NUMBER SYSTEM
1) For a positive integer n, let Pn denote the product of the digits of n and Sn denote the
sum of the digits of n. The number of integers between 10 and 1000 for which Pn+Sn=n
a. 9
b. 100
c. 128
d. 145
2) The digits of a three-digit number A are written in the reverse order to form another three-
digit number B. If B > A and B – A is perfectly divisible by 7, then which of the following is
necessarily true?
a. 100 < A < 299
b. 106 < A < 305
c. 112 < A < 311
d. 118 < A < 317
3) M = abc is a three digit number and N = cba, if M > N and M - N + 396c = 990. Then how
many values of M are more than 300.
a. 20
b. 30
c. 40
d. 200
4) Consider four digit numbers for which the first two digits are equal and the last two digits
are also equal. How many such numbers are perfect square?
a. 2
b. 4
c. 0
d. 1
5) By which number the expression 200!12100 should be multiplied so that the given
expression becomes an integer
a. 216
b. 200
c. 64
d. 9
6) What is the maximum power of 3 in the expansion of 1! × 2! × 3! × . . . . × 100!
a. 11
b. 13
c. 14
d. 18
7) 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
8) LCM of 87 and 145 is :
a. 870
b. 1305
c. 435
d. 1740
9) The traffic lights at three different road crossing change after every 48 sec; 72 sec; and
108 sec., respectively. If they all change simultaneously at 8:20:00 hrs, then they will
again change simultaneously at
a. 8:27:12 Hrs
b. 8:27:24 Hrs
c. 8:27:36 Hrs
d. 8:27:48 Hrs
10) The greatest number by which if 1657 and 2037 are divided the remainders will be 6 and
5 respectively is
a. 127
b. 235
c. 260
d. 305
11) The HCF and LCM of two numbers are 44 and 264 respectively. If the first number is
divisible by 3, then the first number is
a. 264
b. 132
c. Both a and b
d. 33
12) What least number must be subtracted from 1294 so that the remainder when divided 9,
11, 13 will leave in each case the same remainder 6 ?
a. 0
b. 1
c. 2
d. 3
13) The least number which is divisible by 12, 15, 20 and is a perfect square, is
a. 400
b. 900
c. 1600
d. 3600
14) Find the number of factors of 64 which are even.
a. 6
b. 7
c. 4
d. 3
15) Find the number of factors of 64 which are perfect squares
a. 4
b. 5
c. 6
d. 7
16) Find the number of factors of 64 which are perfect cubes.
a. 6
b. 9
c. 4
d. 3
17) How many numbers below 100 have exactly 2 factors.
a. 25
b. 10
c. 17
d. 18
18) How many factors of 81 are odd.
a. 4
b. 5
c. 1
d. 2
19) Find the sum of the factors of 72
a. 152
b. 195
c. 205
d. 216
20) Find the number of ways of writing 140 as a product of two factors
a. 6
b. 9
c. 10
d. 12
