Rte-m1 Algebra & Trigonometry

RTE-MI:

AJ.gebra

&

Trigonomdtry

1.

Three numbers are in A.p. such that the sum of the first and third is 12 _{and the product of the first and second is 24. Find} the largest of the three numbers.

2.

ln a

potato race,

8

potatoes

are

placed

6

feet apail on

a straight line, the first being 6 ft frorn the basket. _{A iontestani} starts from the basket and puts one potato at a time into the basket. Find the total distance he must run in order to finistr

4.4

8.8

_c.6

c.342fl

D.10

D.222ff.

ftid

m if

sre

of

the

D- t2,-18

iB. 432 ft

1"-3.

Find the sum of the first 100 positive integers exacfly divisibre

bv _.7.

A.35,350

8.2,053

_c.53,350

_D.25,536

the race: A. 532 ft.

4.

Two workers A and B tqgether can complete a job in 7 days. A works twice as fast as B. How many days woutO it take B to do the job _{wgrking alone?}

5.

The first of the three

numbers exceeds twice

the

second number by 4, while the third number is twice the first.

lf

the sum of the three numbers is 54, find the largest of the three numbers.

A. 10.Sdays: B.21days C. 9 days D. 18 days

4.12

8.32

c.

16

D.6

7-

h

h

ery.-m&2a(m+Ilx+24:O.

dbHG"[Eotg-A-!9"17

B.-tar8

A,24min.

B.20 min. C. 15 min. D.25 min.

B. -32.2,69.3 D. 20.9, -61.9

8.

A

caper(er

_{and his helper together can repair a house in 10}

days. h takes the helper E days longer than the carpenter to do the repair _{wften each works alone. How many days would}

[{ake

the helper to do the repair if he is to work alone? ' A. 22.8

days

B. 7.2

days

C. 17.8

days

D. 12.2 days

L

Two friends

A

and B are respectively S and

g

years old. ln how many years will the ratio of their

iges

be

3:4i

4.5

8.6

_..c.'.

D,7

10.

Roy

and

RR can

jog

around

a

circular

park

in

g

and

12 minutes, respectively. If they start at the same instant from ihe

same place, in fiow many _{minutes will they pass each other}

_if

they jog _{around the track in the same aireition?}

6.

The speed of tr,"

_@re

b

120 mi/rrr in a carm.

with

the wind it

cm

aer

a certain

dbErce

in 4 hours, but against the wind it cEn

oorrr

or*y 3rE

d

tlrd

distance in the same time. Find the

Ehcfydtuphd.

A

10

dtr

8.

flt

ni,tr

C.

Zl

milhr

D. 40 mi/hr

{g,rs,-rz

11.

Find the_term containing

x'

in the expansion _{of [x3+(a/g110}

A.12lat.f

-

C.

tioa?

B.21oa6*

D

.32oa?

12,

lf sinxcosx+sin2x _{=1 ,} what are the values of x in degrees? A.

32.2,69.3

,.._Q.

ZO.g, Ot.g

13.

Find the 1Sth term of the progrBsqion

1!4Jn,1fiA,...

A.46

B.

1/56

i

C:'1t46

D. 56

14.

Find the geometric mean betwgen -2 and -g.

4.4

B. 16

_D.6

B. 2: 48.636 sec

D.2:48

min & 30 sec

i

c.i+

15. ln how manyminutes after 2 o'clock will the hands of the clock extend in opposite directions for the first time?

A. 2: 43min & 0.636

sec

C.2:43

min & 38 sec

h,,

16.

Vvhicfi of the following is a factor of

xa-+f-lf+2}x+24.

1of 4

17. A number is divided into two parts such that when the .greater part is divided by the smaller, the quotient _{is 3 and}

the remainder is S. Find the smaller number if the sum of the two numbers is 37.

=reeEa=EE.

-e-ffiL

_ _ _ _ _

_

-:'.

A.

(x-3)

B. (x-2) C.

(x-1)

D. (x+3)

'4.I

8.12

c.32

_D.16

4.3ft

B.5ff

c.4

ft

18- What is the probabitity of getting a g exacily once in 3 throws with a pair of

dicef

A.0.033

B.0.263

c.0.862

D.0.751

19.

