Loyola Jesuit College Entrance Examination (May 2004) Mathematics

Loyola Jesuit College Entrance Examination (May 2004)

MATHEMATICS
Samples:
A. In the sequence: 2, 3, 6, 11, 18, …, what number should come next?
a) 28
b) 25
c) 29
d) 27
e) 26

The correct answer is (d).

B. What number added to 11 makes 7 times 5?
a) 35
b) 18
c) 24
d) 23
e) 14

The correct answer is (c).

C. Examine (A), (B) and (C) and find the best answer.
(A) (16 – 3) – 5
(B) (16 – 5) – 3
(C) 16 – (5 – 3)
a) (A) is greater than (C).
b) (A) and (B) are equal.
c) (B) is greater than (C).
d) (A), (B) and (C) are equal.

The correct answer is (b).

Choose the LETTER of the correct answer to questions 1 through 50.

1. Evaluate 4.37 x 5.6 4. If the area of a square is 289 square units. What is the
a) 24.472 length of a side of the square?
b) 244.72 a) 13 units
c) 2.4472 b) 14 units
d) .24472 c) 23 units
e) 24472 d) 19 units
e) 17 units
2. Express 90,019 in words.
a) nine thousand and nineteen 5. Hours Minutes Seconds
b) nine thousand, one hundred and nine 21 11 16
c) ninety thousand and nineteen – 8 24 48
d) ninety thousand, one hundred and nine
e) nine hundred and nineteen
a) eleven hours, 47 minutes, 34 seconds
3. Add 8.73, 2.58, 36.4 and 0.17 b) twelve hours, 46 minutes, 28 seconds
a) 46.88 c) twelve hours, 47 minutes, 54 seconds
b) 48.92 d) twelve hours, 47 minutes, 28 seconds
c) 48.98 e) eleven hours, 46 minutes, 28 seconds
d) 47.88
e) 47.78 Go on to the next page.


6. What number divided by 13 is 1/7 of 126? 13. As a train departs from station A, it has 12 empty seats,
a) 138 14 seated passengers, and 4 standing passengers. At the
b) 18 next stop, 8 passengers get off, 13 passengers get on, and
c) 104 everyone takes a seat. How many empty seats are there?
d) 136 a) 1
e) 234 b) 2
c) 3
7. Look at this series: 1,V, 6, X, …. What number should d) 4
come next? e) 5
a) XIV
b) 10 14. What number is 7 less than 14 squared?
c) XI a) 203
d) 14 b) 21
e) 11 c) 89
d) 189
8. Find the volume of a box measuring 12 cm by 9 cm by e) 91
26 cm.
a) 2,808 cm3 15. A car travels at an average speed of 68 km per hour.
b) 2,088 cm3 How many kilometres does it cover in 6 1/2 hours?
c) 2,806 cm3 a) 284 km
d) 2,708 cm3 b) 442 km
e) 2,086 cm3 c) 408 km
d) 224 km
9. Find the circumference of a circle whose diameter is 28 e) 342 km
cm (Take π = 22/7)
a) 176 cm
b) 84 cm 16. What is the smallest number that can be divided exactly
c) 48 cm by 4, 7 and 12?
d) 88 cm a) 108
e) 96 cm b) 112
c) 144
10. Find the average of 19, 27, 0, 7, 11 and 8. d) 168
a) 13 e) 252
b) 20
c) 11 17. Which one of the following fractions has the same value
d) 12 as 3/8 ?
e) 15 a) 3 - 2
8-2
11. ½ of what number is 16 times 4? b) 3 x 2
a) 128 8x2
b) 64 c) 3 + 2
c) 122 8+2
d) 84 d) 6 2
e) 32 9 1
e) 4 - 1
12. Look at this series: A, 8, F, 13, K, …. What should 3+4
come next?
18.How many 40 kobo can we get in ₦ 10.00?
a) 17, P a) 5
b) 18, P b) 10
c) 18, O c) 15
d) 17, O d) 20
e) none of these e) 25


