Mathematics
Number System
Find the next term in the series: 25, 36, 49, 64, 81, ?
A. 117
B. 98
C. 100
D. 102
Correct Answer: C
The first differences are [11, 13, 15, 17]; their second difference is constant at 2. Continuing the pattern gives 100.
Mathematics
Number System
What is the least positive number exactly divisible by 8, 6, and 5?
A. 125
B. 240
C. 8
D. 120
Correct Answer: D
The required number is LCM(8, 6, 5) = 120.
Mathematics
Number System
Find the next term: 37, 74, 135, 226, ?
A. 360
B. 353
C. 343
D. 206
Correct Answer: B
Each term is n³ + 10. Thus the next term is 7³ + 10 = 353.
Mathematics
Number System
Find the next number: 9, 31, 97, 295, 889, ?
A. 2667
B. 2671
C. 2668
D. 2675
Correct Answer: B
Each term is obtained by ×3 + 4. So 889 × 3 + 4 = 2671.
Mathematics
Number System
Find the next number in the alternating series: 29, 32, 36, 37, 43, 42, ?
A. 47
B. 57
C. 43
D. 50
Correct Answer: D
Odd-position terms are 29, 36, 43, ... with difference 7. Hence the next odd-position term is 50.
Mathematics
Number System
How many trailing zeros are there in 35! ?
A. 3
B. 9
C. 8
D. 7
Correct Answer: C
Trailing zeros = ⌊35/5⌋ + ⌊35/25⌋ + ... = 7 + 1 = 8.
Mathematics
Number System
Find the next number: 2, 6, 24, 120, 720, ?
A. 4320
B. 5047
C. 5040
D. 720
Correct Answer: C
The multipliers are ×3, ×4, ×5, ×6; the next multiplier is ×7. Thus 720 × 7 = 5040.
Mathematics
Number System
A two-digit number is 50. What is the absolute difference between the number and the number formed by reversing its digits?
A. 36
B. 45
C. 54
D. 5
Correct Answer: B
Reversed number = 5. Absolute difference = |50 - 5| = 45.
Mathematics
Number System
Find the missing number: 11, 17, 23, ?, 35, 41
A. 35
B. 23
C. 41
D. 29
Correct Answer: D
This is an arithmetic series with common difference 6; the missing term is 29.
Mathematics
Number System
What is the units digit of 7^82?
A. 9
B. 1
C. 5
D. 3
Correct Answer: A
Units digits repeat cyclically; applying the cycle for base 7 gives units digit 9.
Mathematics
Number System
How many integers from 15 to 103, inclusive, are divisible by 7?
A. 11
B. 14
C. 12
D. 13
Correct Answer: C
Count = ⌊103/7⌋ - ⌊(15-1)/7⌋ = 14 - 2 = 12.
Mathematics
Number System
Find the next number in the series: 43, 47, 51, 55, 59, ?
A. 63
B. 67
C. 71
D. 59
Correct Answer: A
The common difference is 4. So the next term is 59 + 4 = 63.
Mathematics
Number System
What is the least positive number exactly divisible by 4, 10, and 6?
A. 120
B. 60
C. 64
D. 10
Correct Answer: B
The required number is LCM(4, 10, 6) = 60.
Mathematics
Number System
How many integers from 6 to 396, inclusive, are divisible by 7?
A. 61
B. 56
C. 55
D. 57
Correct Answer: B
Count = ⌊396/7⌋ - ⌊(6-1)/7⌋ = 56 - 0 = 56.
Mathematics
Number System
What is the least positive number exactly divisible by 5, 14, and 10?
A. 140
B. 75
C. 14
D. 70
Correct Answer: D
The required number is LCM(5, 14, 10) = 70.
Mathematics
Number System
Find the next term: 7, 8, 15, 23, 38, 61, ?
A. 76
B. 122
C. 114
D. 99
Correct Answer: D
Each term is the sum of the previous two. Therefore 38 + 61 = 99.
Mathematics
Number System
Find the next number: 1, 9, 22, 40, 63, ?
A. 91
B. 86
C. 71
D. 96
Correct Answer: A
The differences are 8, 13, 18, 23, increasing by 5. The next difference is 28, so the answer is 91.
Mathematics
Number System
Classify √50.
A. Whole number
B. Irrational
C. Rational
D. Prime number
Correct Answer: B
50 is not a perfect square, so √50 is irrational.
Mathematics
Number System
Find the next term: 15, 34, 71, 132, ?
A. 216
B. 115
C. 223
D. 229
Correct Answer: C
Each term is n³ + 7. Thus the next term is 6³ + 7 = 223.
Mathematics
Number System
Find the missing number: 11, 15, ?, 23, 27, 31
A. 23
B. 27
C. 15
D. 19
Correct Answer: D
This is an arithmetic series with common difference 4; the missing term is 19.