Mathematics
Number System
How many integers from 37 to 254, inclusive, are divisible by 4?
A. 54
B. 53
C. 63
D. 55
Correct Answer: A
Count = ⌊254/4⌋ - ⌊(37-1)/4⌋ = 63 - 9 = 54.
Mathematics
Number System
Find the next number: 20, 25, 33, 44, 58, ?
A. 75
B. 63
C. 78
D. 72
Correct Answer: A
The differences are 5, 8, 11, 14, increasing by 3. The next difference is 17, so the answer is 75.
Mathematics
Number System
Find the next number in the alternating series: 7, 34, 9, 31, 11, 28, ?
A. 13
B. 15
C. 11
D. 25
Correct Answer: A
Odd-position terms are 7, 9, 11, ... with difference 2. Hence the next odd-position term is 13.
Mathematics
Number System
How many trailing zeros are there in 75! ?
A. 18
B. 7
C. 17
D. 19
Correct Answer: A
Trailing zeros = ⌊75/5⌋ + ⌊75/25⌋ + ... = 15 + 3 = 18.
Mathematics
Number System
A two-digit number is 34. What is the absolute difference between the number and the number formed by reversing its digits?
A. 18
B. 0
C. 1
D. 9
Correct Answer: D
Reversed number = 43. Absolute difference = |34 - 43| = 9.
Mathematics
Number System
Find the next number in the alternating series: 28, 23, 33, 15, 38, 7, ?
A. 43
B. -1
C. 48
D. 38
Correct Answer: A
Odd-position terms are 28, 33, 38, ... with difference 5. Hence the next odd-position term is 43.
Mathematics
Number System
Find the next number: 5, 9, 18, 34, 59, ?
A. 89
B. 95
C. 84
D. 101
Correct Answer: B
The increments are consecutive squares: 4, 9, 16, 25; next add 6² = 36. So the answer is 95.
Mathematics
Number System
Classify 25/15.
A. Irrational
B. Rational
C. Whole number
D. Prime number
Correct Answer: B
25/15 is a ratio of two integers with a non-zero denominator, so it is rational.
Mathematics
Number System
Find the missing number: 40, 51, ?, 73, 84, 95
A. 62
B. 84
C. 73
D. 51
Correct Answer: A
This is an arithmetic series with common difference 11; the missing term is 62.
Mathematics
Number System
What least number must be subtracted from 801 so that the result is exactly divisible by 15?
A. 6
B. 5
C. 9
D. 21
Correct Answer: A
The remainder is 6; subtracting the remainder makes the number divisible by 15.
Mathematics
Number System
Two positive integers have HCF 12 and LCM 780. What is their product?
A. 792
B. 780
C. 9360
D. 9372
Correct Answer: C
For two positive integers, product = HCF × LCM = 12 × 780 = 9360.
Mathematics
Number System
Find the missing number: 13, 18, 23, 28, ?, 38
A. 38
B. 43
C. 28
D. 33
Correct Answer: D
This is an arithmetic series with common difference 5; the missing term is 33.
Mathematics
Number System
What is the remainder when 2284 is divided by 20?
A. 4
B. 7
C. 6
D. 5
Correct Answer: A
2284 = 20 × 114 + 4; therefore the remainder is 4.
Mathematics
Number System
Find the next number in the series: 37, 41, 45, 49, 53, ?
A. 65
B. 61
C. 57
D. 53
Correct Answer: C
The common difference is 4. So the next term is 53 + 4 = 57.
Mathematics
Number System
Find the next number in the series: 2, 4, 8, 16, 32, ?
A. 64
B. 34
C. 32
D. 66
Correct Answer: A
Each term is multiplied by 2. Therefore 32 × 2 = 64.
Mathematics
Number System
Find the HCF (GCD) of 80 and 224.
A. 17
B. 8
C. 16
D. 32
Correct Answer: C
The greatest common divisor of 80 and 224 is 16.
Mathematics
Number System
What is the greatest positive integer that can divide both 482 and 407 leaving the same remainder?
A. 75
B. 37
C. 76
D. 74
Correct Answer: A
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 482-407 = 75; the greatest possible divisor is 75.
Mathematics
Number System
What digit x makes the number 849x divisible by 9?
A. 7
B. 9
C. 6
D. 1
Correct Answer: C
A number is divisible by 9 when its digit sum is divisible by 9. Thus 8+4+9+x must be a multiple of 9, giving x = 6.
Mathematics
Number System
The sum of 4 consecutive integers is 162. What is the smallest integer?
A. 38
B. 43
C. 40
D. 39
Correct Answer: D
Let the integers be n, n+1, ..., n+3. Their sum is 162; solving gives n = 39.
Mathematics
Number System
What least number must be subtracted from 2630 so that the result is exactly divisible by 17?
A. 29
B. 5
C. 11
D. 12
Correct Answer: D
The remainder is 12; subtracting the remainder makes the number divisible by 17.