19. A cyclist is travelling at an average speed of 18 km per 26. When a certain number is divided by 25, the result is 32
hour. How long will it take to travel a distance of 117 km? with a remainder of 17. What is the number?
a) 4 1/2 hours a) 857
b) 5 1/2 hours b) 817
c) 6 1/2 hours c) 837
d) 6 hours
e) 7 hours
d) 827
e) 847
20. How many minutes are there from 11:15 P.M. to 27. If a student had a score of 70%, how many marks out of
2:35 A.M.? 140 did he obtain?
a) 160 a) 68
b) 170
c) 190
b) 58
c) 78
d) 200
d) 98
e) 210
e) 88
21. If 16/20 = 3a/30, find the value of a. 28. Express 144/360 in its lowest form.
a) 2 a) 4/5
b) 5 b) 2/5
c) 6 c) 3/5
d) 8 d) 1/3
e) 12 e) 2/3
29. If 1/5 of 100 oranges is given to John and 1/4 of the
22. Simplify 7/8 of 2/21 + 11/12.
remaining oranges is given to Mary, what fraction of the
a) 85/96 oranges is left?
b) 1/2 a) 4/5
c) 1 b) 3/5
d) 2 c) 2/5
e) 3
d) 9/20
e) 11/20
23. Express 1 + 1/10 + 11/100 + 7/100 as a decimal.
a) 1.18 30. Given that 8 km = 5 miles, how many miles are in
b) 1.28 144 km?
c) 1.38 a) 80 miles
d) 1.48 b) 96 miles
e) 1.58 c) 72 miles
d) 90 miles
24. What is the difference between 3.5 kg and 6.24 kg? e) 75miles
(Give your answer in grammes.)
31. A tin measuring 10 cm by 5 cm by 4 cm is to be used in
a) 2.74 g
filling a tank 20 cm by 8 cm by 5 cm with water. How
b) 9.74 g
many times will the tin be used to fill the tank?
c) 274 g
a) 4
d) 2470 g
b) 5
e) 2740 g
c) 2
d) 8
25. Find the area of a circle whose diameter is 14 cm (π = e) 6
22
/7).
a) 616 cm2 32. Express 10/1000 as a decimal.
b) 176 cm2 a) 0.00001
c) 154 cm2 b) 0.0001
d) 44 cm2 c) 0.001
e) 38.5 cm2 d) 0.01
e) 0.1

Go on to the next page.


33. If 8 books cost ₦ 48.00, how many books can I buy for 39. An angle that is greater than 90o and less than 180o is
a(n)
₦ 114.00? a) complementary angle
a) 13 b) obtuse angle
b) 15 c) right angle
c) 16 d) acute angle
d) 19 e) reflex angle
e) 21
40. If a pie is divided into 40 parts, what percent is one part
1 of the whole pie?
34. /4 y - 9 = 36. What is the value of y?
a) 40
a) 100
b) 25
b) 140
c) .25
c) 160
d) 4.0
d) 180
e) 2.5
e) 200
41. A basketball team won 18 games, which was 40% of its
35. Which of the following statements is true about the season. How many games did the team lose?
calendar year? a) 27
a) Six months have 31 days and five months have 30 b) 45
days. c) 36
b) Odd numbered months have 31 days and the even d) 25
numbered months, except February, have 30 days. e) 32
c) The months that are one syllable have 31 days.
42. A sailor on leave drove to Gurara Falls from his home at
d) Four months have 30 days and seven months have
60 kilometres per hour. On his trip home, his rate was 10
31 days.
kilometres per hour less, and the trip took one hour longer.
e) Six months have 30 days and five months have 31
How far is his home from the falls?
days.
a) 250 kilometres
b) 300 kilometres
36. How many numbers between 1 and 60 are divisible
c) 200 kilometres
evenly by both the number 4 and the number 6?
d) 150 kilometres
a) 3
e) 350 kilometres
b) 4
c) 5
43. If one pipe can fill a tank in 1½ hours and another can
d) 6
fill the same tank in 45 minutes, how long will it take for the
e) 7
two pipes to fill the tank together?
a) 1 hour
37. A boy M years old has a brother six years older and a b) 45 minutes
sister four years younger. The combined age of the three is c) 30 minutes
a) M + 10 d) 1 hour, 15 minutes
b) 3M – 2 e) 50 minutes
c) 2M – 6
d) 3M + 2 44. Six girls sold the following number of boxes of cookies:
e) 2M + 6 42, 35, 28, 30, 24, 27. What was the average number of
boxes sold by each girl?
38. On a blueprint, 2 centimetres represent 24 kilometres.
a) 26
How long must a line be to represent 72 kilometres?
b) 28
a) 36 cm
c) 29
b) 6 cm
d) 30
c) 12 cm
e) 31
d) 4 cm
e) 8 cm
45. 8 1/3 + 2 3/4=
a) 11 1/12
b) 10 1/12
c) 11 5/12
d) 10 4/7
e) None of these


