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
Prime numbers
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x is a positive integer, GCD of 150 and x a prime numberDarshan.D wrote: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)
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.