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QUESTION: 1

If *m *and *n *are two different prime numbers, then the least common multiple of the two numbers must equal which one of the following?

Solution:

QUESTION: 2

Is the product of two numbers *x *and *y *a prime number?

1) *x *and *y *are two prime numbers.

2) *x *and *y *are two odd numbers not equal to 1.

Solution:

**Correct Answer :- a**

**Explanation **: The answer should be D. Only the possibility of 2 different numbers multiplying and creating a prime number is when one number is 1 and another is prime itself. Both the statements clear that situation.

QUESTION: 3

How many prime numbers exist between 200 and 220?

Solution:

Odd numbers between 200 and 220 are:

201, 207, 210, 213, 219 are divisible by 3 (because the sum of their digits is divisible by 3).

205, 215 are divisible by 5.

Hence, we have to check just the following numbers: 203, 209, 211 and 217. Now,

203 = 7*29 (Not prime).

209 = 11*19 (Not prime).

211 = Prime

217 = 7*31 (Prime).

So there is only one prime number between 200 and 220.

QUESTION: 4

If x and y are prime numbers, which of the following CANNOT be the sum of x and y?

Solution:

If x = 2 and y = 3 then the sum of these prime numbers is 5..

If x = 2 and y = 7, then sum of these prime numbers 9

If x = 3 and y = 13, then then sum of these prime numbers is 16

But in case of option D there are no two prime numbers that can be added to get 23.

Hence option D is correct.

QUESTION: 5

An integer greater than 1 that is not prime is called composite. If the two-digit integer *n* is greater than 20, is *n* composite?

1) The tens digit of *n* is a factor of the units digit of *n*

2) The tens digit of *n* is 2

Solution:

QUESTION: 6

If *x* is a positive integer, is *x* prime?

1) *x* has the same number of factors as *y2*, where *y* is a positive integer greater than 2.

2) *x* has the same number of factors as *z*, where *z* is a positive integer greater than 2.

Solution:

QUESTION: 7

Which of the following could be the median of a set consisting of 6 different primes?

Solution:

QUESTION: 8

Set A consists of 8 distinct prime numbers. If *x* is equal to the range of set A and *y* is equal to the median of set A, is the product *xy* even? ?

1) The smallest integer in the set is 5.

2) The largest integer in the set is 101. ?

Solution:

QUESTION: 9

If x is an integer, is x! + (x + 1) a prime number?

1) x < 10

2) x is even

Solution:

QUESTION: 10

If *k* is a positive integer. Is *k* a prime number??

1) No integers between "2" and "square root of *k*" inclusive divides *k* evenly

2) No integers between 2 and *k*/2 divides *k* evenly, and *k* is greater than 5.

Solution:

QUESTION: 11

Is the product of three integers *xyz* a prime number?

1) *x = -y*

2) z* = 1 *

Solution:

**Correct Answer :- a**

**Explanation :** xyz will be prime only when x = 1, y = -1, z = -2

or x = -1, y = 1, z = -2

(Sufficient)

if z=1, no other possible values of x and y make a prime product.

QUESTION: 12

If p is a prime number greater than 2, what is the value of p?

1) There are a total of 100 prime numbers between 1 and p + 1

2) There are a total of p prime numbers between 1 and 3912

Solution:

QUESTION: 13

Is the product of two numbers *x *and *y *a prime number?

1) x + y = prime

2) y is not prime

Solution:

**Correct Answer :- d**

**Explanation :** Given: x,y are integers > 0.

is x*y = prime?

prime number = 1*prime.

statement 1:

x = prime - y

possible values of x,y:

(3,1): product is a prime

(4,1):product is not a prime

not sufficient

statement 2:

y ≠≠ prime

nothing is specified about x.

not sufficient

combining both statements,

possible values of x,y:

(3,1): product is a prime

(4,1):product is not a prime

QUESTION: 14

Is the product of two numbers *x *and *y *a prime number?

1) x - y = prime

2) y is not prime

Solution:

**Correct Answer :- d**

**Explanation :** Given: x,y are integers > 0.

is x*y = prime?

prime number = 1*prime.

statement 1:

x = prime + y

possible values of x,y:

(3,1): product is a prime

(4,1):product is not a prime

not sufficient

statement 2:

y ≠≠ prime

nothing is specified about x.

not sufficient

combining both statements,

possible values of x,y:

(3,1): product is a prime

(4,1):product is not a prime

QUESTION: 15

Is the product of two numbers *x *and *y *a prime number?

1) x/y = prime

2) x and y are consecutive integers

Solution:

**Correct Answer :- b**

**Explanation : **Both the statements are required to answer the question.

Because it is given x and y are consecutive integers

Let x = 2, y = 1

When dividing x/y = 2/1

= 2(prime).

QUESTION: 16

Is the product of two numbers *x *and *y *a prime number?

1) x is even

2) y is odd

Solution:

**Correct Answer :- d**

**Explanation : **Given: x,y are integers > 0.

is x*y = prime?

prime number = 1*prime.

statement 1:

x is even

possible values of x,y:

(1,2): product is a prime

(1,4):product is not a prime

not sufficient

statement 2:

y is odd

nothing is specified about x.

not sufficient

combining both statements,

possible values of x,y:

(3,1): product is a prime

(4,1):product is not a prime

QUESTION: 17

Is the product of two numbers *x *and *y *a prime number?

1) x + y = even

2) x is even

Solution:

**Correct Answer :- B**

**Explanation :** 1) x + y = even

If x=2, y=2, xy=4 which is not prime

If x=1, y=3, xy=3 which is prime

1 is not sufficient

(2) x is even

If x=2, y=2, xy=4 which is not prime

If x=2, y=1, xy=2 which is prime

2 is not sufficient

(1)+(2)

x+y=even and x=even

So y=even

xy=even*even which must be divisible by 4 and so xy is not prime

(1)+(2) is sufficient

QUESTION: 18

If *k* is a positive integer, is *k* a prime number??

1) *k* can be written as 6*n* + 1, where *n* is a positive integer.

2) k > 4!

Solution:

QUESTION: 19

If *k* is a positive integer, is *k* a prime number?

1) *k* is the sum of three consecutive prime numbers

2) *k* has only 2 factors

Solution:

Statement 1: k is the sum of three consecutive prime numbers

2 + 3 + 5 = 10, which is not a prime number.

11 + 13 + 17 = 41, which is a prime number.

Therefore Statement 1 Alone is Insufficient. Answer options could be B, C or E

Statement 2: k has only 2 positive factors

If k has only 2 positive factors, then they have to be 1 and k itself, which is the definition of a prime number. k is a prime number.

Therefore Statement 2 Alone is Sufficient.

QUESTION: 20

Is the integer *x* a prime number?

1) * x + 1 * is prime

2) x* + 2 *is not prime

Solution:

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