Mathematics
Number System
The sum of 4 consecutive integers is 206. What is the smallest integer?
A. 50
B. 54
C. 49
D. 51
Correct Answer: A
Let the integers be n, n+1, ..., n+3. Their sum is 206; solving gives n = 50.
Mathematics
Number System
Find the missing number: 25, 30, 35, ?, 45, 50
A. 45
B. 35
C. 40
D. 50
Correct Answer: C
This is an arithmetic series with common difference 5; the missing term is 40.
Mathematics
Number System
Find the next term: 9, 29, 38, 67, 105, 172, ?
A. 210
B. 315
C. 344
D. 277
Correct Answer: D
Each term is the sum of the previous two. Therefore 105 + 172 = 277.
Mathematics
Number System
What is the greatest multiple of 23 that is less than 4111?
A. 4071
B. 4095
C. 4117
D. 4094
Correct Answer: D
4111 ÷ 23 has integer quotient 178; 23 × 178 = 4094.
Mathematics
Number System
Find the next number in the alternating series: 16, 56, 25, 60, 34, 64, ?
A. 68
B. 43
C. 34
D. 52
Correct Answer: B
Odd-position terms are 16, 25, 34, ... with difference 9. Hence the next odd-position term is 43.
Mathematics
Number System
The sum of 4 consecutive integers is 234. What is the smallest integer?
A. 56
B. 57
C. 61
D. 58
Correct Answer: B
Let the integers be n, n+1, ..., n+3. Their sum is 234; solving gives n = 57.
Mathematics
Number System
Find the HCF (GCD) of 140 and 220.
A. 10
B. 20
C. 21
D. 40
Correct Answer: B
The greatest common divisor of 140 and 220 is 20.
Mathematics
Number System
What least number must be subtracted from 2470 so that the result is exactly divisible by 7?
A. 6
B. 1
C. 13
D. 5
Correct Answer: A
The remainder is 6; subtracting the remainder makes the number divisible by 7.
Mathematics
Number System
Find the next number: 33, 40, 51, 64, 81, ?
A. 102
B. 100
C. 81
D. 117
Correct Answer: B
Successive prime numbers are added: 7, 11, 13, 17, 19. Add 19 next, giving 100.
Mathematics
Number System
What digit x makes the number 465x divisible by 9?
A. 3
B. 4
C. 8
D. 6
Correct Answer: A
A number is divisible by 9 when its digit sum is divisible by 9. Thus 4+6+5+x must be a multiple of 9, giving x = 3.
Mathematics
Number System
Find the next number: 36, 41, 48, 59, 72, ?
A. 91
B. 89
C. 72
D. 102
Correct Answer: B
Successive prime numbers are added: 5, 7, 11, 13, 17. Add 17 next, giving 89.
Mathematics
Number System
How many integers from 96 to 365, inclusive, are divisible by 7?
A. 39
B. 40
C. 38
D. 52
Correct Answer: A
Count = ⌊365/7⌋ - ⌊(96-1)/7⌋ = 52 - 13 = 39.
Mathematics
Number System
What is the greatest positive integer that can divide both 284 and 150 leaving the same remainder?
A. 135
B. 67
C. 133
D. 134
Correct Answer: D
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 284-150 = 134; the greatest possible divisor is 134.
Mathematics
Number System
What least number must be subtracted from 3216 so that the result is exactly divisible by 20?
A. 4
B. 15
C. 16
D. 36
Correct Answer: C
The remainder is 16; subtracting the remainder makes the number divisible by 20.
Mathematics
Number System
A two-digit number is 70. What is the absolute difference between the number and the number formed by reversing its digits?
A. 63
B. 7
C. 72
D. 54
Correct Answer: A
Reversed number = 7. Absolute difference = |70 - 7| = 63.
Mathematics
Number System
Find the next number: 21, 29, 39, 51, 65, ?
A. 79
B. 73
C. 81
D. 83
Correct Answer: C
The differences are 8, 10, 12, 14, increasing by 2. The next difference is 16, so the answer is 81.
Mathematics
Number System
Find the next term in the series: 39, 60, 85, 114, 147, ?
A. 180
B. 188
C. 184
D. 217
Correct Answer: C
The first differences are [21, 25, 29, 33]; their second difference is constant at 4. Continuing the pattern gives 184.
Mathematics
Number System
Find the next number in the series: 75, 78, 81, 84, 87, ?
A. 90
B. 87
C. 96
D. 93
Correct Answer: A
The common difference is 3. So the next term is 87 + 3 = 90.
Mathematics
Number System
Find the next number in the series: 7, 21, 63, 189, 567, ?
A. 1704
B. 570
C. 1701
D. 567
Correct Answer: C
Each term is multiplied by 3. Therefore 567 × 3 = 1701.
Mathematics
Number System
Find the missing number: 33, 41, 49, 57, ?, 73
A. 57
B. 65
C. 81
D. 73
Correct Answer: B
This is an arithmetic series with common difference 8; the missing term is 65.