46. (7 – 1/4) 3 =
a) 2 1/9
b) 2 1/4
c) 20 1/4
d) 4/9
e) None of these

47. 7 1/2 % expressed in decimal form is
a) 75
b) 7.5
c) .75
d) .075
e) .0075

48. In a triangle the measure of one angle is twice the
measure of another angle, and the measure of the third angle
is 48o. What is the measure of the largest angle of the
triangle?
a) 48o
b) 64o
c) 76o
d) 80o
e) 88o

49. A circle graph is used to represent the total annual
expense budget of a city. What fractional part of the
expense budget is represented by a sector whose central
angles measures 80o?
a) 1/3
b) 2/9
c) 4/9
d) 1/5
e) 4/5

50. A carpenter sold a simple wooden chair for ₦ 2,800 at a
profit of 40%. How much did the chair cost the carpenter?
a) ₦ 2,000
b) ₦ 2,100
c) ₦ 2,200
d) ₦ 2,400
e) ₦ 2,500

STOP


MATHEMATICS – Quantitative Aptitude

Directions: This paper is divided into six sections, labeled A to F. Work out the pattern being
followed in the sample. Then following the same pattern, find the answer to each of the questions.
Circle the LETTER of the choice you make.
SECTION A SECTION B
Sample: Sample:

( 5, 8 ) Y ( 4 , 2 ) → ( 1, 6 ) → 5 → 9 = 13
→ 8 → 3 = 10
( 4, 3 ) Z ( 2, 1 ) → ( 6, 4 ) →7←3=5
→ 35 ← 15 = 21
( 1, 2 ) Z ( 3, 2 ) Y ( 4, 4 ) → ( 0, 0 )

Use the sample above to answer questions 51 Use the sample above to answer questions 56
through 55. through 61.
51) ( 4, 7 ) Y ( 2, 1 ) → ( 2, ? ) 56) → ? → 7 = 11
a) 6 a) 4
b) 5 b) 5
c) 3 c) 6
d) 1 d) 10
e) 0 e) 18

57) → 6 ← 4 = ?
52) ( 2, 2 ) Y ( 0, ? ) → ( 2, 1 ) a) 11
a) 1 b) 10
b) 2 c) 9
c) 6 d) 3
d) 7 e) 2
e) 8
58) → 9 → 2 = ?
53) ( 3, 8 ) Z ( ?, 1 ) → ( 7, 9 ) a) 12
a) 11 b) 11
b) 10 c) 10
c) 9 d) 8
d) 7 e) 7
e) 4
59) → ? ← 7 = 4
54) ( 5, 7 ) Y ( 3, 5 ) Z ( 1, 2 ) → ( ?, 4 ) a) 12
a) 0 b) 11
b) 1 c) 10
c) 2 d) 4
d) 3 e) 3
e) 4
60) → 6.4 → 4.8 = ?
55) ( 10, 13 ) Z ( 8, 10 ) → ( ?, 23 ) a) 12.2
a) 2 b) 11.6
b) 18 c) 11.2
c) 20 d) 10.2
d) 21 e) 2.6
e) 23