Find the value _{of A for which the equation A(2x+l)_} .

(x-4) = gx+{g is an identity.

A.

-1

B.

3

c.2

_D. _3

20.

lf coversed _{Sin0 =} 0.134 , find the value of versed Sin0 .

A.

0.8

B.

0.3

c.

0

5

D. 0.2

21.

A_wheel, 5 ft in diameter, rolls up an incline of 1g"20'. What is the height of the center of the wheelabove the base of the incline when the wheel has rolled up S ft

up the incline?

D.6ft

22.

A tree broken over by the wind _{forms a right triangle} w!!fr

tle

ground. tf the broken part

makejan

angle of b0" with the ground and the top ofthe tree is now ZO n ftom

its base, how tall was the tree?

c.45

ft D.36

fi

23.

Serren carpefiters and 5 masons eam a total of 2,300 per day. At

tre

sarne rate of pay 3 carpenters and g masons earn 2,0rl0. $Jtra( are the wages per day of a carpenter ,and a mason?

h.:no

a

tao

_c.

210

&17o

B.3m&210

D.270&

150

24.

Alady started a chain lefter by writing to four ftiends

and requesting each to copy the letter and send it to four other friends. lf the chain was unbroken until the

sth

-

-'

set of letters was mailed, how much was spent for postage at P8.00 per letter?

A.55fi

B.&+fi

A.12,219

8."10,912

A.5

kmlhr B. +

rWnr

c.21,435

D. 11,291

,

Q.8 km/hr

D.6

km/hr 25. 28.

Determine _{how much wat0r should be evaporqted from} 50kg of 30% satt solution to produce a OO* sait solution. All"percentages are by weight.

!,25

ks

B.35

kg

C. 15

ks

D. 18 kg

A machine costs PS0,000.00 and depreciates 20%

of

the original costduripg the first year,160/o during the second year,12% during the third year, and so on, for 5 years. What is the value at

thi

end of 5 years?

A.

15,000

_c.30,000

B.

25,ooo

_,'b.,zojooo

A boat going across a lake 8 km wide proceeds 2 km at a.certain speed and then completesthe kip at a speed

otlzkmlhr

faster. By doing this, the boat arrives 10 '

minutes earlier than if the original speed had been maintained. Find the original speed of the boat. 27.

28.

29.

z varies direc;tly as x and inversely as

f.

tt

x = 1 and y = 2, then z ₌ 2. Find zwhen _{x = 3 and y = 4.}

A:1.5

B.3

c.2.5

D.3.5

An audience of 540 people is seated in rows having the same number of persons in each row. lf 3 more'peisons seai in each row, it would require 2 rows less to seat

30. A

group consists

of

n engineers and

n

nurses. If two of the engineers are replaced by _{two other nurses, then 51% of} the group members will be nurses. Find the value of n.

D.31

4.80

B.110

c.55

D. 100

4.3

B.5

_c.4

_D.9

33.

Assuming the earth to be a sphere of radius 3g60 mi, find the distance of a point _{36"N latitude from the equalor.}

REE-MI:

Algebra

&

Trigonometry

the audience. How many persons were in each row originally?

4.17

B. 30

C.2484mi

D.4288 mi

c.

1360800 D.263

c.27

c.2&6

D.4&4

31.

lf Juan is 1070 taller than PedrO and pedro is 10% taller than Maria, then Juan is taller than Maria by how many percent?

A.2Oo/o

B.

18o/o

C.21Yo

_{D. 11yo}

32.

A piece of wire of length E2 cm. is cut into two unequal.parts. Each part is then bent to form

a

square.

lt

is found

tfrit

ttre

total area of the two sguares

is

g7'cm2. Find the difference between the sides of each square.

4.2844mi.

B- z+ag mi

3a.

11

_[ow

many ways can 10 different books be divided among

A, B,

and

C

so that

A

gets

5

books,

B

3

books, and

C

2 books?

4.2,520

B. so40

35.

