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Test: Prime Numbers- 1


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

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Test: Prime Numbers- 1 - 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? 

Detailed Solution for Test: Prime Numbers- 1 - Question 1

One of the great things about Integer Properties questions if that we can often solve them by finding values that satisfy the given condition.

And this question to given condition is: m and n are two different prime numbers
So, it COULD be the case that m = 2 and n = 3
If m = 2 and n = 3, then the least common multiple of m and n is 6 (since 6 is the least common multiple of 2 and 3)

Now we can plug m = 2 and n = 3 into each answer choice to see which one yields an output of 6

A) mn = (2)(3) = 6. KEEP!
B) m + n = 2 + 3 = 5. No good. We want an output of 6.
C) m - n = 2 - 3 = -1. No good. We want an output of 6.
D) m + mn = 2 + (2)(3) = 8. No good. We want an output of 6.

By the process of elimination, the correct answer must be A

Test: Prime Numbers- 1 - 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. 

Detailed Solution for Test: Prime Numbers- 1 - Question 2

Correct Answer :- a

Explanation : The answer should be A. 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.

Test: Prime Numbers- 1 - Question 3

How many prime numbers exist between 200 and 220? 

Detailed Solution for Test: Prime Numbers- 1 - Question 3

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.

Test: Prime Numbers- 1 - Question 4

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

Detailed Solution for Test: Prime Numbers- 1 - Question 4

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.

Test: Prime Numbers- 1 - 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

Detailed Solution for Test: Prime Numbers- 1 - Question 5

Test: Prime Numbers- 1 - 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.

Detailed Solution for Test: Prime Numbers- 1 - Question 6

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

y2 is a perfect square. The number of distinct factors of a positive perfect square is ALWAYS ODD, while the number of factors of a prime is two (1 and itself). Thus since x has the same number of factors as a perfect square it cannot be a prime. Sufficient.

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

Test: Prime Numbers- 1 - Question 7

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

Test: Prime Numbers- 1 - 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. ?

Test: Prime Numbers- 1 - Question 9

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

1) x < 10

2) x is even

Test: Prime Numbers- 1 - 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. 

Test: Prime Numbers- 1 - Question 11

Is the product of three integers xyz a prime number?

1) x = -y

2) z = 1 

Detailed Solution for Test: Prime Numbers- 1 - Question 11

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.

Test: Prime Numbers- 1 - 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

Test: Prime Numbers- 1 - Question 13

Is the product of two numbers and a prime number?

1) x + y = prime

2) y is not prime

Detailed Solution for Test: Prime Numbers- 1 - Question 13

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

Test: Prime Numbers- 1 - Question 14

Is the product of two numbers and a prime number?

1) x - y = prime

2) y is not prime

Detailed Solution for Test: Prime Numbers- 1 - Question 14

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

Test: Prime Numbers- 1 - Question 15

Is the product of two numbers and a prime number?

1) x/y = prime

2) x and y are consecutive integers

Detailed Solution for Test: Prime Numbers- 1 - Question 15

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).

Test: Prime Numbers- 1 - Question 16

Is the product of two numbers and a prime number?

1) x is even

2) y is odd

Detailed Solution for Test: Prime Numbers- 1 - Question 16

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

Test: Prime Numbers- 1 - Question 17

Is the product of two numbers and a prime number?

1) x + y = even

2) x is even

Detailed Solution for Test: Prime Numbers- 1 - Question 17

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

Test: Prime Numbers- 1 - 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!

Test: Prime Numbers- 1 - 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

Detailed Solution for Test: Prime Numbers- 1 - Question 19

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.

Test: Prime Numbers- 1 - Question 20

Is the integer x a prime number?

1)  x + 1  is prime

2) x + 2 is not prime

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