61) → 5← 3 = ? 65)
a) 1 6 ¼ 8¾
b) 2 8¼ ?
c) 3
10¼ 6
d) 7
e) 8
a) 9
b) 10
SECTION C c) 11
d) 20
Sample: e) 26 ¾
3 1 5½ 7½ 8 10 ½ SECTION D
2 6 2 2½ 2½ 0
7 5 3½ 1 3½ 3½ Sample:
The circle represents the set of radios that can
receive Kaduna.
Use the sample above to answer questions 62 The triangle represents the set of radios that
through 65. can receive Enugu.
The rectangle represents the set of radios that
62) can receive Ibadan.
8½ 13 ½
? 6½
4½ 5½
2
1
a) 9½ 5
4 1 8
b) 11 ½ 3
c) 12 ½ 6 9
d) 13 ½ 7
e) 15 ½

63)
Use the diagram to answer questions 66
45 ?
through 70.
12 27
4 34 66) Which number represents the radios that can receive
Enugu only?
a) 0 f) 3
b) 1 g) 4
c) 10 h) 5
i) 6
d) 11
j) 8
e) 20
67) Which of the following shapes represents the radios
64) that receive Ibadan and Kaduna only?
18 7
f)
6 34
27 ?

a) 0 g)
b) 9
c) 10
d) 19
e) 20 Go on to the next page.


h) SECTION E
Sample:
i)
6(S)2=3 5 ( R ) 4 = 20
8(S)4=2 ⅓(R)9=3
3 ( R ) 2 ( S ) 4 = 1½ 4 ( R ) 7 ( R ) 5 = 140
j)

68) Which of the following shapes represents the radios
that receive Kaduna and Enugu? Use the sample above to answer questions 71
through 75.
a)
71) 21 ( S ) 7 = ?
a) 1/3
b) 3
b) c) 14
d) 28
e) 147

72) 13 ( R ) 2 ( S ) 4 = ?
c) a) 104
b) 26
c) 15
d) 11 1/2
d) e) 6 1/2

73) 18 ( R ) ? = 36
a) 54
b) 18
e) c) 2
d) 1/2
69) Which number represents the radios that can receive e) 0
Kaduna, Enugu and Ibadan at the same time?
a) 3 74) 7 ( R ) 8 ( S ) ? = 14
b) 4 a) 1
c) 5 b) 2
d) 6 c) 3
e) 8 d) 4
e) 6
70) Which number(s) represent(s) the radios that can
receive Ibadan and Enugu only? 75) 3 ( R ) 11 ( R ) 6 = ?
a) 2 a) 1/22
b) 4 b) 22
c) 5 c) 39
d) 4 and 7 d) 66
e) 4 and 5 e) 198



SECTION F
Sample: 80) 9 ?

Use the sample below to answer questions 76
through 80. 49
a) 58
b) 40
7 2 8 1 5 2 c) 7
d) 2
e) 1
25 49 9
STOP
76)
8 3 Circle the letter of the correct answer.

81. Which of the following statements is true about the
? calendar year?
a) 9 f) Six months have 31 days and five months have 30
b) 11 days.
c) 24 g) Odd numbered months have 31 days and the even
d) 25 numbered months, except February, have 30 days.
e) 64 h) The months that are one syllable have 31 days.
i) Four months have 30 days and seven months have
77) ? 13 31 days.
j) Six months have 30 days and five months have 31
days.
169
82. How many numbers between 1 and 50 are divisible
a) 182 evenly by both the number 2 and the number 3?
b) 156 f) 5
c) 39 g) 6
d) 26 h) 7
e) 13 i) 8
j) 9
78)
? 7
83. In the figure below, BCD is a straight line. If ∠DCA =
122o and ∠ABC = 26o which statement is true?
16
a) 4 D C B
b) 9
c) 11 122o 26o
d) 17
e) 23

