Mathematics
Number System
Find the missing number: 32, 52, 72, 92, ?, 132
A. 152
B. 132
C. 92
D. 112
Correct Answer: D
This is an arithmetic series with common difference 20; the missing term is 112.
Mathematics
Number System
Find the next number: 29, 38, 54, 79, 115, ?
A. 171
B. 157
C. 151
D. 164
Correct Answer: D
The increments are consecutive squares: 9, 16, 25, 36; next add 7² = 49. So the answer is 164.
Mathematics
Number System
What is the greatest positive integer that can divide both 490 and 345 leaving the same remainder?
A. 144
B. 72
C. 146
D. 145
Correct Answer: D
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 490-345 = 145; the greatest possible divisor is 145.
Mathematics
Number System
What digit x makes the number 481x divisible by 9?
A. 8
B. 6
C. 5
D. 0
Correct Answer: C
A number is divisible by 9 when its digit sum is divisible by 9. Thus 4+8+1+x must be a multiple of 9, giving x = 5.
Mathematics
Number System
What is the remainder when 768 is divided by 13?
A. 2
B. 4
C. 3
D. 1
Correct Answer: D
768 = 13 × 59 + 1; therefore the remainder is 1.
Mathematics
Number System
Find the next number: 5, 16, 49, 148, 445, ?
A. 1336
B. 1333
C. 1337
D. 1335
Correct Answer: A
Each term is obtained by ×3 + 1. So 445 × 3 + 1 = 1336.
Mathematics
Number System
What is the greatest multiple of 7 that is less than 4721?
A. 4719
B. 4718
C. 4711
D. 4725
Correct Answer: B
4721 ÷ 7 has integer quotient 674; 7 × 674 = 4718.
Mathematics
Number System
Find the next term in the series: 22, 37, 56, 79, 106, ?
A. 133
B. 164
C. 137
D. 141
Correct Answer: C
The first differences are [15, 19, 23, 27]; their second difference is constant at 4. Continuing the pattern gives 137.
Mathematics
Number System
Two positive integers have HCF 3 and LCM 396. What is their product?
A. 396
B. 1188
C. 399
D. 1191
Correct Answer: B
For two positive integers, product = HCF × LCM = 3 × 396 = 1188.
Mathematics
Number System
How many integers from 19 to 265, inclusive, are divisible by 13?
A. 20
B. 21
C. 19
D. 18
Correct Answer: C
Count = ⌊265/13⌋ - ⌊(19-1)/13⌋ = 20 - 1 = 19.
Mathematics
Number System
Find the next term: 11, 12, 23, 35, 58, 93, ?
A. 174
B. 151
C. 116
D. 186
Correct Answer: B
Each term is the sum of the previous two. Therefore 58 + 93 = 151.
Mathematics
Number System
Find the next number in the alternating series: 27, 37, 36, 34, 45, 31, ?
A. 54
B. 63
C. 28
D. 45
Correct Answer: A
Odd-position terms are 27, 36, 45, ... with difference 9. Hence the next odd-position term is 54.
Mathematics
Number System
How many trailing zeros are there in 105! ?
A. 26
B. 24
C. 10
D. 25
Correct Answer: D
Trailing zeros = ⌊105/5⌋ + ⌊105/25⌋ + ... = 21 + 4 = 25.
Mathematics
Number System
Find the next number: 31, 38, 49, 62, 79, ?
A. 98
B. 115
C. 79
D. 100
Correct Answer: A
Successive prime numbers are added: 7, 11, 13, 17, 19. Add 19 next, giving 98.
Mathematics
Number System
What is the greatest multiple of 15 that is less than 2798?
A. 2790
B. 2775
C. 2791
D. 2805
Correct Answer: A
2798 ÷ 15 has integer quotient 186; 15 × 186 = 2790.
Mathematics
Number System
Two positive integers have HCF 7 and LCM 1001. What is their product?
A. 7007
B. 7014
C. 1001
D. 1008
Correct Answer: A
For two positive integers, product = HCF × LCM = 7 × 1001 = 7007.
Mathematics
Number System
Find the next term: 100, 107, 102, 109, 104, 111, ?
A. 111
B. 106
C. 118
D. 99
Correct Answer: B
The operations alternate +7, -5. After the last +7, subtract 5: 111 - 5 = 106.
Mathematics
Number System
Find the next number: 4, 16, 52, 160, 484, ?
A. 1456
B. 1460
C. 1452
D. 1453
Correct Answer: A
Each term is obtained by ×3 + 4. So 484 × 3 + 4 = 1456.
Mathematics
Number System
The sum of 3 consecutive integers is 222. What is the middle integer?
A. 75
B. 73
C. 74
D. 77
Correct Answer: C
The middle integer equals the average: 222 ÷ 3 = 74.
Mathematics
Number System
Find the next number in the series: 67, 78, 89, 100, 111, ?
A. 122
B. 144
C. 111
D. 133
Correct Answer: A
The common difference is 11. So the next term is 111 + 11 = 122.