Mathematics
Number System
Classify √69.
A. Rational
B. Whole number
C. Irrational
D. Prime number
Correct Answer: C
69 is not a perfect square, so √69 is irrational.
Mathematics
Number System
Find the HCF (GCD) of 136 and 255.
A. 18
B. 8
C. 17
D. 34
Correct Answer: C
The greatest common divisor of 136 and 255 is 17.
Mathematics
Number System
Find the next number: 31, 38, 49, 64, 83, ?
A. 110
B. 90
C. 102
D. 106
Correct Answer: D
The differences are 7, 11, 15, 19, increasing by 4. The next difference is 23, so the answer is 106.
Mathematics
Number System
How many trailing zeros are there in 135! ?
A. 33
B. 34
C. 13
D. 32
Correct Answer: A
Trailing zeros = ⌊135/5⌋ + ⌊135/25⌋ + ... = 27 + 5 + 1 = 33.
Mathematics
Number System
The sum of 3 consecutive integers is 117. What is the middle integer?
A. 40
B. 42
C. 38
D. 39
Correct Answer: D
The middle integer equals the average: 117 ÷ 3 = 39.
Mathematics
Number System
Find the next term: 14, 33, 70, 131, ?
A. 222
B. 216
C. 114
D. 228
Correct Answer: A
Each term is n³ + 6. Thus the next term is 6³ + 6 = 222.
Mathematics
Number System
Find the next term: 17, 24, 33, 44, 57, ?
A. 56
B. 72
C. 73
D. 88
Correct Answer: B
The terms follow 1n² + 8 for consecutive n. For n = 8, the term is 1×8² + 8 = 72.
Mathematics
Number System
What is the greatest positive integer that can divide both 342 and 219 leaving the same remainder?
A. 61
B. 122
C. 124
D. 123
Correct Answer: D
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 342-219 = 123; the greatest possible divisor is 123.
Mathematics
Number System
Find the next term: 16, 35, 72, 133, ?
A. 224
B. 116
C. 230
D. 216
Correct Answer: A
Each term is n³ + 8. Thus the next term is 6³ + 8 = 224.
Mathematics
Number System
Find the next number in the series: 7, 20, 33, 46, 59, ?
A. 98
B. 72
C. 59
D. 85
Correct Answer: B
The common difference is 13. So the next term is 59 + 13 = 72.
Mathematics
Number System
How many trailing zeros are there in 20! ?
A. 2
B. 5
C. 3
D. 4
Correct Answer: D
Trailing zeros = ⌊20/5⌋ + ⌊20/25⌋ + ... = 4 = 4.
Mathematics
Number System
How is the integer 84 classified?
A. Prime
B. Neither prime nor composite
C. Irrational
D. Composite
Correct Answer: D
84 = 7 × 12, so it has factors other than 1 and itself and is composite.
Mathematics
Number System
Find the next term: 33, 54, 81, 114, 153, ?
A. 198
B. 150
C. 246
D. 201
Correct Answer: A
The terms follow 3n² + 6 for consecutive n. For n = 8, the term is 3×8² + 6 = 198.
Mathematics
Number System
Find the next term: 4, 15, 19, 34, 53, 87, ?
A. 106
B. 174
C. 159
D. 140
Correct Answer: D
Each term is the sum of the previous two. Therefore 53 + 87 = 140.
Mathematics
Number System
How many trailing zeros are there in 21! ?
A. 2
B. 4
C. 3
D. 5
Correct Answer: B
Trailing zeros = ⌊21/5⌋ + ⌊21/25⌋ + ... = 4 = 4.
Mathematics
Number System
Find the next number: 18, 34, 59, 95, 144, ?
A. 208
B. 216
C. 193
D. 200
Correct Answer: A
The increments are consecutive squares: 16, 25, 36, 49; next add 8² = 64. So the answer is 208.
Mathematics
Number System
What is the greatest positive integer that can divide both 671 and 540 leaving the same remainder?
A. 130
B. 131
C. 132
D. 65
Correct Answer: B
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 671-540 = 131; the greatest possible divisor is 131.
Mathematics
Number System
Find the next term: 63, 75, 71, 83, 79, 91, ?
A. 75
B. 103
C. 87
D. 91
Correct Answer: C
The operations alternate +12, -4. After the last +12, subtract 4: 91 - 4 = 87.
Mathematics
Number System
Find the next number in the series: 42, 57, 72, 87, 102, ?
A. 132
B. 117
C. 147
D. 102
Correct Answer: B
The common difference is 15. So the next term is 102 + 15 = 117.
Mathematics
Number System
Find the next number: 8, 27, 84, 255, 768, ?
A. 2304
B. 2537
C. 2310
D. 2307
Correct Answer: D
Each term is obtained by ×3 + 3. So 768 × 3 + 3 = 2307.