Bunuel wrote:
If y is an integer, is y^2 divisible by 4?
(1) y is even.
(2) y^3 is divisible by 4.
Kudos for a correct solution.
VERITAS PREP OFFICIAL SOLUTION:Question Type: Yes/No. This question asks: “Is y^2 divisible by 4.”
Given information in the question stem or diagram: y is an integer.
Statement 1: y is even. With a conceptual understanding of factors, you know that if y is an even number then y^2 will have to be a multiple of 4. If you want to quickly test this you can use some small even numbers. For example, if y = 2, then y^2=4; yes, that is divisible by 4. If y = 4, then y^2 = 16; this is also divisible by 4. Even 0, which is an even number, will work. 0^2 = 0; and yes, 0 is divisible by 4. This confirms what we already knew from our conceptual understanding: an even
number when squared is a multiple of 4. The answer is either A or D.
Statement 2: y^3 is divisible by 4. For some, this may not seem sufficient at first glance. y^3 might be divisible by 4 while y^2 is not. For example, y could be the cube root of 4. However, if you leverage properly the information in the question stem (always so important!) then you know that “y is an integer.” So y cannot be the cube root of 4; it must be an integer. Once you have established that y must be an integer then the only way for y^3 to be divisible by 4 is for y to be an even number. In other words, it gives you the same information that you already found sufficient in Statement 1. Thus,
the correct answer is D.
Note: This is another good example of “When one statement is easy, the other is hard/counterintuitive.” The first statement is relatively simple so you should be extra careful analyzing the second statement. As is often the case, the key with Statement 2 is to make sure you properly leverage the given information.