From _{the eguation}

_{12f-af+U+18=0,}

_find

_the

_value

_of

_k

_if

one root is the negalive of the"ofrrer.

A

-18

B.-12

c-a7

D. -31

36- tf ore

rod

d

$f2€I+k=O

exceeds the ortrer by 2, find the vafue

ofk

AB

_h-)

8.5

D. -6

37.

The arithmeti! rnean of two numbers is 5, and their harmonic mean is 2415. Find the numbers.

38.

A

man has

P100,000,

part

of

which he

invested

al

12%

interest,and

the rest

at

18%.

He

received

a

total

annual interest of P15;300. How much did he invest

at

18% interest

i,qj

55,000

D.75,000

39.

Simplify the equation Sin2x(1+cot2x). A.

sin'x

C. 1

40.

A

vertical pole consists

of two

parts, each

one

half

of

the

whole pole.

_{At a}

point in

the

horizontal plane which passes through the fqot of the pole and 36 m frorn it, the upper half of

the pole subtend an angle whose tangent

is

1/3. How high is the pole?

4.72

8.25

c.46

D. 16

41.

ABDE is a square section and BDC is an equilateraltriangle

pitfr C outside the sguare. Compute the value of angle ACE.

i" A. 30

deg.

C. 50 deg.

8.60

deg.

D. 20 deg.

42.

The angle of elevation of the top of a tower from a point A is

23o30'. From another point B, the angle of elevation of the top of the tower

is

55"30' . The points A and

B

are 217.45 m

apart and

on the

same horizontal plane

as the foot of

the

'

tower. The horizontal angle subtended by A and B at the foot

of$e

tower is 90 degrees. Find the height of the tower.

,A.90.6

m

c.

89.s m

&3&5

.8:4&6

* rate? 4.45,000 B.60,000 2

of4

43.

At a meeting, after everyone had shaken hands with everyone else, it was _{found that 66} handshakes Were exchanged. How many were at the meeting? .A.

10

B.

20

c.12

-

D.24

44.

A number between 1 and 1000 (inclusive) is randomly selected. What is the probabitity that it wiil be divisibti

3411g(rsBm

D.55.9 m

o.

1t32 D.1t120

c.45ft

D.36ft

47.

Which is identically equalto secx(cok+tanx)?

8.86.7

m

4.1t28

a.

u64

4.55ft

8.64ft

A. cso< B. sinx

A.:2,60

8.2,17

Y=x"

Y =x2 C. cosx D. -secx G. 17,-60

D.2,60

c.

160,490 D.260,354

c'Y=x

D.Y=3x

by4

and

5?

l

A.0.03

.8. 0.05

_c.0.04

_D.0.06

45.

ln the series 1, 1, 1t2, 1t6, 1t24,,..., determine the 6th ternt

46.

A tree broken over by the wind forms a right triangle with the ground. lf the broken part makes an

ingle

of 50. with the ground and the top of the tree is now 20 ft from its base, how tallwas the tree?

48.

Woodz was four times as old as LC ten years ago. lf she is now twice as old as LC, how old is

Woodz?

-4.15

B.20

c.30

D.25

49.

A boat propelled to move at 25 miftrr in still water. trauets 4.2 miles upstream in the same time that lt

c n tra**

SE

roiles downstream. Find the speed

dthe

stsn

iA

4

B,

10

c.8

D. 12

50.

Find the value of x which will satisfy the equation

Ji-zlJi

_=t.

c.4

D.0,4

A. 1 B. 1,4

51.

Find the sum and product of roots qf the equation x3 +2x2

_-23x

_-60

₌

0.

52.

The probability _{that A can solve a given} problem is 4/5, that B can solve it is 2/3 and that C can solve it is 3/7. tf all three try, compute the probability _{that the} problem will be solved.

A.0.64

.b. o.go

8.0.52

D. 0.81

53.

ln how many ways can g different books be arranged on a shelf so that 3 of the books are never all 3 together?

A.

