Mathematics
Number System
Find the next number in the series: 1, 5, 25, 125, 625, ?
A. 3125
B. 630
C. 3130
D. 625
Correct Answer: A
Each term is multiplied by 5. Therefore 625 × 5 = 3125.
Mathematics
Number System
The sum of 4 consecutive integers is 178. What is the smallest integer?
A. 42
B. 47
C. 43
D. 44
Correct Answer: C
Let the integers be n, n+1, ..., n+3. Their sum is 178; solving gives n = 43.
Mathematics
Number System
What least positive number must be added to 693 so that the result is divisible by 11?
A. 22
B. 0
C. 1
D. 11
Correct Answer: D
693 is already divisible by 11; the least positive addition preserving divisibility is 11.
Mathematics
Number System
Find the next number in the series: 34, 36, 38, 40, 42, ?
A. 42
B. 44
C. 46
D. 48
Correct Answer: B
The common difference is 2. So the next term is 42 + 2 = 44.
Mathematics
Number System
Find the next number: 5, 22, 73, 226, 685, ?
A. 2059
B. 2069
C. 2062
D. 2055
Correct Answer: C
Each term is obtained by ×3 + 7. So 685 × 3 + 7 = 2062.
Mathematics
Number System
Find the next number: 12, 25, 51, 103, 207, ?
A. 415
B. 416
C. 414
D. 413
Correct Answer: A
Each term is obtained by ×2 + 1. So 207 × 2 + 1 = 415.
Mathematics
Number System
Classify 39/24.
A. Whole number
B. Irrational
C. Rational
D. Prime number
Correct Answer: C
39/24 is a ratio of two integers with a non-zero denominator, so it is rational.
Mathematics
Number System
Classify 38/13.
A. Whole number
B. Rational
C. Irrational
D. Prime number
Correct Answer: B
38/13 is a ratio of two integers with a non-zero denominator, so it is rational.
Mathematics
Number System
Find the next number: 24, 27, 32, 39, 50, ?
A. 74
B. 65
C. 50
D. 63
Correct Answer: D
Successive prime numbers are added: 3, 5, 7, 11, 13. Add 13 next, giving 63.
Mathematics
Number System
Classify 27/5.
A. Irrational
B. Prime number
C. Rational
D. Whole number
Correct Answer: C
27/5 is a ratio of two integers with a non-zero denominator, so it is rational.
Mathematics
Number System
Find the next number in the alternating series: 4, 77, 7, 75, 10, 73, ?
A. 13
B. 71
C. 16
D. 10
Correct Answer: A
Odd-position terms are 4, 7, 10, ... with difference 3. Hence the next odd-position term is 13.
Mathematics
Number System
How many trailing zeros are there in 87! ?
A. 19
B. 20
C. 21
D. 8
Correct Answer: B
Trailing zeros = ⌊87/5⌋ + ⌊87/25⌋ + ... = 17 + 3 = 20.
Mathematics
Number System
What is the units digit of 10^36?
A. 4
B. 6
C. 2
D. 0
Correct Answer: D
Units digits repeat cyclically; applying the cycle for base 10 gives units digit 0.
Mathematics
Number System
Find the next term: 42, 56, 53, 67, 64, 78, ?
A. 61
B. 78
C. 92
D. 75
Correct Answer: D
The operations alternate +14, -3. After the last +14, subtract 3: 78 - 3 = 75.
Mathematics
Number System
Find the next number: 24, 33, 49, 74, 110, ?
A. 146
B. 166
C. 159
D. 152
Correct Answer: C
The increments are consecutive squares: 9, 16, 25, 36; next add 7² = 49. So the answer is 159.
Mathematics
Number System
What is the remainder when 355 is divided by 11?
A. 4
B. 3
C. 5
D. 6
Correct Answer: B
355 = 11 × 32 + 3; therefore the remainder is 3.
Mathematics
Number System
Classify √60.
A. Irrational
B. Prime number
C. Whole number
D. Rational
Correct Answer: A
60 is not a perfect square, so √60 is irrational.
Mathematics
Number System
Find the next number in the alternating series: 26, 31, 29, 33, 32, 35, ?
A. 32
B. 38
C. 35
D. 37
Correct Answer: C
Odd-position terms are 26, 29, 32, ... with difference 3. Hence the next odd-position term is 35.
Mathematics
Number System
Find the next term: 8, 27, 64, 125, ?
A. 108
B. 222
C. 237
D. 216
Correct Answer: D
Each term is n³ + 0. Thus the next term is 6³ + 0 = 216.
Mathematics
Number System
Find the next term in the series: 7, 15, 25, 37, 51, ?
A. 65
B. 67
C. 69
D. 81
Correct Answer: B
The first differences are [8, 10, 12, 14]; their second difference is constant at 2. Continuing the pattern gives 67.