Olympiad Mathematics - Playing with Numbers
Exam Duration: 45 Mins Total Questions : 30
What are the numbers which have more than two factors called?
- (a)
Even numbers
- (b)
Prime numbers
- (c)
Composite numbers
- (d)
Odd numbers
What are the numbers which have only two factors (1 and the number itself) called?
- (a)
Composite numbers
- (b)
Even numbers
- (c)
Prime numbers
- (d)
Odd numbers
What is the L.C.M.of 17 and 5 ?
- (a)
105
- (b)
95
- (c)
85
- (d)
5
What is the H.C.F.of 17 and 5 ?
- (a)
1
- (b)
5
- (c)
17
- (d)
85
Which of the following is an example of an even number?
- (a)
10351
- (b)
20989
- (c)
69007
- (d)
973572
What is the H.C.F.of 120, 144 and 216 ?
- (a)
38
- (b)
24
- (c)
120
- (d)
144
Every number is a __________ and a _________ of itself.
- (a)
factor, multiple
- (b)
prime, composite
- (c)
even, odd
- (d)
prime, twin prime
What is the H.C.F. of the two numbers equal to?
- (a)
Product of the numbers \(\div \) their L.CM
- (b)
Product of the numbers \(\times\) their L.C.M.
- (c)
Product of the numbers.
- (d)
Quotient of the numbers.
What is the number of prime numbers between 50 and 60 ?
- (a)
1
- (b)
2
- (c)
3
- (d)
4
Which of the following is the prime factorisation of 140 ?
- (a)
2 \(\times\) 2 \(\times\)7
- (b)
2 \(\times\) 2 \(\times\)5
- (c)
2 \(\times\) 2 \(\times\)5 \(\times\) 7
- (d)
2 \(\times\) 2 \(\times\)5 \(\times\)7 \(\times\)3
The successor of every even number is
- (a)
even
- (b)
prime.
- (c)
odd.
- (d)
composite
What is the sum of the first five multiples of 6 ?
- (a)
90
- (b)
60
- (c)
30
- (d)
120
What is the least number which when decreased by 7 is exactly divisible by 12, 16,18,21 and 28?
- (a)
1012
- (b)
1008
- (c)
1015
- (d)
1022
Which of the following numbers is a perfect number?
- (a)
6
- (b)
28
- (c)
6 and 28
- (d)
34
Every even number greater than 4 can be expressed as a sum of two odd prime numbers. Which of the following is an example for this statement?
- (a)
8 = 1 + 7
- (b)
8 = 3 + 5
- (c)
4 = 1 + 3
- (d)
4 = 2 + 2
The answers of four students A, B,C and o for prime factorisation of 24 are given. Whose answer is wrong?
- (a)
2 \(\times\) 2 \(\times\) 2 \(\times\) 3
- (b)
8 \(\times\) 3
- (c)
3 \(\times\) 2 \(\times\)2 \(\times\) 2
- (d)
2 \(\times\) 3 \(\times\) 2 \(\times\) 2
The table given lists the number of factors for some numbers.
Number | Number of factors |
---|---|
21 | 4 |
23 | 2 |
25 | 3 |
27 | 4 |
29 | 2 |
What is the number of prime numbers between 20 and 30 from the given table?
- (a)
0
- (b)
2
- (c)
3
- (d)
4
Which of the following is a prime number?
- (a)
117
- (b)
171
- (c)
179
- (d)
143
Three bells toll together at intervals of 9, 12 and 15 minutes. If they start tolling together, after what time will they toll next?
- (a)
1 hour
- (b)
\(1\frac { 1 }{ 2 } \) hours
- (c)
\(2\frac { 1 }{ 2 } \)hours
- (d)
3 hours
Observe the given multiples of 37.
37 \(\times\) 3 = 111
37 \(\times\) 6 = 222
37 \(\times\) 9 = 333
37 \(\times\) 12 = 444
____________
____________
Find the product of 37 \(\times\) 27
- (a)
999
- (b)
The greatest 3 digit number.
- (c)
Both (A) and (B)
- (d)
The smallest 3-digit number.
67,61, p, q, r, s, 41. is an arrangement of prime numbers In decreasing order. Among the following, which is the number 53?
- (a)
p
- (b)
r
- (c)
q
- (d)
s
What is the possible value of the product of P and Q, given that their H.C.F is 12 and L.C.M is 120 ?
- (a)
1200
- (b)
120
- (c)
1440
- (d)
144
What is the L.C.M. of 12, 15,20 and 27?
- (a)
270
- (b)
360
- (c)
480
- (d)
540
The HCF of two consecutive odd numbers is________
- (a)
2
- (b)
0
- (c)
4
- (d)
1
Which of the following numbers has exactly 4 factors?
- (a)
16
- (b)
14
- (c)
18
- (d)
None of these
There are 153 apples and 119 oranges. These fruits are to be arranged in heaps containing the same number of fruits. Then the greatest number of fruits possible in each heap is______
- (a)
15
- (b)
23
- (c)
17
- (d)
20
The length, breadth and height of a room are 403 cm, 434 cm and 465 cm respectively. Find the longest tape which can measure the three dimensions of the room exactly.
- (a)
31 cm
- (b)
30 cm
- (c)
25 cm
- (d)
35 cm
State 'T' for true and 'F' for false.
(i) If an even number is divided by 2, the quotient is always odd.
(ii) All even numbers are composite numbers.
(iii) The LCM of two co-prime numbers cannot be equal to their product.
(iv) Every number is a factor of itself.
- (a)
i ii iii iv T T F F - (b)
i ii iii iv F F F T - (c)
i ii iii iv T F T T - (d)
i ii iii iv F F T T
Find the value of a + b + c, if 373a is divisible by 9, 473b is divisible by 11 and 371C is divisible by 6.
- (a)
7
- (b)
6
- (c)
0
- (d)
9
Match the following
Column I | Column II |
(i) 49 | (p) Multiple of 3 |
(ii) 25 | (q) Multiple of 4 |
(iii) 16 | (r) Multiple of 7 |
(iv) 39 | (s) Multiple of 5 |
- (a)
i ii iii iv (s) (p) (r) (q) - (b)
i ii iii iv (r) (s) (q) (p) - (c)
i ii iii iv (s) (r) (p) (q) - (d)
i ii iii iv (p) (q) (r) (s)