1. Find the factors of 330.
(a) 2 x 4 x 5 x 11
(b) 2 x 3 x 7 x 13
(c) 2 x 3 x 5 x 13
(d) 2 x 3 x 5 x 11
2. Find the factors of 1122.
(a) 3 x 9 x 17 x 2
(b) 3 x 11 x 17 x 2
(c) 9 x 9 x 17 x 2
(d) 3 x 11 x 17 x 3
3. 252. Can be expressed as a product of primes as
(a) 2 x 2 x 3 x 3 x 7
(b) 2 x 2 x 3 x 3 x 7
(c) 3 x 3 x 3 x 3 x 7
(d) 2 x 2 x 3 x 3 x 7
4. Which of the following has most number of divisors ?
(a) 99
(b) 101
(c) 176
(d) 182
5. A number n is said to be perfect if the sum of all its
divisors (excluding n itself) is equal to n. An example of
perfect number is
(a) 6
(b) 9
(c) 15
(d) 19
1095
6. 1168 when expressed in simplest form is
13
(a) 16
15
(b) 16
17
(c) 26
25
(d) 26
116,690,151
8. The simplest reduction to the lowest terms of 427,863,887
3
(a) 11
7
(b) 11
11
(c) 3
(d) None of these
9. The highest common factor of 0 and 6 is
(a) 0
(b) 3
(c) 6
(d) Undefined
63. About the number of pairs which have 16 as their
H.C.F. and 136 as their L.C.M. we can definitely say that
(a) no such pair exists
(b) only one such pair exists
(c) only two such pairs exist
(d) many such pairs exist
64. The H.C.F. and L.C.M. of two numbers are 21 and
4641 respectively. If one of the numbers lies between 200
and 300, the two numbers are
(a) 273, 357
(b) 273, 359
(c) 273, 361
(d) 273, 363
65. Two numbers, both greater than 29, have H.C.F. 29
and L.C.M. 4147. The sum of the numbers is
(a) 666
(b) 669
(c) 696
(d) 966
21. Mango trees, 42 apple trees and 56 orange trees have
to be planted in rows such that each row contains the
same number of trees of one variety only. Minimum
number of rows is which the trees may be planted is
(a) 3
(b) 15
(c) 17
(d) 20
69. The greatest possible length which can be used to
measure exactly the lengths 7 m, 2 cm 85 cm, 12 m 95 cm
is
(a) 15 cm
(b) 25 cm
(c) 35 cm
(d) 42 cm
70. The capacity of two pots is 120 litres and 56 litres
respectively. Find the capacity of a container which can
exactly measure the contents of the two pots.
(a) 7500 cc
(b) 7850 cc
(c) 8000 cc
(d) 9500 cc
71. A daily wage labourer was engage for a certain
number of days for ₹5750, but being absent on some of
those days he was paid only ₹ 5000. What was his
maximum possible daily wage ?
(a) ₹ 125
(b) ₹ 250
(c) ₹ 385
(d) ₹ 500
72. A person has to completely put each of three liquids:
403 litres of petrol, 465 litres of diesel and 496 litres of
Mobil Oil in bottles of equal size without maxing any of the
above three types of liquids such that each bottle is
completely filled. What is the least possible number of
bottles required ?
(a) 34
(b) 44
(c) 46
(d) None of these
73. The maximum number of students among whom 1001
pens and 910 pencils can be distributed in such a way that
each student gets the same number of pens and same
number of pencils is
(a) 91
(b) 910
(c) 1001
(d) 1911
74. A rectangular courtyard 3.78 metres long and 5.25
metres wide is to be paved exactly with square tiles, all of
the same size. What is the largest size of the tile which
could be used for the purpose ?
(a) 14 cm
(b) 21cm
(c) 42 cm
(d) None of these
75. The least number of square tiles required to pave the
ceiling of a room 15 m 17 cm long and 9 m 2 cm broad is
(a) 656
(b) 738
(c) 814
(d) 902
76. Three sets English, Mathematics and Science books
containing 336, 240 and 96 books respectively have to be
stacked in such a way that all the books are stored subject
wise and the height of each stack is the same. Total
number of stack will be
(a) 14
(b) 21
(c) 22
(d) 48
77. Four metal roads of lengths 78 cm, 104 cm, 117 cm
and 169 cm are to be cut into parts f equal length. Each
part must be a long as possible. What is the maximum
number of pieces that can be cut ?
