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Re: M0335
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11 Jul 2019, 07:35
I will keep this one relatively short, writing in a different style from my typical responses. The issue here is that we need to assess whether a certain product, abcd, is even. I am surprised that the problem does not state that we are working with integers, but I guess that is presupposed by the question itself (since decimals or fractions cannot be considered even or odd). The fact that there are four numbers instead of, say, two is irrelevant. All we need to do is consider the basic product relationships between even and odd numbers:
odd x odd = odd (e.g., 1 x 3 = 3) even x even = even (e.g., 2 x 2 = 4) odd x even = even (e.g., 1 x 2 = 2)
If we understand that a product involving four numbers is the same as two sets of a product of two numbers, ([#][#]) x ([#][#]), then the groups would follow the same product relationship outlined above. We just need to keep tabs on how many of the four unknowns are odd or even.
In terms of the two statements, the second one would likely appear simpler than the first to most people, if for no other reason than that statement (1) requires more symbols to interpret. If a = b = c = d, then we can either think in terms of odds or evens, or we can substitute numbers themselves. Keep it simple: an odd is an odd for the purposes of the relationship in the question, so there is no need to choose different numbers.
odd x odd x odd x odd = odd (e.g, 1 x 1 x 1 x 1 = 1) even x even x even x even = even (e.g., 2 x 2 x 2 x 2 = 16)
Clearly, statement (2) is NOT sufficient, yielding one type of answer or another depending on whether the unknowns are odd or even, so we can scrap choices (B) and (D). What about statement (1)? If the sum of the squares of four numbers is 0, then all the numbers have to be 0 itself. Why? First, the complex number i does not appear on the GMAT™you have to understand the rules of the test you are taking. Second, regardless of whether any number is positive or negative, given the previous statement about i, as soon as you square it, it cannot be negative anymore. Before you might say that the calculator tells you that, for instance, 2^2 = 4, consider that the calculator is following the order of operations, taking 2, squaring it, and then applying the negative sign. If you type in the number correctly, as in (2), and square it, you will most definitely get positive 4. Now it should be clear why all the numbers in this problem must be 0, which happens to be an even number. (There is no separate category for 0, in terms of evens or odds.) Statement (1) is sufficient, so (A) is the answer.
