Question 1
Question
If n = 4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?
Question 2
Question
For positive integers x and y, which of the following can be written as y^2?
Answer

(x+1)!

(x+9)!

x^29

x^2+1

(x+1)^2)!

I Don't Know
Question 3
Question
What are the last two digits of (301*402*503*604*646*547*448*349)^2 ?
Answer

96

76

56

36

16

I don't know
Question 4
Question
A set of five positive integers has an arithmetic mean of 150. A particular number among the five exceeds another by 100. The rest of the three numbers lie between these two numbers and are equal. How many different values can the largest number among the five take?
Answer

18

19

21

42

59

I don't know
Question 5
Question
Integer x is equal to the product of all even numbers from 2 to 60, inclusive. If y is the smallest prime number that is also a factor of x1, then which of the following expressions must be true?
Answer

0<y<4

4<y<10

10<y<20

20<y<30

y>30

I don't know
Question 6
Question
s(n) is a ndigit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits are in s(99)?
Answer

350

353

354

356

357

I don't know
Question 7
Question
If x is an odd negative integer and y is an even integer, which of the following statements must be true?
I. (3x  2y) is odd
II. xy^2 is an even negative integer
III. (y^2  x) is an odd negative integer
Answer

I only

II only

I and II

I and III

II and III

I don't Know
Question 8
Question
A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 5 is
Answer

3

7

21

27

189

I don't know
Question 9
Question
The integer K is positive, but less than 400. If 21K is a multiple of 180, how many unique prime factors does K have?
Question 10
Question
How many positive even integers less than 100 contain digits 4 or 7?
Answer

16

17

18

19

20

I don't know
Question 11
Question
Two integers x and y are chosen without replacement out of the set {1, 2, 3,......, 10}. Then the probability that x^y is a single digit number.
Answer

11/90

13/90

17/90

19/90

23/90

I don't know
Question 12
Question
How many positive integers less than 20 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3?
Answer

14

13

12

11

10

I don't know
Question 13
Question
How many prime numbers exist between 200 and 220?
Question 14
Question
If 3 < x < 100, for how many values of x is x/3 the square of a prime number?
Question 15
Question
An integer between 1 and 300, inclusive, is chosen at random. What is the probability that the integer so chosen equals an integer raised to an exponent that is an integer greater than 1?
Answer

17/300

1/15

2/25

1/10

3/25

I don't know
Question 16
Question
If two integers are chosen at random out of the set {2, 5, 7, 8}, what is the probability that their product will be of the form a^2 – b^2, where a and b are both positive integers?
Answer

2/3

1/2

1/3

1/4

1/6

I don't know
Question 17
Question
Consider a sequence of numbers given by the expression 5 + (n  1) * 3, where n runs from 1 to 85. How many of these numbers are divisible by 7?
Question 18
Question
If x/(11p) is an odd prime number, where x is a positive integer and p is a prime number, what is the least value of x?
Answer

22

33

44

66

99

I don't know
Question 19
Question
When a certain perfect square is increased by 148, the result is another perfect square. What is the value of the original perfect square?
Answer

1296

1369

1681

1764

2500

I don't know
Question 20
Question
If, for all positive integer values of n, P(n) is defined as the sum of the smallest n prime numbers, then which of the following quantities are odd integers?
I. P(10)
II. P(P(10))
III. P(P(P(10)))
Answer

I only

I & II only

I & III only

II & III only

I, II & III

I don't know