130,240

'9.

ggZ,O+O

Find the equation whose roots are numerically eqqal but qpposite _in sign to the roots of the equation

t'+7f+11x+S-O

|

_{$,ixl-l{1llx-5=0}

C. x3+7f+11x-S=0 B.

x"+7x2-11x+5=0

D. x3-7f-1 1x+S=0 Determine the sum of the first 10 terms of the sequence whose general term is given

by

3n

-2

.

4.88225

C.88255

8t88552

D.88522

lf.3logx

_-logy

₌

0,

express y in terms of x. 54.

55.

56.

,h:

B.

RTE-M1:

Algebra

&

frigonometry

lf he has twice as many dimes as quarters, and the number of nickels is two less than twice the number of dimes, how many quarters does he have?

A:3

8,8

c.6

D.10

58.

An organization has 25 members, 5 of whom are ECE's. ln how many ways c;ln a committee of 3 be formed so as to

include at leastone ECE?

A.540

.,4.

ttOO

C.970

59.

Sotve for x in the following equation:

x +3x +5x +7x +... +49x ₌ 625

4.1t4

B. 1

c.112

D.3t2

60.

lf

x '.

_!'.2

=

4:

-3'.2

and 2x + 4y

_-32

_{= 20} , find x,y,2.

A. 4, -5,

2

B. -8, 6,

-4

C. 5, -6,

I

D. 2,

-7,4

61. A

Caf6 Mocha Grande contains 16oz

of a

mixture of coffee and Chocolate which is 40% coffee by volume. How much of

the

mixture should

be

removed .and replaced

by an

equal volume oJ chocolate so that the resulting Caf6 Mocha will be

25o/o cofiee by volume? A. 7,5 liters

8.4

oz

C.2.4 oz

62.

lf the sides of the triangle are 2x+3,1+3x+3, and x2+2x, find the grcatest angle.

A. 100 deg. B. 130 deg.

Tte

sum and

dftrence

of

turo angles

in a

triangle are 90

desees

and

g)

degrees, respedively. lf the side opposite the

sr#

angle

b

Z) crn.,

fird

Ute area of the tsiangle.

ffi.

D.31'l

D.6oz

C:120 deg. D. 110 deg

c.289-6

D- 268.4 C. 120 deg. D. 140 deg.

A:t46_4

g_?31.5

64.

kr

tiaqte

ABG,

angb

A=80 deg. and point

D is

inside the

Eiangb,

lf

BD and CD are bisectors of angle B and C, solve

turthe angle BDC. A. _-!00 deg.

t:,lPoo"n'

65.

A statistical clert submitted the following reports. The average rate of production of radios is 1.5 units for every 1.5 hrs work

by

1.5

workers.

How many

radios

were

produced

in

one rronth by 30 men working 200 hrs during the month?

A.4000

B: seoo

66. A

class of

40

students took examination

in

Etectronics and Communications.

lf

30

passed

in

Electronics,

36

passed in Communication

and

2

failed

in

both

subjects,

how

many students passed in both subjects?

c.5000

D.4200

c.26

D.32

The excess of the sum of the fourth and

fifih

parts over the difference of the half and third parts of a number is 119. Find the number,

4.240

8.320

67. ,.

A.28

_B.30 A. bearing B. azimuth \.c..420 D.430

,

C, direction D. course

68.

How many terms of the progression 4,

7,

10,

13,.

. . must be taken so that the sum will be 69.

4,6

B.

I

C.8

D.12

69. What is the angle measured

in

degrees clockwise from the north to the direction in which the

carier

is traveling.

An urn contains 4 white balls and 3 black balls. Another urn contains 3 white balls and

5

black balls.

lf

one ball is drawn from each urn, determine the probability that the balls drawn will be 1 white and 1 black.

70.

3

of4

71.

Three friends A, B, and C can do a piece of work in

t

hours working together. Working alone, A can do the work in 6 hours more, B in

t

hour more, and C in twice the time if all working together. How long would it take to finish the work if att working,together?

4.27t56

B. 9/56

A.20

mins,

8.30

mins. the incline?

