Mathematics
Number System
Two positive integers have HCF 9 and LCM 936. What is their product?
A. 936
B. 945
C. 8424
D. 8433
Correct Answer: C
For two positive integers, product = HCF × LCM = 9 × 936 = 8424.
Mathematics
Number System
Find the next number in the series: 41, 53, 65, 77, 89, ?
A. 113
B. 101
C. 125
D. 89
Correct Answer: B
The common difference is 12. So the next term is 89 + 12 = 101.
Mathematics
Number System
Find the next number: 12, 19, 30, 43, 60, ?
A. 60
B. 96
C. 79
D. 81
Correct Answer: C
Successive prime numbers are added: 7, 11, 13, 17, 19. Add 19 next, giving 79.
Mathematics
Number System
Find the next number: 16, 32, 57, 93, 142, ?
A. 191
B. 198
C. 214
D. 206
Correct Answer: D
The increments are consecutive squares: 16, 25, 36, 49; next add 8² = 64. So the answer is 206.
Mathematics
Number System
The sum of 5 consecutive integers is 405. What is the middle integer?
A. 82
B. 80
C. 81
D. 86
Correct Answer: C
The middle integer equals the average: 405 ÷ 5 = 81.
Mathematics
Number System
Find the next number: 6, 14, 30, 62, 126, ?
A. 252
B. 279
C. 256
D. 254
Correct Answer: D
Each term is obtained by ×2 + 2. So 126 × 2 + 2 = 254.
Mathematics
Number System
Classify √28.
A. Rational
B. Whole number
C. Prime number
D. Irrational
Correct Answer: D
28 is not a perfect square, so √28 is irrational.
Mathematics
Number System
Find the next number in the series: 27, 44, 61, 78, 95, ?
A. 146
B. 95
C. 112
D. 129
Correct Answer: C
The common difference is 17. So the next term is 95 + 17 = 112.
Mathematics
Number System
Find the next number in the alternating series: 6, 38, 11, 44, 16, 50, ?
A. 16
B. 21
C. 56
D. 26
Correct Answer: B
Odd-position terms are 6, 11, 16, ... with difference 5. Hence the next odd-position term is 21.
Mathematics
Number System
Find the next number: 8, 25, 76, 229, 688, ?
A. 2064
B. 2065
C. 2062
D. 2066
Correct Answer: B
Each term is obtained by ×3 + 1. So 688 × 3 + 1 = 2065.
Mathematics
Number System
Find the next number in the series: 28, 31, 34, 37, 40, ?
A. 40
B. 43
C. 49
D. 46
Correct Answer: B
The common difference is 3. So the next term is 40 + 3 = 43.
Mathematics
Number System
Find the next number: 22, 23, 27, 36, 52, ?
A. 77
B. 82
C. 68
D. 72
Correct Answer: A
The increments are consecutive squares: 1, 4, 9, 16; next add 5² = 25. So the answer is 77.
Mathematics
Number System
What least number must be subtracted from 3503 so that the result is exactly divisible by 13?
A. 19
B. 5
C. 6
D. 7
Correct Answer: C
The remainder is 6; subtracting the remainder makes the number divisible by 13.
Mathematics
Number System
Find the next term: 51, 56, 50, 55, 49, 54, ?
A. 59
B. 54
C. 43
D. 48
Correct Answer: D
The operations alternate +5, -6. After the last +5, subtract 6: 54 - 6 = 48.
Mathematics
Number System
Find the HCF (GCD) of 209 and 38.
A. 38
B. 9
C. 19
D. 20
Correct Answer: C
The greatest common divisor of 209 and 38 is 19.
Mathematics
Number System
Find the next number: 1, 9, 33, 105, 321, ?
A. 969
B. 963
C. 966
D. 975
Correct Answer: A
Each term is obtained by ×3 + 6. So 321 × 3 + 6 = 969.
Mathematics
Number System
What is the units digit of 53^44?
A. 5
B. 1
C. 3
D. 7
Correct Answer: B
Units digits repeat cyclically; applying the cycle for base 53 gives units digit 1.
Mathematics
Number System
What is the greatest positive integer that can divide both 543 and 479 leaving the same remainder?
A. 64
B. 32
C. 63
D. 65
Correct Answer: A
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 543-479 = 64; the greatest possible divisor is 64.
Mathematics
Number System
Find the LCM of 27 and 20.
A. 27
B. 594
C. 540
D. 541
Correct Answer: C
LCM = (27 × 20) ÷ HCF(27,20) = 540.
Mathematics
Number System
Find the next term: 12, 28, 40, 68, 108, 176, ?
A. 284
B. 352
C. 324
D. 216
Correct Answer: A
Each term is the sum of the previous two. Therefore 108 + 176 = 284.