Prime numbers

[Darshan.D]

I] If x is a positive integer, is the greatest common factor of 150 and x a prime number?

1. x is a prime number

2. x < 4

(Correct answer is C - Both statements together are sufficient)

II] If P is a set of integers and 3 is in P, is every positive multiple of 3 in P?

1. For any integer in P, the sum of 3 & that integer is also in P

2. For any integer in P, that integer minus 3 is also in P

(Correct answer is A)

Kindly give detailed explanation

Thanks in advance

[parallel_chase]

I] If x is a positive integer, is the greatest common factor of 150 and x a prime number?

1. x is a prime number

2. x < 4

(Correct answer is C - Both statements together are sufficient)

x is a positive integer, GCD of 150 and x a prime number

150 = 2*5*5*3

Statement I

x is prime number, x could be 5,3,2 or x could be 17,13,11

Insufficient.

Statement II

x<4

x could be 1,2,3

Insufficient.

Combining I & II
x is a prime number
x<4

x could be 2 or 3

GCD of 150 and x can either be 2 or 3, in both cases its a prime number.

Sufficient.

Hence C is the answer.

II] If P is a set of integers and 3 is in P, is every positive multiple of 3 in P?

1. For any integer in P, the sum of 3 & that integer is also in P

2. For any integer in P, that integer minus 3 is also in P

(Correct answer is A)

Kindly give detailed explanation

Thanks in advance

Set P = 3 at least

Statement I

Set P = 3+3 = 6, 6+3 = 9, therefore it consists of every POSITIVE multiple of 3.

Sufficient.

Statement II

Set P = 6-3 = 3, 3-3 =0, 0-3 = -3

This set consists of NEGATIVE, POSITIVE and 0 (not negative and not positive) multiples of 3.

Insufficient.

Hence A is the answer.

Hope this helps.