A.3ft

B.5ft

A:240 km. B. 180 km A. 17.545 '8.19.806

4.45.74

8.63.62,

A2:43.64

B.2:43.46 4.3144 rad

a

3le+ rad A. function B. domain

,Io:1uJr-G. 29/56 D.5t14

I

C.40

mins. 'D. _{50 mins} C.2A.87 m D.24.27 m c..4

fi

C.320 km. D.200 km

c.

18.525 D. 14.507 C.2:34.64 .D.2:34.46 C.4/33 rad D- 4143rad

72.

A golf ball is dropped from a height of 6 meters. On each rebound it rises 2/3 of the height from which it last fe[.

What distance has it

traveledlt

the instant it strikes the grognd for the 7th time?

A.27.89 m B. 19.86 m

73,

A wheel, 5

fi

in diameter, rolls up an incline of 18"20'. What is the height of the center of the wheel above the base of the incline when the wheel has rolled up 5 ff up

D.6ft

74.

The velocity of an airplane in still air

is

125 kph. The velocity.of the wind due east is 25 kph. If the ptane travels dast and returns back to its base again in 4 hours, at what distance does the plane travel due east?

75.

ln a racing contest, there are 240 cars which will have provisions that will last for 15 hours. Assuming constant

hourfi consumption for eacfr car, how long will the fuel

prwisions last if

I

cars withdraw from the race every hour afier the first?

4.16

8.18

c.20

D.25

76.

The sum of the sides of a triangle is equal to 100 cm. lf the angles of the triangle are in the continued proportions of

1:2:4. Compule the shortest side of the triangle.

77.

The sides of a triangular field which contains an area

of

2400 sq. cm. are in continued proportion of 3:5:7. Find the smallest side of the triangle,

G.95.43

',D.57.67

78.

What time after 2 o'clock will the hands of the clock extend ,,in.opposite directions for the first time?

79.

Tvrlo cities 270 mi apart lie on the same meridian. Find ther

difference in latitude.

80.

lt is a set of ordered pairs of numbers.

81.

The set of points in a plane such that the difference of the distances of each point of the set from two fixed points (foci) in the plane is constant.

C. range . D. relation C, Circle D. Ellipse C. 180 ways D. 320 ways A. Parabola

.8.

Hyperbola

82.

ln how many ways can a party of 6 people be seated on a row of 6 seats if a certain 2 refuse to sit next to each other?

A. 240 ways B: 480 ways

_rE lrrvlauq:,rlrv,

95. The vibration frequency of a string varjes as the square length and diameter of ihe string. lf the itring is 3 feet long and 0.03 inch in diameter vibrates at

7i0

times per second under g0 lbs tension, at what frequencv will a 2 feet long, 0.025 inch string vibrate under 2500 tbs tension.

A.6210

c.6830

8.7514

_D.5645

96.

The hypothesis of conditionalstatement. _The

_"if

_{part of} an "if-then" statement.

{'antecedent

B. postulate 97. 98. 4.349,800 ts.549,600 C. condition . D. theorem c.469,500

o.369,600

A compound statement that says one sentence is true

if

and only if the other sentence is true.

f.

dependent

statement

_{C. independent statement}

B.biconditionalstatement

D.conditionalstaiement

T_here are 3 copies each of 4 different books. ln how many different ways can they be arranged on a shelf?

99.

The distance passed over by a certain pendulum bob in succeeding swings form the geometric progression 16, 12,9,... feet respectively. Calculate the totai distance traversed by the bob before coming to rest.

4.64ft

B.75ft

c.54ft

D.96ft

100.At what price should Book Latte mark a book that costs F30O in order that it may ofier a

disount

of 20yo on tfre marked price and still make a profit ol 21o/o on the selling price?

A.400

.

B.5@

C.450

D.70O

83.

Find the real vatues of'x and y satisfiing the given equation:(2x+3y)+ i(3x-5y) = 8-i7 .

C. x=2,y=1 D,"x=2,y=-1

Algebra

&

Trigonometry

c.

1500 D. 1250 C. 3.1 days , D.f.03 days

c.

10, 11, 11 , D: 1.1, 11, 11 A. x=1 _, y=-2 B. x=-2, y=-1

84.

