Mathematics
Number System
Two positive integers have HCF 11 and LCM 726. What is their product?
A. 7986
B. 737
C. 7997
D. 726
Correct Answer: A
For two positive integers, product = HCF × LCM = 11 × 726 = 7986.
Mathematics
Number System
How many trailing zeros are there in 88! ?
A. 21
B. 8
C. 20
D. 19
Correct Answer: C
Trailing zeros = ⌊88/5⌋ + ⌊88/25⌋ + ... = 17 + 3 = 20.
Mathematics
Number System
Find the next term: 5, 11, 21, 35, 53, ?
A. 77
B. 51
C. 75
D. 99
Correct Answer: C
The terms follow 2n² + 3 for consecutive n. For n = 6, the term is 2×6² + 3 = 75.
Mathematics
Number System
What digit x makes the number 902x divisible by 9?
A. 0
B. 8
C. 7
D. 2
Correct Answer: C
A number is divisible by 9 when its digit sum is divisible by 9. Thus 9+0+2+x must be a multiple of 9, giving x = 7.
Mathematics
Number System
Find the next number in the series: 3, 9, 27, 81, 243, ?
A. 246
B. 243
C. 732
D. 729
Correct Answer: D
Each term is multiplied by 3. Therefore 243 × 3 = 729.
Mathematics
Number System
What is the units digit of 80^67?
A. 0
B. 6
C. 2
D. 4
Correct Answer: A
Units digits repeat cyclically; applying the cycle for base 80 gives units digit 0.
Mathematics
Number System
Find the next number in the series: 19, 30, 41, 52, 63, ?
A. 85
B. 74
C. 96
D. 63
Correct Answer: B
The common difference is 11. So the next term is 63 + 11 = 74.
Mathematics
Number System
How many integers from 67 to 429, inclusive, are divisible by 7?
A. 61
B. 52
C. 51
D. 53
Correct Answer: B
Count = ⌊429/7⌋ - ⌊(67-1)/7⌋ = 61 - 9 = 52.
Mathematics
Number System
The sum of 3 consecutive integers is 96. What is the middle integer?
A. 32
B. 31
C. 35
D. 33
Correct Answer: A
The middle integer equals the average: 96 ÷ 3 = 32.
Mathematics
Number System
Classify 30/24.
A. Rational
B. Irrational
C. Whole number
D. Prime number
Correct Answer: A
30/24 is a ratio of two integers with a non-zero denominator, so it is rational.
Mathematics
Number System
Find the next term: 8, 17, 32, 53, 80, ?
A. 113
B. 77
C. 149
D. 116
Correct Answer: A
The terms follow 3n² + 5 for consecutive n. For n = 6, the term is 3×6² + 5 = 113.
Mathematics
Number System
What is the greatest multiple of 28 that is less than 4926?
A. 4901
B. 4872
C. 4900
D. 4928
Correct Answer: C
4926 ÷ 28 has integer quotient 175; 28 × 175 = 4900.
Mathematics
Number System
What least number must be subtracted from 3995 so that the result is exactly divisible by 24?
A. 35
B. 10
C. 13
D. 11
Correct Answer: D
The remainder is 11; subtracting the remainder makes the number divisible by 24.
Mathematics
Number System
Find the next term: 30, 67, 128, 219, ?
A. 353
B. 343
C. 199
D. 346
Correct Answer: D
Each term is n³ + 3. Thus the next term is 7³ + 3 = 346.
Mathematics
Number System
What least number must be subtracted from 1641 so that the result is exactly divisible by 23?
A. 8
B. 7
C. 15
D. 31
Correct Answer: A
The remainder is 8; subtracting the remainder makes the number divisible by 23.
Mathematics
Number System
Two positive integers have HCF 12 and LCM 1584. What is their product?
A. 19008
B. 1596
C. 1584
D. 19020
Correct Answer: A
For two positive integers, product = HCF × LCM = 12 × 1584 = 19008.
Mathematics
Number System
What is the greatest positive integer that can divide both 383 and 326 leaving the same remainder?
A. 28
B. 58
C. 57
D. 56
Correct Answer: C
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 383-326 = 57; the greatest possible divisor is 57.
Mathematics
Number System
Find the LCM of 16 and 22.
A. 176
B. 178
C. 352
D. 22
Correct Answer: A
LCM = (16 × 22) ÷ HCF(16,22) = 176.
Mathematics
Number System
Find the next term: 12, 22, 36, 54, 76, ?
A. 102
B. 104
C. 130
D. 74
Correct Answer: A
The terms follow 2n² + 4 for consecutive n. For n = 7, the term is 2×7² + 4 = 102.
Mathematics
Number System
What is the least positive number exactly divisible by 9, 7, and 10?
A. 637
B. 10
C. 630
D. 1260
Correct Answer: C
The required number is LCM(9, 7, 10) = 630.