If x is a positive integer, is the greatest common factor of 150 and x

Question

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

sashiim20 · Answer

(1) x is a prime number.

If x = 2. Greatest common factor of 150 and 2 = 2 ----- (Prime number)

If x = 7. Greatest common factor of 150 and 7 = 1 ------ (Not a Prime number)

I is Not Sufficient.

(2) x < 4

x could be 1 , 2 or 3.

If x = 1. Greatest common factor of 150 and 1 = 1 ------ (Not a Prime number)

If x = 2. Greatest common factor of 150 and 2 = 2 ----- (Prime number)

II is Not Sufficient.

Combining (1) and (2) we get x has to be prime number and less than 4. Therefore x could be 2 or 3.

If x = 2. Greatest common factor of 150 and 2 = 2 ----- (Prime number)

If x = 3. Greatest common factor of 150 and 3 = 3 ----- (Prime number)

I and II together are Sufficient. Answer (C)...

pushpitkc · Answer

150, when prime factorized, 2 * 3 * 5^2. 
The GCF of 2 numbers is the greatest number which divides the 2 numbers.

(1) x is a prime number.
If x is a prime number (2,3 or 5), the GCF of the 2 numbers is the same prime number(which is x)
However, having a prime number greater than 5, will have a GCF of 1. 
We cannot determine, if the GCF is indeed a prime number. Insufficient.

(2) x < 4
If x=1, the GCF is 1. If x=2,3 the GCF is a prime number. Insufficient.

However, on combining the information, the only numbers we need to test are x=2 or 3.
For both these numbers the GCF is prime always. Sufficient(Option C)

harikrish · Answer

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

Solution:

Given: xis a positive integer, x>0.

Statement 1: 
Case 1: If x=2. The G.C.F of 150 and 2 is 2, a prime number.
Case 2: If x=11. The G.C.F of 150 and 11 is 1, not a prime number.
Therefore this statement is insufficient.

Statement 2: 
Case 1: If x=2.The G.C.F of 150 and 2 is 2, a prime number.
Case 2:If x=1. The G.C.F of 150 and 1 is 1, not a prime number.

Therefore combining Statements 1 and Statement 2,
The Only possible values of x are 2 & 3. In either of the cases the G.C.F is a prime number.

Therefore the answer is Option C.

Luckisnoexcuse · Answer

For the GCF of 150 and x to be prime x has to be a prime with no repetition in 150 (2 or 3 but not 5)
Prime Factors of 150 = 2, 3, 5 (2*3*5*5)

(1) x is a prime number...not sufficient

(2) x<4 Not sufficient as x can be 1 which is not a prime number while 2,3 are prime number

On combining both only 2,3 satisfy and hence the question can be answered

C

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If x is a positive integer, is the greatest common factor of 150 and x

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