## Quantitative Analysis and Numerical Reasoning Part 4

PROBLEM SOLVING:
1.   What part of an hour elapse between 50 am and 12.14 pm?
1)   2/5
2)   7/30
3)   17/30
4)   1/6
5)   ¼
Ans: 1
10 minutes by noon and 14 minutes after noon makes a total of 24 minutes
1hr. = 60 mins.     24 mins. / 60 mins = 2/5 hr.
2.   A motion was passed by a vote of 6 is to 4. What part of votes cast were in favor of the motion?
1)   6/10
2)   6/4
3)   4/6
4)   4/10
5)   3/2
Ans: 1
3.   if three miles is equivalent to 4.83 kilometers, then 11.27 kms. is equivalent to how many miles?
1)   2 1/3 miles
2)   7 1/3 miles
3)   5 miles
4)   7 miles
5)   6 ½ miles
Ans: 4
3 =    X               = 4.83X     =   33.81       =  X = 7 miles
483    11.27            4.83            4.83
4.   Ever good Systems employs 115 people. During the low season, it laid off 20% of its employees. By what percent must be company increase its’ manpower to return to full capacity?
1)   20%
2)   22%
3)   23%
4)   25%
5)   30%
Ans: 4
20% = 1/5 manpower after lay-off : 20% x 115 = 23 people laid off.
115 – 23  =  92 pax employed
to return to full capacity : 23/92 = .025 x 100 = 25%

5.   Gold town Books offers 2006 World Almanac marked at P2,450.00 less discounts of 10% and 5%. Another bookstore offers the same book but with a single discount of 15%. How much does the buyer save by buying   at the best price?
1)   P12.25
2)   P12.50
3)   P12.00
4)   P10.50
5)   P15.00
Ans: 1
Goldtown Bookstore         : P2,450 x 10% =P245.00
: P2,450 – P245.00 = P2,205
: P2,205 X 5% = P335.25
Total Discount                  : P245.00 + p 110.25 = p355.25
Net Price                          : P2,450.00 – P355.25 = P2,082.50

: P2,094.75 – P2,082.50 = P12.25
6.   Josef travels a distance of 20 kilometers at 60 kms. per hour (khp) and then returns over the same route at 40 kph. What is his average rate for the round trip in kms. per hour?
1)   50 kms
2)   48 kph
3)   47 kph
4)   46 kph
5)   45 kph
Ans: 2
Average rate = total distance
total time
total distance = 20kms + 20 kms = 40 kms
time   = distance
rate
time for the first trip        : 20 kms / 60 kph = 1/3 hr.
time for 2nd trip               : 20 kms/ 40 kph = 1/2hr.
total time                        : 1/3 + ½ = 5/6 hr. (LCD =6)

Average rate:       40or 40 (6/5) = 240 = 48 kms. per hr.
5/6                      5
7.   Mr. Mondragon took his four children to the trade exhibit. The total cost of their six children had to pay P220.00 What was the cost of an adult ticket and that of a child’s ticket?
1)   P35.00 & P25.00
2)   P25.00 & P35.00
3)   P24.00 & P35.00
4)   P35.00 & P28.00
5)   P40.00 & P30.00
Ans: 1
Let X = cost of an adult ticket ; let Y = cost of a child’s ticket
For Mr. Mondragon  : X + 4Y = P135.00
For Santos Family   : 2X + 6Y = P220.00
1stequation           : X = 135 – 4Y
2nd                             :2 (135 – 4Y) + 6Y = 220
: 270     8Y + 6Y = 220
:        -8Y + 6Y      = 220 – 270
:             -2Y         = -50
-2              -2

Y      =         25

Substitution:         X + 4(25) = 135             2(35) +6(25) = 220
X +  100   =135                   70 +  150
X        =135 – 100                 220   = 220

