Mathematics
Number System
What is the greatest positive integer that can divide both 497 and 417 leaving the same remainder?
A. 79
B. 81
C. 40
D. 80
Correct Answer: D
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 497-417 = 80; the greatest possible divisor is 80.
Mathematics
Number System
Find the next term: 2, 9, 28, 65, ?
A. 51
B. 131
C. 126
D. 125
Correct Answer: C
Each term is n³ + 1. Thus the next term is 5³ + 1 = 126.
Mathematics
Number System
Find the next term: 11, 19, 30, 49, 79, 128, ?
A. 237
B. 158
C. 207
D. 256
Correct Answer: C
Each term is the sum of the previous two. Therefore 79 + 128 = 207.
Mathematics
Number System
Find the next number in the alternating series: 18, 25, 26, 22, 34, 19, ?
A. 34
B. 16
C. 42
D. 50
Correct Answer: C
Odd-position terms are 18, 26, 34, ... with difference 8. Hence the next odd-position term is 42.
Mathematics
Number System
What is the least positive number exactly divisible by 14, 15, and 11?
A. 4620
B. 15
C. 2321
D. 2310
Correct Answer: D
The required number is LCM(14, 15, 11) = 2310.
Mathematics
Number System
What is the greatest multiple of 16 that is less than 4722?
A. 4736
B. 4721
C. 4704
D. 4720
Correct Answer: D
4722 ÷ 16 has integer quotient 295; 16 × 295 = 4720.
Mathematics
Number System
What least number must be added to 844 so that the result is exactly divisible by 18?
A. 2
B. 20
C. 16
D. 3
Correct Answer: A
844 leaves remainder 16 on division by 18. Add 18 - 16 = 2.
Mathematics
Number System
What is the least positive number exactly divisible by 15, 16, and 8?
A. 248
B. 480
C. 240
D. 16
Correct Answer: C
The required number is LCM(15, 16, 8) = 240.
Mathematics
Number System
How many integers from 82 to 435, inclusive, are divisible by 13?
A. 26
B. 28
C. 27
D. 33
Correct Answer: C
Count = ⌊435/13⌋ - ⌊(82-1)/13⌋ = 33 - 6 = 27.
Mathematics
Number System
Find the next term: 4, 19, 23, 42, 65, 107, ?
A. 195
B. 130
C. 214
D. 172
Correct Answer: D
Each term is the sum of the previous two. Therefore 65 + 107 = 172.
Mathematics
Number System
How many trailing zeros are there in 109! ?
A. 24
B. 26
C. 10
D. 25
Correct Answer: D
Trailing zeros = ⌊109/5⌋ + ⌊109/25⌋ + ... = 21 + 4 = 25.
Mathematics
Number System
What least number must be subtracted from 1538 so that the result is exactly divisible by 28?
A. 2
B. 25
C. 26
D. 54
Correct Answer: C
The remainder is 26; subtracting the remainder makes the number divisible by 28.
Mathematics
Number System
Find the next number in the series: 2, 7, 12, 17, 22, ?
A. 22
B. 32
C. 37
D. 27
Correct Answer: D
The common difference is 5. So the next term is 22 + 5 = 27.
Mathematics
Number System
How many integers from 4 to 316, inclusive, are divisible by 13?
A. 26
B. 25
C. 23
D. 24
Correct Answer: D
Count = ⌊316/13⌋ - ⌊(4-1)/13⌋ = 24 - 0 = 24.
Mathematics
Number System
Find the next number in the series: 46, 57, 68, 79, 90, ?
A. 101
B. 123
C. 90
D. 112
Correct Answer: A
The common difference is 11. So the next term is 90 + 11 = 101.
Mathematics
Number System
Find the next term: 15, 18, 33, 51, 84, 135, ?
A. 168
B. 270
C. 219
D. 252
Correct Answer: C
Each term is the sum of the previous two. Therefore 84 + 135 = 219.
Mathematics
Number System
What is the remainder when 2021 is divided by 19?
A. 9
B. 10
C. 8
D. 7
Correct Answer: D
2021 = 19 × 106 + 7; therefore the remainder is 7.
Mathematics
Number System
Find the next number in the alternating series: 19, 57, 23, 62, 27, 67, ?
A. 72
B. 35
C. 31
D. 27
Correct Answer: C
Odd-position terms are 19, 23, 27, ... with difference 4. Hence the next odd-position term is 31.
Mathematics
Number System
Find the next term: 29, 66, 127, 218, ?
A. 345
B. 352
C. 198
D. 343
Correct Answer: A
Each term is n³ + 2. Thus the next term is 7³ + 2 = 345.
Mathematics
Number System
Find the next number in the alternating series: 29, 41, 38, 46, 47, 51, ?
A. 47
B. 65
C. 56
D. 61
Correct Answer: C
Odd-position terms are 29, 38, 47, ... with difference 9. Hence the next odd-position term is 56.