Missy goes to a bake shop to buy some pastries for resale at Booklatte. She spends half her money for Revel Bars, and one-third of what remains for Triple Chocolate Brownies. She spends 150 for other pastries and still has 200 left from the amount she originally _{had. How much money did shq have}

atthe start?

85.

86.

Roy met Mark and RR walking hand in hand in Trinoma, and because of jealousy he decided to walk northward _{away from}

the two at the rate of 2 _{m/s while the two went to the east at}

the rate of 0.5 m/s. afler how many minutes will the distance between them be 250 m?

A. 121

mins

,"C,2

mins

8.60

mins

"ii.

1 min

How many liters of

a

25o/o acid solution must be added _to g0

liters of

a

40o/o acid solution tci have

a

solution that is 30%

i*",tosa

_*9.5100

A. 10, 10, 11

B; 10,11 , 12

87.

Engr. RR walks at the rate of

6

mph to the LRT station. She

then

takes

the

LRT

to work,

averaging

at 60

mph.

if

she spends 15 minutes less time on the LRT than walking, and the distance

fiom her

house

to

work

is

29

miles, wtrat

is

the disEnce fro{n her house to the LRT station?

acid?

A. 160

L

8.90

L

c.

100 L D. 120 L

A

3

.8.1

'.-_j

c.5

D.6

Three

fienG

A, B, and C are in a rztce. The odds

trat

A will win ale 7 to 5, and the odds that B

willwin'are

1 to 3. What are the odds in favor of C?

A.1to4 B.3to2

'Q,

1,to5

D.2to5

Two numbers differ by 40 and their arithmetic mean exceeds their geometric mean by 2. Whalare these numbers? A. 75 &

115

B. 45 &

85

C.8.1

&121

D. 88 &128 Which of the following is a prime number?

A.437

8.483

c.417

,iD.4g7

91. A

and B working together can

do

a

job in 3

days, B and C

together can do the same job in 4 days, and A and C in 2.5 days. ln how many days can all of them finish the job working together?

A. 1.07 days B. 2.8 days "

Find the mean, median and mode respectiv.ely of the following numbers; 13,13,

14,12,11,10,9, 11,8,11,5,

and 15. 88.

89.

90.

93. The age

of

Diophantus,

a

Greek

mathematician

may

be

calculated

from

the

epitaph

which reads

as

follows: 'Diophantus passed 1/6 of his life in ohildhood, 1112 in youth,

117 as

a

bachelor. Five years after his marriage was born a son who died 4 years before his father at half his father's final

age.'How old was,Diophantus when he died?

A.80

8.82

Your father

told you "[ was your age

now when you were

bom'. lf you are 21 years old today, how old is your father?

.c.78

'.D"'84

A50

Br42

i-,.

c.48

D.44

k

94.

4ot4

UIIU . AIIU t tr. VgV I

---r----Algebra

& Erigonometry

101. This states that every integral rational equation has at least

one root.

A. Fundamental Theorem of Arithmetic

p. _{Fundamental Theorem of Counling}

,C. Fundamental Theorem of Algebra D. Fundamental Theorem of Eq-uations

102. The logarithm of the reciprocal of a numberis called

103. How many differenl signals, each consisting of 8 flags hung in a vertical line, can be formed from 4 identical white flags and 4 identical blue flags?

&.70

B. 1680

104. Find lhe mean deviation for the following set of data: {10, 20,

A. lnverse Logarithm B. Cologarithm C. lndex D. Briggsian Logarithm

c.

140 D.3360

c.60

D. 3.33 C,r28.6 mph D. 38.5 mph

c.4.83

D.6.63

c.3t26

D.1t2197

c.

13/3888 D.25t7776

c.1t16

D.1t21A

c.

0.051 D.0.238

c.84/14s

D.37t425

c.0.0584

D.0.0093 301

A.6.67

8.20

105. Rex travels 50 miles at the rate of 20 mph and then on a free way travels the next 50 miles at the rate of 50 mph. Wtrat is his average speed?

