hazelnut01 wrote:x, y, and z are positive integers and x < y < z. If x+y+z is an even number less than 15, is x equal to 2?
1) The product of any two numbers of x, y, and z is an even number.
2) One of x, y, and z is twice the one of the other numbers.
We are given that x, y, and z are all positive integers, that x < y < z, and that x + y + z is an even number less than 15. We need to determine whether x = 2.
If the sum of three integers is even, then either 1) all integers are even or 2) one of them is even and the other two are odd.
Statement One Alone:
The product of any two numbers of x, y, and z is an even number.
Using the information in statement one, we know that at least two of the three numbers, x, y, and z, have to be even numbers. That is, either 1) all three numbers are even or 2) two of them are even and the other is odd. However, it can't be the latter case because in the stem analysis, we see that we cannot have two even integers and one odd integer. Thus all three numbers must be even.
Since the sum of x, y, and z is less than 15, the only even numbers that will work for x, y, and z, respectively, are 2, 4, and 6. Thus, x = 2. Statement one alone is sufficient to answer the question.
Statement Two Alone:
One of x, y, and z is twice the one of the other numbers.
The information in statement two is not sufficient to answer the question. For instance, x = 2, y = 4, and z = 6, or x = 1, y = 2, and z = 3.
Answer:
A
