Mathematics
Number System
Find the next number: 4, 9, 17, 28, 42, ?
A. 62
B. 47
C. 59
D. 56
Correct Answer: C
The differences are 5, 8, 11, 14, increasing by 3. The next difference is 17, so the answer is 59.
Mathematics
Number System
Find the next number: 22, 26, 35, 51, 76, ?
A. 118
B. 106
C. 101
D. 112
Correct Answer: D
The increments are consecutive squares: 4, 9, 16, 25; next add 6² = 36. So the answer is 112.
Mathematics
Number System
Classify √68.
A. Prime number
B. Whole number
C. Rational
D. Irrational
Correct Answer: D
68 is not a perfect square, so √68 is irrational.
Mathematics
Number System
Find the next term in the series: 65, 100, 143, 194, 253, ?
A. 320
B. 312
C. 328
D. 379
Correct Answer: A
The first differences are [35, 43, 51, 59]; their second difference is constant at 8. Continuing the pattern gives 320.
Mathematics
Number System
Find the next number: 38, 41, 46, 53, 64, ?
A. 64
B. 88
C. 79
D. 77
Correct Answer: D
Successive prime numbers are added: 3, 5, 7, 11, 13. Add 13 next, giving 77.
Mathematics
Number System
Find the next term in the series: 53, 86, 127, 176, 233, ?
A. 298
B. 290
C. 306
D. 355
Correct Answer: A
The first differences are [33, 41, 49, 57]; their second difference is constant at 8. Continuing the pattern gives 298.
Mathematics
Number System
Classify 38/16.
A. Rational
B. Prime number
C. Irrational
D. Whole number
Correct Answer: A
38/16 is a ratio of two integers with a non-zero denominator, so it is rational.
Mathematics
Number System
Find the next number: 11, 24, 50, 102, 206, ?
A. 416
B. 455
C. 412
D. 414
Correct Answer: D
Each term is obtained by ×2 + 2. So 206 × 2 + 2 = 414.
Mathematics
Number System
Find the next number: 15, 24, 40, 65, 101, ?
A. 137
B. 143
C. 150
D. 157
Correct Answer: C
The increments are consecutive squares: 9, 16, 25, 36; next add 7² = 49. So the answer is 150.
Mathematics
Number System
Find the next number: 25, 26, 30, 39, 55, ?
A. 85
B. 75
C. 71
D. 80
Correct Answer: D
The increments are consecutive squares: 1, 4, 9, 16; next add 5² = 25. So the answer is 80.
Mathematics
Number System
Find the next number in the series: 53, 55, 57, 59, 61, ?
A. 61
B. 67
C. 65
D. 63
Correct Answer: D
The common difference is 2. So the next term is 61 + 2 = 63.
Mathematics
Number System
Find the next number: 4, 19, 64, 199, 604, ?
A. 1826
B. 1819
C. 1812
D. 1816
Correct Answer: B
Each term is obtained by ×3 + 7. So 604 × 3 + 7 = 1819.
Mathematics
Number System
Two positive integers have HCF 4 and LCM 336. What is their product?
A. 340
B. 336
C. 1348
D. 1344
Correct Answer: D
For two positive integers, product = HCF × LCM = 4 × 336 = 1344.
Mathematics
Number System
What is the least positive number exactly divisible by 11, 8, and 15?
A. 1320
B. 1328
C. 15
D. 2640
Correct Answer: A
The required number is LCM(11, 8, 15) = 1320.
Mathematics
Number System
Classify √5.
A. Whole number
B. Rational
C. Irrational
D. Prime number
Correct Answer: C
5 is not a perfect square, so √5 is irrational.
Mathematics
Number System
What is the greatest positive integer that can divide both 619 and 598 leaving the same remainder?
A. 21
B. 20
C. 22
D. 10
Correct Answer: A
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 619-598 = 21; the greatest possible divisor is 21.
Mathematics
Number System
Find the next number in the series: 2, 6, 18, 54, 162, ?
A. 486
B. 165
C. 489
D. 162
Correct Answer: A
Each term is multiplied by 3. Therefore 162 × 3 = 486.
Mathematics
Number System
Find the next number: 10, 19, 35, 60, 96, ?
A. 138
B. 132
C. 145
D. 152
Correct Answer: C
The increments are consecutive squares: 9, 16, 25, 36; next add 7² = 49. So the answer is 145.
Mathematics
Number System
The sum of 4 consecutive integers is 242. What is the smallest integer?
A. 59
B. 60
C. 63
D. 58
Correct Answer: A
Let the integers be n, n+1, ..., n+3. Their sum is 242; solving gives n = 59.
Mathematics
Number System
Find the missing number: 74, 87, 100, ?, 126, 139
A. 126
B. 113
C. 100
D. 139
Correct Answer: B
This is an arithmetic series with common difference 13; the missing term is 113.