A. 35.0 mph

8.48.8

mph

106. Find the quadratic mean of {2, 4, 6, 8, 10}

107. Find the probability of obtaining an ace on three draws frcm a

dd

of cards when there is no replacement befiore the next one is draam.

A. 1/525

'8.

115525

108. The probability of throwing at least

4

aces in 5 throvra of a die.

4.23t648

B.5t1944

109. A new phone is being installed at the Allado's residence. Find

the

probability

that

lhe

final

four digits

in

the

telephone number will be odd.

4.4t7

8.256t2401

110. Find the probability of throwing at least one ace

in

10 throws of,a die.

4.0.838

B. 0.161

11 1. Two cards are drawn at random from a standard deck of E2

cards. What is the probability that both are diamonds?

A.3.33

8.5.50

4.13t52

8.7t13

4.0.0385 8.0.0835

c.7t26

1,.p."1t17

1'12. A committee of 5 people is to be selecded from a group of 6 men and 7 women. VUhat is the probability that the committee will have at leasl 3 men?

A.59/143 8.14At292

113. Billie guesses

on all

10 questions

on

multiple choice quiz, each number having four choices, What is the probability that exactly hatf of the'answers arc correct?

114. A line map was drawn at a scale of 1:50,000. An enor of 0.05

mm

in the

drawing

is

equivalent

to

how

many rneters in _ac{ual?

,A. p.s m

c.0.25

m

5of5

!ola!@p@s

gc$\t

8.250

m

D.25

m

115. A flagpole 3 m high stands at the top of a pedestat 2 m hii:rh

located at one side of a pathway. At the opposite side of tire pathway directly facing

the

flagpole,

the

flagpole subten:ls

the

same angle

as the

pedestal. \A/hat

is the

width

of il

e pathway?

116. Two sides of a triangle measure 18 cm and

6

cm. The third side may be:

A. 12 cm

B.

13 cm A.3.21 m B. 5.25 m

A.

Unary matrix Ef Unit matrix A. nonillion B- ododecillion

A.

1.15 hrs B. 1.125 hrs A. P180.00 B. P170.00 C. rt.47 m D.6.28 m C. 10 cnr D. 11 cm C. tdentity matrix D. Nullmatrix C. novemdecillion D. octillion C. 1.325 hrs D. 1.525 hrs Q.3:22.22 D.3:44.44

c.

P150.00 D. P225.00

118.

are functions which can be expressed using arithmelic operations and vrrhose values are either rational or a root 01 a rational number.

A.Transcedentalfunctions

C. lnationalfunctions

B. Algebraic

functions

D. Logarithmic functions

'l _{19. The number follow ed by 27 zeroes is called}

120. The hypothesis that an integer

"n'

is prime

ifi

it satisfies tiie

condition

2

n-2

is divisible by

n-A. Goldbach's

conje€ture

C. Chinese hlryothesis B. Wlson's Theorem D. Ob typothesis

121. The ages

ofthe

molher and her daughter are 45

ard

5 year;,

rcspectivety.

Hor

many years will the mother be

thre

tim: s as old as herdaughterwill?

A.5

B.

10

_!.c.

15

122. A pipe can fill up a tank with the drain open in three hours.

lf

the pipe runs with the drain open for one hour and then trre drain is closed, it will take 45 more minutes for the pipe to iill the tank, if the drain will be closed at the start of filling, h<rw

long will it take the pipe to fill the tank?

D.20

123.

_'

A man left his home at

pasl3:00

PM as indicated in his wllll clock. Between two

to

three hours after, he retumed horile and noticed that the hands of the clock interchanged. At wl.rat time did he left his home?

4.3:27.27

d.s:gl.lz

124.

A

group consist of

n

boys and

n

girls. If two of the boys

*re

replaced by two other girls, then 49olo of the group memh#r will be boys. Find the value of n.

A.

100

8.49

c.50

D.51

125. On his Christmas sale, a merchant marked

a

pair

of

slipp,r*n

P180.00, which is 2oolo olf the normal retail price. lf the retall

price

is

500/o higher than

the

wholesale price,

what is

fl,le wholesale price of the slipper?