3/2 or ½
              = 3/2X = Part of the work done by Aling Tina
              = 2/3 + 3 / 3X            =       1
        3/2X             =       1/3 / 3/2
          X                =       2/9 or 2.22

Ans: 2
15. A couple wants to have only four children so spaced that the first is older than the second by  2 years, the second older than the third by three years, the third older than the fourth by 4 years. If their plan is realized, how old will the eldest child be  when the youngest is nine years old?
1.   18 yrs. Old
2.   9 yrs. Old
3.   16 years old
4.   17 years old
5.   18 years

Solution: Let X = age of the eldest by the time the younest is nine years. Old
             2 ÷ 3 + 4 = total no. of years.
                     9 = total no. of age difference.
                   If the youngest would be 9 years old, adding the no. of age
                   Difference: X + 9 years   =       18 years old
                                      Youngest   =          9 years old
                                   2nd to the youngest   =       9 + 4 = 13
                                      2nd eldest     =       9 = 4 = 13
                                          2nd         =       13 + 3 = 16
Eldest   =    16 + 2 = 18

Ans: 1

16. Mary purchased 4 lbs. of mixed nuts at P20.00 per lb. Rita purchased 2 lbs of peanuts at P15.00 per lb. What is the average price per pound for the mixture of both purchases?
1.   P18.33
2.   P17.50
3.   P20.00
4.   P18.75
Solution:  4 lbs  x  P20       = P80.00
               2 lbs  x P15.00   = P30.00
                                         P110.00 / 6lbs = P18/lb.

Ans: 1

17. Mr. Vergara paid a total of P28,650 in taxes for income earned in s2006. His tax rate is 34 ¼ of his gross annual income. What is his monthly income?
1.   P7,000
P6,970
P6,950
6,850
Solution: Tax paid = rate x annual gross income
             tax rate  = 34 ¼ % or .3425
             p28.650 / .3425 = P83.650
   Monthly salary : gross annual incoming /12 months
                       P83,650/12 = P 6,970

Ans: 2

18. On January 01, 2006. Margarita invested P100,000.00 ofr two years at a rate of 12% p.a compounded annually. By April 01, 2008, how much interest would she have earned?
1.   P29,250.50
2.   P29,203.20
3.   P29,204.20
4.   P29,205.50
5.   P29,200.00

Solution: for 2006 : P 100,000 X 12% = p12,000 (yearly interest)
            for 2007 : P112,000 x 12%   = P13,440 (yearly interest)
            for until April 01,2008    : P 125,440 x 12% = P15,052.80/12
                                                              P1,254.40(monthly interest) x23 months =
                                          P3,363.20
          Total interest earned : P12,000 + p13,440 + p3,763.20
                                         P29,203.20
Ans: 2

19. On march 01, 2006.George opened a savings account of P50,000 at the rate of 6% per annum compound monthly. By June 01, 2006, how much is his money in the bank ?
1.   P50,250
2.   P50,753.75
3.   P50,717.75
4.   P50,500

Solution: annual interest : 6% ; monthly interest : ½ or .5%
            by March 31     : (p50,000 x .005) + P50,000 = P50,250
            by April 30        : (P50,250 x .005 ) + P52.250 = P50,501.25
            BY May 31         : ( P50,501 .25x.005) + p50,501.25 = P50,753.75

Ans: 2

20. A Department store had a Megasale of Jackets at the ff. prices?
a.    P395.00 jackets reduced to P300.00
b.    P685.00 jackets reduced to p580.00
c.    P995.00 jackets reduced to P890.00
d.   P1,450.00 jackets reduced to P890.00
e.     
which group of jackets was offered at the greatest rates of discounts from its original price?
a.    24%
b.    15%
c.    10%
d.   15%
e.    25%

SOLUTION: P395.00 – P300.00 = P95.00 difference
A. 95. 00 = .24% x 100%         C.P995.00 – P 890.00 = P105.00
      395.00                                                                   995.00
                   95.00                                          =.10 x 100% = 10%
                   395.00
   
B. P685.00 – P580.00 = P 105.00/685.00     D. P1,450 – P1,250 = P200.00
                                = .15 x 100% = 15%                               1,450.00              
                                                                             =.13 x 100% = 13%
Ans: b

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