If x is a positive integer, then is x prime?
(1) 3x + 1 is prime
(2) 5x + 1 is prime
E
OG If x is a positive integer, then is x prime?
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Given: x is a positive integerAbeNeedsAnswers wrote:If x is a positive integer, then is x prime?
(1) 3x + 1 is prime
(2) 5x + 1 is prime
E
To find out: is x prime?
Statement 1: 3x + 1 is prime
Since x is a positive integer, the minimum value of x = 1, thus the minimum value of 3x + 1 = 3*1 + 1 = 4, but '4' is non-prime, thus x = 1 is not a valid value.
Let's try with x = 2, then 3x = 1 = 3*2 + 1 = 7, a prime number. So, if x = 2, then x is prime.
We know that all the prime numbers except 2 are odd, thus, 3x + 1 = Odd.
3x + 1 = Odd
3x = Odd - 1 = Odd - Odd = Even
x = Even / 3 = Even / Odd = Even (since x is a positve integer);
Note that if an even integer is completely divisible by an odd integer, the quotient is even.
So, we have x = Even
If x = 2, the answer is Yes; however, if x ≠2, the answer is No. Insufficient.
Statement 2: 5x + 1 is prime
At x = 2, we see that 5x + 1 = 5*2 + 1 = 11, a prime number, so if x = 2, the answer is yes.
As discussed in Statement 1, we know that all the prime numbers except 2 are odd, thus, 5x + 1 = Odd.
5x + 1 = Odd
5x = Odd - 1 = Odd - Odd = Even
x = Even / 5 = Even / Odd = Even (since x is a positve integer);
So, we have x = Even
If x = 2, the answer is Yes; however, if x ≠2, the answer is No. Insufficient.
Statement 1 & 2:
x = 2, implying x is prime, and x = other even integers are applicable in both the statements, thus there is no unique answer. Insufficient.
The correct answer: E
Hope this helps!
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We are given that x is a positive integer and must determine whether x is prime.AbeNeedsAnswers wrote:If x is a positive integer, then is x prime?
(1) 3x + 1 is prime
(2) 5x + 1 is prime
Statement One Alone:
3x + 1 is prime.
Using the information in statement one, x does not necessarily have to be prime. For instance, if x = 2, then 3x + 1 = 7 is prime, or if x = 4, then 3x + 1 = 13 is prime. In the former case, x = 2 is prime; however, in the latter case, x = 4 is not prime. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
5x + 1 is prime.
Using the information in statement two, x does not necessarily have to be prime. For instance, if x = 2, then 5x + 1 = 11 is prime, or if x = 6, then 5x + 1 = 31 is prime. In the former case, x = 2 is prime; however, in the latter case, x = 6 is not prime. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.
Statements One and Two Together:
Using the information from statements one and two, we still cannot determine whether x is prime. For instance, if x = 2, then both 3x +1 = 7 and 5x + 1 = 11 are prime, or if x = 12, then both 3x + 1 = 37 and 5x + 1 = 61 are prime. In the former case, x = 2 is prime; however, in the latter case, x = 12 is not prime.
Answer: E
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Hi All,
We're told that X is a positive integer. We're asked if X is PRIME. This is a YES/NO question and can be solved by TESTing VALUES.
1) (3X + 1) is PRIME
IF.... X=2, then (3X+1) = 7 and the answer to the question is YES
IF.... X=6, then (3X+1) = 19 and the answer to the question is NO
Fact 1 is INSUFFICIENT
2) 5X + 1 is prime
IF.... X=2, then (5X+1) = 11 and the answer to the question is YES
IF.... X=6, then (5X+1) = 31 and the answer to the question is NO
Fact 2 is INSUFFICIENT
Combined, we already have two values for X that 'fit' both Facts and produce different answers (one "YES" and on "NO").
Combined, INSUFFICIENT
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
We're told that X is a positive integer. We're asked if X is PRIME. This is a YES/NO question and can be solved by TESTing VALUES.
1) (3X + 1) is PRIME
IF.... X=2, then (3X+1) = 7 and the answer to the question is YES
IF.... X=6, then (3X+1) = 19 and the answer to the question is NO
Fact 1 is INSUFFICIENT
2) 5X + 1 is prime
IF.... X=2, then (5X+1) = 11 and the answer to the question is YES
IF.... X=6, then (5X+1) = 31 and the answer to the question is NO
Fact 2 is INSUFFICIENT
Combined, we already have two values for X that 'fit' both Facts and produce different answers (one "YES" and on "NO").
Combined, INSUFFICIENT
Final Answer: E
GMAT assassins aren't born, they're made,
Rich