Test: Prime Numbers- 1


20 Questions MCQ Test Quantitative Aptitude for GMAT | Test: Prime Numbers- 1


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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 and 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 and 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 and 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 and 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 and a prime number?

1) x + y = even

2) x is even

Solution:
QUESTION: 18

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

1) k can be written as 6n + 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:
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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