Mathematics
Number System
What is the greatest positive integer that can divide both 332 and 223 leaving the same remainder?
A. 110
B. 54
C. 109
D. 108
Correct Answer: C
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 332-223 = 109; the greatest possible divisor is 109.
Mathematics
Number System
Find the next number: 39, 44, 51, 62, 75, ?
A. 75
B. 92
C. 94
D. 105
Correct Answer: B
Successive prime numbers are added: 5, 7, 11, 13, 17. Add 17 next, giving 92.
Mathematics
Number System
Find the next term: 7, 15, 22, 37, 59, 96, ?
A. 192
B. 118
C. 155
D. 177
Correct Answer: C
Each term is the sum of the previous two. Therefore 59 + 96 = 155.
Mathematics
Number System
Find the next number: 1, 2, 6, 24, 120, ?
A. 720
B. 120
C. 600
D. 726
Correct Answer: A
The multipliers are ×2, ×3, ×4, ×5; the next multiplier is ×6. Thus 120 × 6 = 720.
Mathematics
Number System
Find the HCF (GCD) of 144 and 128.
A. 32
B. 8
C. 16
D. 17
Correct Answer: C
The greatest common divisor of 144 and 128 is 16.
Mathematics
Number System
What is the greatest multiple of 15 that is less than 3489?
A. 3481
B. 3465
C. 3495
D. 3480
Correct Answer: D
3489 ÷ 15 has integer quotient 232; 15 × 232 = 3480.
Mathematics
Number System
How is the integer 28 classified?
A. Neither prime nor composite
B. Composite
C. Irrational
D. Prime
Correct Answer: B
28 = 14 × 2, so it has factors other than 1 and itself and is composite.
Mathematics
Number System
What least number must be added to 1696 so that the result is exactly divisible by 25?
A. 4
B. 5
C. 21
D. 29
Correct Answer: A
1696 leaves remainder 21 on division by 25. Add 25 - 21 = 4.
Mathematics
Number System
What is the greatest multiple of 34 that is less than 1339?
A. 1327
B. 1326
C. 1292
D. 1360
Correct Answer: B
1339 ÷ 34 has integer quotient 39; 34 × 39 = 1326.
Mathematics
Number System
How many integers from 28 to 200, inclusive, are divisible by 8?
A. 22
B. 25
C. 23
D. 21
Correct Answer: A
Count = ⌊200/8⌋ - ⌊(28-1)/8⌋ = 25 - 3 = 22.
Mathematics
Number System
What is the units digit of 81^43?
A. 3
B. 7
C. 1
D. 5
Correct Answer: C
Units digits repeat cyclically; applying the cycle for base 81 gives units digit 1.
Mathematics
Number System
Find the next term: 2, 8, 18, 32, 50, ?
A. 72
B. 96
C. 74
D. 48
Correct Answer: A
The terms follow 2n² + 0 for consecutive n. For n = 6, the term is 2×6² + 0 = 72.
Mathematics
Number System
Find the next number in the alternating series: 14, 44, 21, 40, 28, 36, ?
A. 32
B. 42
C. 35
D. 28
Correct Answer: C
Odd-position terms are 14, 21, 28, ... with difference 7. Hence the next odd-position term is 35.
Mathematics
Number System
Find the missing number: 33, 47, ?, 75, 89, 103
A. 75
B. 61
C. 47
D. 89
Correct Answer: B
This is an arithmetic series with common difference 14; the missing term is 61.
Mathematics
Number System
What is the units digit of 37^56?
A. 7
B. 3
C. 5
D. 1
Correct Answer: D
Units digits repeat cyclically; applying the cycle for base 37 gives units digit 1.
Mathematics
Number System
Find the next number: 2, 6, 14, 30, 62, ?
A. 124
B. 138
C. 128
D. 126
Correct Answer: D
Each term is obtained by ×2 + 2. So 62 × 2 + 2 = 126.
Mathematics
Number System
Find the LCM of 22 and 26.
A. 26
B. 572
C. 286
D. 288
Correct Answer: C
LCM = (22 × 26) ÷ HCF(22,26) = 286.
Mathematics
Number System
Find the next number: 10, 32, 98, 296, 890, ?
A. 2672
B. 2670
C. 2674
D. 2669
Correct Answer: A
Each term is obtained by ×3 + 2. So 890 × 3 + 2 = 2672.
Mathematics
Number System
How many trailing zeros are there in 139! ?
A. 33
B. 13
C. 32
D. 34
Correct Answer: A
Trailing zeros = ⌊139/5⌋ + ⌊139/25⌋ + ... = 27 + 5 + 1 = 33.
Mathematics
Number System
Find the next term: 100, 113, 111, 124, 122, 135, ?
A. 135
B. 148
C. 120
D. 133
Correct Answer: D
The operations alternate +13, -2. After the last +13, subtract 2: 135 - 2 = 133.