(a) 27
(b) 36
(c) 43
(d) 480
78. Find the greatest number that will divide 43, 91 and
183 so as to leave the same remainder in each case.
(a) 4
(b) 7
(c) 9
(d) 13
79. If r is the remainder when each of 7654, 8506 and
9997 is divided by the greatest number d (d > 1), then d –
r is equal to
(a) 14
(b) 18
(c) 24
(d) 28
81. A milkman has3 jars containing 57 litres, 129 litres and
177 litres of pure milk respectively. A measuring can, after
a different number of exact measurements of milk in each
jar, leaves the same amount of milk unmeasured in each
jar. What is the volume of largest such can ?
(a) 12 litres
(b) 16 litres
(c) 24 litres
(d) None of these
112. A gardener ha to plant trees is rows containing equal
number of trees. If he plants in rows of 6, 8, 10 or 12, then
five trees are left unplanted. But if he plants in rows of 13
trees each, then no tree is left. What is the number of
trees that the gardener plants ?
(a) 485
(b) 725
(c) 845
(d) None of these
113. When Seeta made necklaces of either 16 beads, 20
beads or 36 beads, not a single bead was left over. What
could be the least number of beads Seeta had ?
(a) 700
(b) 720
(c) 750
(d) 780
114. An electronic device makes a beep after every 60
sec. Another device makes a beep after every 62 sec.
They beeped together at 10 a.m. the next time, when they
would beep together at the earliest is
(a) 10.30 a.m.
(b) 10.31 a.m.
(c) 10.59 a.m.
(d) 11 a.m.
115. Six bells commence tolling together and toll at
intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In
30 minutes, how many times do they toll together ?
(a) 4
(b) 10
(c) 15
(d) 16
116. Four bells begin to toll together and toll respectively
at intervals of 6,7, 8 and 9 seconds. In 1.54 hours, how
many times do they tool together and in what interval
(seconds)?
(a)14, 504
(b) 14, 480
(c) 12, 504
(d) 16, 580
117. Four different electronic devices make a beep after
1
every 30 minutes, 1 hour, 1 2 hour and 1 hour 45 minutes
respectively. All the devices beeped together at 12 noon.
They will again beep together at
(a) 12 midnight
(b) 3 a.m.
(c) 6 a.m.
(d) 9 a.m.
118. Three girls start jogging from the same point around
a circular track and each one completes one round in 24
seconds, 36 seconds and 48 seconds respectively. After
how much time will they meet at one point ?
(a) 2 minutes 20 seconds
(b) 2 minutes 24 seconds
(c) 3 minutes 36 seconds
(d) 4 minutes 12 seconds
119. Three persons walking around a circular track
1
complete their respective single revolution in 15 6 seconds,
1 2
16 4 seconds and 18 3 seconds respectively. They will be
again together at the common starting point after an hour
and
(a) 10 seconds
(b) 20 seconds
(c) 30 seconds
(d) 40 seconds
120. A, B and C start at the same time in the same
direction to run around a circular stadium. A completes a
round in 252 seconds, B in 308 seconds and C in 198
seconds, all starting at the same point. ?
(a) 26 minutes 18 seconds
(b) 42 minutes 36 seconds
(c) 45 minutes
(d) 46 minutes 12 seconds
121. Three wheels can complete 40, 24 and 16 revolutions
per minute respectively. There is a red spot on each wheel
that touches the ground at time Zero. After how much
time, all these spots will simultaneously touch the ground
again ?
1
(a) 7 2 sec
(b) 18 sec
1
(c) 7 2 min
(d) 18 min
122. A pendulum strikes 5 times in 3 seconds and another
pendulum strikes 7 time in 4 seconds. If both pendulums
start striking at the same time, how many clear strikes can
be listened in 1 minute ?
(a) 195
(b) 199
(c) 200
(d) 205
130. The traffic lights at three different signal points
change after every 45 seconds, 75 seconds and 90
seconds respectively. If all change simultaneously at 7 :
20 : 15 hours, then they will change again Simultaneously
at
(a) 7 : 28 : 00 hours
(b) 7 : 27 : 45 hours
(c) 7 : 27 : 30 hours
(d) 7 : 27 : 50 hours