79) A
5 1
a) ∠BCA = 58o and ∠CAB = 76o

? b) ∠CAB = 86o and ∠BCA = 68o
a) 36 c) ∠BCA = 48o and ∠CAB = 86o
b) 16
c) 6 d) ∠BCA = 58o and ∠CAB = 86o
d) 4 e) ∠BCA = 58o and ∠CAB = 96o
e) 2


For question 84, use the following figure. 89. A basketball team won 18 games, which was 40% of its
season. How many games did the team lose?
1 cm f) 27
g) 45
3 cm h) 36
i) 25
3 cm j) 32
90. A sailor on leave drove to Gurara Falls from his home at
7 cm 60 kilometres per hour. On his trip home, his rate was 10
kilometres per hour less, and the trip took one hour longer.
How far is his home from the falls?
f) 250 kilometres
g) 300 kilometres
5 cm
h) 200 kilometres
i) 150 kilometres
84. The area of the shaded figure (at the bottom of the
j) 350 kilometres
previous column) is
a) 19 cm2
91. If one pipe can fill a tank in 1½ hours and another can
b) 26 cm2
fill the same tank in 45 minutes, how long will it take for the
c) 30 cm2
two pipes to fill the tank together?
d) 44 cm2
f) 1 hour
e) 29 cm2
g) 45 minutes
85. A boy M years old has a brother six years older and a h) 30 minutes
sister four years younger. The combined age of the three is i) 1 hour, 15 minutes
f) M + 10 j) 50 minutes
g) 3M – 2
h) 2M – 6 92. Six girls sold the following number of boxes of cookies:
i) 3M + 2 42, 35, 28, 30, 24, 27. What was the average number of
j) 2M + 6 boxes sold by each girl?
f) 26
86. On a blueprint, 2 centimetres represent 24 kilometres.
g) 28
How long must a line be to represent 72 kilometres?
h) 29
f) 36 cm
i) 30
g) 6 cm
j) 31
h) 12 cm
i) 4 cm
93. 8 1/3 + 2 3/4=
j) 8 cm
f) 11 1/12
87. An angle that is greater than 90o and less than 180o is g) 10 1/12
a(n) h) 11 5/12
f) complementary angle i) 10 4/7
g) obtuse angle j) None of these
h) right angle
i) acute angle
94. (7 – 1/4) 3 =
j) reflex angle
f) 2 1/9
88. If a pie is divided into 40 parts, what percent is one part g) 2 1/4
of the whole pie? h) 20 1/4
f) 40 i) 4/9
g) 25 j) None of these
h) .25
i) 4.0 95. 7 1/2 % expressed in decimal form is
j) 2.5 f) 75
g) 7.5
h) .75
i) .075
j) .0075


96. In a triangle the measure of one angle is twice the e) 100 + 50π
measure of another angle, and the measure of the third angle
is 48o. What is the measure of the largest angle of the
100. A carpenter sold a simple wooden chair for ₦ 2,800 at a
triangle?
f) 48o profit of 40%. How much did the chair cost the carpenter?
g) 64o f) ₦ 2,000
h) 76o
g) ₦ 2,100
i) 80o
j) 88o h) ₦ 2,200
i) ₦ 2,400
97. Use the diagram below to answer the question at the top
of the next column. j) ₦ 2,500

O
STOP
40o
B The measure of ∠AOB =
40o, and the area of the
A
circle is 72 square centimetres. What is the
area of sector AOB in square centimetres?
a) 10
b) 9
c) 8
d) 12
e) None of these

98. A circle graph is used to represent the total annual
expense budget of a city. What fractional part of the
expense budget is represented by a sector whose central
angles measures 80o?
f) 1/3
g) 2/9
h) 4/9
i) 1/5
j) 4/5

99. Use the diagram below.

D C

O

A B
10
O is the centre of a circle inscribed in square ABCD. If AB
= 10, find the area of the shaded portion.
a) 100 - 100π
b) 100 - 50π
c) 100 + 25π
d) 100 - 25π

Loyola Jesuit College Entrance Examination (May 2004) Mathematics

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Loyola Jesuit College Entrance Examination (May 2004) Mathematics