Mathematics
Number System
Find the next number: 2, 4, 12, 48, 240, ?
A. 240
B. 1446
C. 1440
D. 1200
Correct Answer: C
The multipliers are ×2, ×3, ×4, ×5; the next multiplier is ×6. Thus 240 × 6 = 1440.
Mathematics
Number System
Find the next term: 4, 12, 16, 28, 44, 72, ?
A. 88
B. 132
C. 116
D. 144
Correct Answer: C
Each term is the sum of the previous two. Therefore 44 + 72 = 116.
Mathematics
Number System
How many trailing zeros are there in 42! ?
A. 9
B. 4
C. 10
D. 8
Correct Answer: A
Trailing zeros = ⌊42/5⌋ + ⌊42/25⌋ + ... = 8 + 1 = 9.
Mathematics
Number System
What digit x makes the number 403x divisible by 9?
A. 3
B. 2
C. 5
D. 7
Correct Answer: B
A number is divisible by 9 when its digit sum is divisible by 9. Thus 4+0+3+x must be a multiple of 9, giving x = 2.
Mathematics
Number System
Find the next number: 7, 10, 18, 31, 49, ?
A. 67
B. 52
C. 77
D. 72
Correct Answer: D
The differences are 3, 8, 13, 18, increasing by 5. The next difference is 23, so the answer is 72.
Mathematics
Number System
How many integers from 57 to 346, inclusive, are divisible by 8?
A. 43
B. 35
C. 37
D. 36
Correct Answer: D
Count = ⌊346/8⌋ - ⌊(57-1)/8⌋ = 43 - 7 = 36.
Mathematics
Number System
Find the next term: 41, 59, 81, 107, 137, ?
A. 171
B. 173
C. 135
D. 207
Correct Answer: A
The terms follow 2n² + 9 for consecutive n. For n = 9, the term is 2×9² + 9 = 171.
Mathematics
Number System
Find the HCF (GCD) of 91 and 169.
A. 14
B. 13
C. 26
D. 6
Correct Answer: B
The greatest common divisor of 91 and 169 is 13.
Mathematics
Number System
Find the next number: 12, 14, 17, 22, 29, ?
A. 42
B. 29
C. 47
D. 40
Correct Answer: D
Successive prime numbers are added: 2, 3, 5, 7, 11. Add 11 next, giving 40.
Mathematics
Number System
What least number must be subtracted from 2936 so that the result is exactly divisible by 22?
A. 12
B. 9
C. 32
D. 10
Correct Answer: D
The remainder is 10; subtracting the remainder makes the number divisible by 22.
Mathematics
Number System
Find the next number: 11, 38, 119, 362, 1091, ?
A. 3283
B. 3278
C. 3273
D. 3275
Correct Answer: B
Each term is obtained by ×3 + 5. So 1091 × 3 + 5 = 3278.
Mathematics
Number System
How many positive divisors does 1125 have?
A. 12
B. 11
C. 7
D. 14
Correct Answer: A
1125 = 3^2 × 5^3. Number of divisors = (2+1)(3+1) = 12.
Mathematics
Number System
What is the greatest positive integer that can divide both 302 and 239 leaving the same remainder?
A. 62
B. 63
C. 64
D. 31
Correct Answer: B
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 302-239 = 63; the greatest possible divisor is 63.
Mathematics
Number System
What is the units digit of 27^87?
A. 9
B. 7
C. 3
D. 5
Correct Answer: C
Units digits repeat cyclically; applying the cycle for base 27 gives units digit 3.
Mathematics
Number System
What is the units digit of 19^21?
A. 5
B. 1
C. 3
D. 9
Correct Answer: D
Units digits repeat cyclically; applying the cycle for base 19 gives units digit 9.
Mathematics
Number System
Find the next number in the series: 72, 89, 106, 123, 140, ?
A. 191
B. 140
C. 174
D. 157
Correct Answer: D
The common difference is 17. So the next term is 140 + 17 = 157.
Mathematics
Number System
How many positive divisors does 135 have?
A. 7
B. 8
C. 10
D. 6
Correct Answer: B
135 = 5^1 × 3^3. Number of divisors = (1+1)(3+1) = 8.
Mathematics
Number System
Find the next number: 27, 31, 39, 51, 67, ?
A. 87
B. 83
C. 71
D. 91
Correct Answer: A
The differences are 4, 8, 12, 16, increasing by 4. The next difference is 20, so the answer is 87.
Mathematics
Number System
Find the next term: 40, 68, 104, 148, 200, ?
A. 260
B. 324
C. 196
D. 264
Correct Answer: A
The terms follow 4n² + 4 for consecutive n. For n = 8, the term is 4×8² + 4 = 260.
Mathematics
Number System
How many trailing zeros are there in 96! ?
A. 9
B. 21
C. 22
D. 23
Correct Answer: C
Trailing zeros = ⌊96/5⌋ + ⌊96/25⌋ + ... = 19 + 3 = 22.