Mathematics
Number System
Find the next number: 37, 40, 45, 52, 63, ?
A. 78
B. 87
C. 63
D. 76
Correct Answer: D
Successive prime numbers are added: 3, 5, 7, 11, 13. Add 13 next, giving 76.
Mathematics
Number System
Find the next number: 2, 8, 17, 29, 44, ?
A. 62
B. 59
C. 65
D. 50
Correct Answer: A
The differences are 6, 9, 12, 15, increasing by 3. The next difference is 18, so the answer is 62.
Mathematics
Number System
Classify 26/15.
A. Prime number
B. Irrational
C. Whole number
D. Rational
Correct Answer: D
26/15 is a ratio of two integers with a non-zero denominator, so it is rational.
Mathematics
Number System
What digit x makes the number 482x divisible by 9?
A. 7
B. 9
C. 4
D. 5
Correct Answer: C
A number is divisible by 9 when its digit sum is divisible by 9. Thus 4+8+2+x must be a multiple of 9, giving x = 4.
Mathematics
Number System
How many positive divisors does 6 have?
A. 3
B. 6
C. 5
D. 4
Correct Answer: D
6 = 3^1 × 2^1. Number of divisors = (1+1)(1+1) = 4.
Mathematics
Number System
Find the next number: 9, 29, 89, 269, 809, ?
A. 2427
B. 2426
C. 2431
D. 2429
Correct Answer: D
Each term is obtained by ×3 + 2. So 809 × 3 + 2 = 2429.
Mathematics
Number System
What is the greatest positive integer that can divide both 444 and 305 leaving the same remainder?
A. 69
B. 138
C. 140
D. 139
Correct Answer: D
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 444-305 = 139; the greatest possible divisor is 139.
Mathematics
Number System
What least positive number must be added to 1547 so that the result is divisible by 7?
A. 0
B. 1
C. 14
D. 7
Correct Answer: D
1547 is already divisible by 7; the least positive addition preserving divisibility is 7.
Mathematics
Number System
Find the next term in the series: 32, 60, 96, 140, 192, ?
A. 260
B. 304
C. 252
D. 244
Correct Answer: C
The first differences are [28, 36, 44, 52]; their second difference is constant at 8. Continuing the pattern gives 252.
Mathematics
Number System
What is the greatest positive integer that can divide both 607 and 548 leaving the same remainder?
A. 59
B. 58
C. 29
D. 60
Correct Answer: A
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 607-548 = 59; the greatest possible divisor is 59.
Mathematics
Number System
Two positive integers have HCF 9 and LCM 351. What is their product?
A. 351
B. 3168
C. 3159
D. 360
Correct Answer: C
For two positive integers, product = HCF × LCM = 9 × 351 = 3159.
Mathematics
Number System
Find the next number in the series: 38, 43, 48, 53, 58, ?
A. 73
B. 58
C. 68
D. 63
Correct Answer: D
The common difference is 5. So the next term is 58 + 5 = 63.
Mathematics
Number System
What is the least positive number exactly divisible by 13, 7, and 5?
A. 910
B. 460
C. 455
D. 13
Correct Answer: C
The required number is LCM(13, 7, 5) = 455.
Mathematics
Number System
Find the next term: 21, 27, 22, 28, 23, 29, ?
A. 35
B. 24
C. 29
D. 18
Correct Answer: B
The operations alternate +6, -5. After the last +6, subtract 5: 29 - 5 = 24.
Mathematics
Number System
Find the next number: 3, 6, 18, 72, 360, ?
A. 2166
B. 360
C. 1800
D. 2160
Correct Answer: D
The multipliers are ×2, ×3, ×4, ×5; the next multiplier is ×6. Thus 360 × 6 = 2160.
Mathematics
Number System
Find the next number: 40, 47, 58, 71, 88, ?
A. 88
B. 107
C. 109
D. 124
Correct Answer: B
Successive prime numbers are added: 7, 11, 13, 17, 19. Add 19 next, giving 107.
Mathematics
Number System
How many trailing zeros are there in 133! ?
A. 31
B. 32
C. 33
D. 13
Correct Answer: B
Trailing zeros = ⌊133/5⌋ + ⌊133/25⌋ + ... = 26 + 5 + 1 = 32.
Mathematics
Number System
What is the greatest multiple of 20 that is less than 993?
A. 981
B. 1000
C. 960
D. 980
Correct Answer: D
993 ÷ 20 has integer quotient 49; 20 × 49 = 980.
Mathematics
Number System
Find the next number: 21, 25, 31, 39, 49, ?
A. 53
B. 59
C. 61
D. 63
Correct Answer: C
The differences are 4, 6, 8, 10, increasing by 2. The next difference is 12, so the answer is 61.
Mathematics
Number System
What is the remainder when 199 is divided by 18?
A. 2
B. 4
C. 1
D. 3
Correct Answer: C
199 = 18 × 11 + 1; therefore the remainder is 1.