Mathematics
Number System
What digit x makes the number 402x divisible by 9?
A. 8
B. 6
C. 4
D. 3
Correct Answer: D
A number is divisible by 9 when its digit sum is divisible by 9. Thus 4+0+2+x must be a multiple of 9, giving x = 3.
Mathematics
Number System
A two-digit number is 40. What is the absolute difference between the number and the number formed by reversing its digits?
A. 45
B. 36
C. 27
D. 4
Correct Answer: B
Reversed number = 4. Absolute difference = |40 - 4| = 36.
Mathematics
Number System
Find the next number in the alternating series: 19, 36, 24, 41, 29, 46, ?
A. 29
B. 34
C. 39
D. 51
Correct Answer: B
Odd-position terms are 19, 24, 29, ... with difference 5. Hence the next odd-position term is 34.
Mathematics
Number System
The sum of 4 consecutive integers is 170. What is the smallest integer?
A. 41
B. 40
C. 42
D. 45
Correct Answer: A
Let the integers be n, n+1, ..., n+3. Their sum is 170; solving gives n = 41.
Mathematics
Number System
Classify √23.
A. Prime number
B. Irrational
C. Rational
D. Whole number
Correct Answer: B
23 is not a perfect square, so √23 is irrational.
Mathematics
Number System
Find the next number in the series: 40, 47, 54, 61, 68, ?
A. 68
B. 82
C. 89
D. 75
Correct Answer: D
The common difference is 7. So the next term is 68 + 7 = 75.
Mathematics
Number System
How is the integer 53 classified?
A. Prime
B. Neither prime nor composite
C. Composite
D. Irrational
Correct Answer: A
53 has exactly two positive divisors, 1 and 53; therefore it is prime.
Mathematics
Number System
Find the missing number: 75, 89, 103, 117, ?, 145
A. 117
B. 145
C. 159
D. 131
Correct Answer: D
This is an arithmetic series with common difference 14; the missing term is 131.
Mathematics
Number System
How many integers from 73 to 370, inclusive, are divisible by 7?
A. 42
B. 43
C. 52
D. 41
Correct Answer: A
Count = ⌊370/7⌋ - ⌊(73-1)/7⌋ = 52 - 10 = 42.
Mathematics
Number System
Find the missing number: 16, 19, ?, 25, 28, 31
A. 19
B. 28
C. 25
D. 22
Correct Answer: D
This is an arithmetic series with common difference 3; the missing term is 22.
Mathematics
Number System
Find the next term: 35, 72, 133, 224, ?
A. 358
B. 351
C. 204
D. 343
Correct Answer: B
Each term is n³ + 8. Thus the next term is 7³ + 8 = 351.
Mathematics
Number System
What is the remainder when 310 is divided by 7?
A. 3
B. 5
C. 4
D. 2
Correct Answer: D
310 = 7 × 44 + 2; therefore the remainder is 2.
Mathematics
Number System
Find the next number: 1, 7, 25, 79, 241, ?
A. 731
B. 724
C. 723
D. 727
Correct Answer: D
Each term is obtained by ×3 + 4. So 241 × 3 + 4 = 727.
Mathematics
Number System
What least positive number must be added to 915 so that the result is divisible by 15?
A. 15
B. 30
C. 0
D. 1
Correct Answer: A
915 is already divisible by 15; the least positive addition preserving divisibility is 15.
Mathematics
Number System
What is the remainder when 1043 is divided by 7?
A. 2
B. 0
C. 1
D. 3
Correct Answer: B
1043 = 7 × 149 + 0; therefore the remainder is 0.
Mathematics
Number System
Classify 34/4.
A. Irrational
B. Whole number
C. Prime number
D. Rational
Correct Answer: D
34/4 is a ratio of two integers with a non-zero denominator, so it is rational.
Mathematics
Number System
Find the next term: 15, 30, 51, 78, 111, ?
A. 150
B. 153
C. 192
D. 108
Correct Answer: A
The terms follow 3n² + 3 for consecutive n. For n = 7, the term is 3×7² + 3 = 150.
Mathematics
Number System
How is the integer 79 classified?
A. Composite
B. Neither prime nor composite
C. Prime
D. Irrational
Correct Answer: C
79 has exactly two positive divisors, 1 and 79; therefore it is prime.
Mathematics
Number System
Find the next term: 23, 43, 71, 107, 151, ?
A. 207
B. 203
C. 259
D. 147
Correct Answer: B
The terms follow 4n² + 7 for consecutive n. For n = 7, the term is 4×7² + 7 = 203.
Mathematics
Number System
How many integers from 61 to 337, inclusive, are divisible by 15?
A. 18
B. 17
C. 19
D. 22
Correct Answer: A
Count = ⌊337/15⌋ - ⌊(61-1)/15⌋ = 22 - 4 = 18.