enigma123 wrote:
Can the positive integer x be expressed as the product of two integers, each of which is greater than 1?
(1) x is a multiple of 2
(2) x is a multiple of 6
Guys - pretty straight question by the looks of it and as far as I am concerned the answer should be E. But this is not the case. below is my solution. Can someone please help?
Statement 1 : x is a multiple of 2
X = 2, 2 * 1. No. Both integers are not greater than 1
X = 4, 2 * 2 yes. Both integers are greater than 1.
2 different answers ---- therefore this statement is insufficient.
Statement 2: x is a multiple of 6
x = 6, 1* 6. No. Both integers are not greater than 1.
x = 12, 2*6 Yes. Both integers are greater than 1.
2 different answers ---- therefore this statement is insufficient.
Combining the 2 statements
x is a multiple of 2 and 6
x = 6 = 1*6 or 2 * 3
x= 12 = 1* 12 or 2*6
Again two different solutions and therefore the answer should be E.
Its from Edvento, the question bank from
e-gmat.
Can the positive integer x be expressed as the product of two integers, each of which is greater than 1?If the positive integer x cannot be expressed as the product of two integers, each of which is greater than 1, then it simply means that p is a prime number. So, basically question asks whether p is a prime number.
(1) x is a multiple of 2. If x=2, then we CANNOT express x as the product of two integers, each of which is greater than 1 but if x is 6, then we CAN as the product of two integers, each of which is greater than 1: 6=2*3. Not sufficient.
OR: we know that the question basically asks whether x is a prime. x from this statement can be a prime (2) as well as non-prime (4). Not sufficient.
(2) x is a multiple of 6. x can be 6, 12, 18, 24, ... x has at least two primes 2 and 3. In any case x CAN be expressed as the product of two integers, each of which is greater than 1. For example, if 6=2*3, 12=3*4, 18=2*9, 24=2*12, ... Sufficient.
OR: we know that the question basically asks whether x is a prime. x from this statement cannot be a prime. Sufficient.
Answer: B.
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