Mathematics
Number System
The sum of 4 consecutive integers is 174. What is the smallest integer?
A. 46
B. 43
C. 41
D. 42
Correct Answer: D
Let the integers be n, n+1, ..., n+3. Their sum is 174; solving gives n = 42.
Mathematics
Number System
How many positive divisors does 1000 have?
A. 18
B. 8
C. 16
D. 15
Correct Answer: C
1000 = 2^3 × 5^3. Number of divisors = (3+1)(3+1) = 16.
Mathematics
Number System
Find the next term: 20, 34, 52, 74, 100, ?
A. 130
B. 162
C. 98
D. 132
Correct Answer: A
The terms follow 2n² + 2 for consecutive n. For n = 8, the term is 2×8² + 2 = 130.
Mathematics
Number System
Find the next term: 10, 18, 28, 46, 74, 120, ?
A. 240
B. 194
C. 222
D. 148
Correct Answer: B
Each term is the sum of the previous two. Therefore 74 + 120 = 194.
Mathematics
Number System
Find the next term: 10, 29, 66, 127, ?
A. 216
B. 218
C. 110
D. 224
Correct Answer: B
Each term is n³ + 2. Thus the next term is 6³ + 2 = 218.
Mathematics
Number System
Find the next number in the series: 2, 8, 32, 128, 512, ?
A. 2048
B. 512
C. 516
D. 2052
Correct Answer: A
Each term is multiplied by 4. Therefore 512 × 4 = 2048.
Mathematics
Number System
Find the next number in the series: 15, 23, 31, 39, 47, ?
A. 71
B. 63
C. 47
D. 55
Correct Answer: D
The common difference is 8. So the next term is 47 + 8 = 55.
Mathematics
Number System
What least number must be subtracted from 2403 so that the result is exactly divisible by 16?
A. 19
B. 2
C. 3
D. 13
Correct Answer: C
The remainder is 3; subtracting the remainder makes the number divisible by 16.
Mathematics
Number System
Find the next number in the alternating series: 18, 54, 23, 60, 28, 66, ?
A. 38
B. 72
C. 28
D. 33
Correct Answer: D
Odd-position terms are 18, 23, 28, ... with difference 5. Hence the next odd-position term is 33.
Mathematics
Number System
What least number must be added to 2110 so that the result is exactly divisible by 8?
A. 3
B. 10
C. 2
D. 6
Correct Answer: C
2110 leaves remainder 6 on division by 8. Add 8 - 6 = 2.
Mathematics
Number System
What is the least positive number exactly divisible by 11, 13, and 14?
A. 2013
B. 4004
C. 2002
D. 14
Correct Answer: C
The required number is LCM(11, 13, 14) = 2002.
Mathematics
Number System
The sum of 3 consecutive integers is 159. What is the middle integer?
A. 53
B. 52
C. 54
D. 56
Correct Answer: A
The middle integer equals the average: 159 ÷ 3 = 53.
Mathematics
Number System
What is the greatest multiple of 35 that is less than 2633?
A. 2660
B. 2590
C. 2626
D. 2625
Correct Answer: D
2633 ÷ 35 has integer quotient 75; 35 × 75 = 2625.
Mathematics
Number System
Find the next term: 39, 76, 137, 228, ?
A. 208
B. 355
C. 362
D. 343
Correct Answer: B
Each term is n³ + 12. Thus the next term is 7³ + 12 = 355.
Mathematics
Number System
What is the units digit of 53^99?
A. 9
B. 1
C. 7
D. 3
Correct Answer: C
Units digits repeat cyclically; applying the cycle for base 53 gives units digit 7.
Mathematics
Number System
Find the next term: 5, 6, 11, 17, 28, 45, ?
A. 56
B. 90
C. 84
D. 73
Correct Answer: D
Each term is the sum of the previous two. Therefore 28 + 45 = 73.
Mathematics
Number System
What is the greatest multiple of 35 that is less than 2191?
A. 2205
B. 2171
C. 2170
D. 2135
Correct Answer: C
2191 ÷ 35 has integer quotient 62; 35 × 62 = 2170.
Mathematics
Number System
Find the next number in the series: 8, 16, 32, 64, 128, ?
A. 130
B. 128
C. 258
D. 256
Correct Answer: D
Each term is multiplied by 2. Therefore 128 × 2 = 256.
Mathematics
Number System
Find the next term in the series: 12, 19, 30, 45, 64, ?
A. 91
B. 83
C. 87
D. 106
Correct Answer: C
The first differences are [7, 11, 15, 19]; their second difference is constant at 4. Continuing the pattern gives 87.
Mathematics
Number System
Find the next number: 5, 7, 14, 26, 43, ?
A. 60
B. 45
C. 65
D. 70
Correct Answer: C
The differences are 2, 7, 12, 17, increasing by 5. The next difference is 22, so the answer is 65.