X  =35

8.   Tim and Bernice both have part time jobs. Last week, Tim worked 8 hours and Bernice, 5 hours and both of them earned a total of P800.00. This week, Bernice worked 12 hours and Tin, 4 hours and they earned a total of P1,250. How much is Tim’s hourly rate?
1)   P48.00
2)   P49.00
3)   P44.08
4)   P44.50
5)   P45.00
Ans: 3
Let X = Tim’s hourly wage rate: Let Y = Bernies hourly wage rate
For the 1st week : 8X + 5Y = P800
For the 2nd week : 4X + 12Y = P1250
Solution:     8X + 5Y = 800                         8X  +  5Y  = 800
-2(4X + 12Y = 1250)               -8X  – 24Y = -2500
8X + 5(89.75) = 800                                        -19Y   = -1700
8X + 447.35   = 800                                        -19           -19
8X     =325.65                                   Y     =   89.47
8              8        X = 44.08
9.   What is Bernice’ hourly rate?
1)   P89.90
2)   P89.00
3)   P88.75
4)   P89.47
5)   89.50
Ans: 4
see # 8 solution
10.                If X located on line segment AB and point Y is located on line segment CD. If AB=CD and AX> CY, then:
1)   XB> YD
2)   AX>XB
3)   XB<YD
4)   AX<XB
5)   AX>AB
Ans: 3
A____________X____B  : C______Y____________D
If unequal quantities are subtracted from equal quantities, the results are unequal on the same order.
11.                If W>X, Y<Z and X>Z then, which of the following equation must be true?
1)   W>X>Y>Z
2)   W>X>Z>Y
3)   X>Z>Y>W
4)   Z<Y<X<W
5)   Z<X<Y<W
Ans: 2
The 1st and 3rd statements assert that W> X and X>Z, therefore, W>X >Z.
The 2nd statement say that Y < Z, thus  W > X > Z > Y
12.                The number of degrees through which the hour hand of a clock moves in two hours and 12 minutes?
1)   66 degrees
2)   72 degrees
3)   126 degrees
4)   732 degrees
5)   792 degrees
Ans: 1
12 hrs = 360 deg. ; 1 hr = 360 deg/ 12 hrs. = 30 deg/ hr or ½ deg./ min.
2 hrs = 30 deg x 2hrs = 60 deg
12 mins = ½ deg./min x 12mins = 6 deg
2 hrs at 60 deg. + 12 mins at 6 deg = 66 deg.
13.                Fatima is 15 years old. Bernice is one –third older. How many years ago was Bernice twice as old as Fatima?
1)   3
2)   5
3)   7.5
4)   8
5)   10
Ans: 5
Let A = Fatima’s age : Let B = Bernice’s age
A= 15 yrs old
B=15 + 1/3 (15)
= 15  + 5 = 20 yrs old
15- N = Fatima’s age # of years ago
20 – N = Bernice’s age# of years ago
(20 –N) = 2 (15-N)
20-N = 30 -2N: 2N –N = 30 20
N= 10
14.                Mel is 67 years old. His son Jay is 29 years old. In how many years will Jay be exactly half his father’s age?
1)   6
2)   7
3)   8
4)   9
5)   10
Ans: 4
Age of Mel when Jay was born : 67 – 29 = 38
When Jay reaches age 38, he will be half his father’s age.
That will occur in X years where:
29 + X = 38 years
X         = 38- 29
X         =9
Jay’s present age is 29 years . In 9 years, he will be 38 years old, (29 + 9) and his father Mel will be 76 years old (67+ 9), twice the age of Jay.
15.                the Marcopper Mining Company has 3,900 workers. Only 3% are noun-union members. How many workers then are members?
1)   3750
2)   3760
3)   3720
4)   2738
Ans: 4
solution: 3,900 x 3/100 = 11,700/100 = 117 are non-union members
3,900- 117 =3738 are union members
16.                A painter can finish painting 25 desks in 6hrs. How many desks can be painted from 6am to 9pm?
1)   60
2)   63.5
3)   62.5
4)   65
Ans: 3
solution: 6am to 9pm =15hrs   25 = 6 = 6N = 375
N      15         6       6
N=62.5
17.                The average of four numbers is 28. If three of the four numbers are 18, 28 and 36, what is the fourth number?
1)   32
2)   30
3)   35
4)   34
Ans: 2
solution: 18 + 28 + 36 = 82    28 = x/4      4(28) = X
112= X
112-82 = 30 I9S THE 4th number
18.                What is the difference in elevation between the top of a mountain 8,520 feet above sea level and a point in a valley 253 feet below sea level?
1)   8777
2)   8700
3)   8773
4)   8774
Ans: 3
solution: 8520 – (-253) = 8,520 + 253 = 8773

19.                If there are three microscopes for every four medical students. how many microscopes are needed for 44 students?
1)   42
2)   33
3)   40
4)   30
Ans: 2
solution: 4 = 3                4N = 3(44)  4N = 132
44   N                                   4       4

N = 33

20.                What is the value of a in the statement 3ab =15 if b = 5?
1)   1
2)   0
3)   2
4)   .5
solution: 3 ab = 15    3ab (5) = 15         15a = 15
15     15

a  =   1
Ans: 1