Hi, there. I'm happy to help with this.

Prompt: if y is an integer , is y^2 divisible by 4?

Fact #1: In order for an integer N to be divisible by 4, N must have at least two factors of 2 in its prime factorization.

Fact #2: When you square a number, say T^2, whatever prime factors are in the prime factorization of T are

doubled in the prime factorization of T^2. Say a particular prime factor appears three times in T --- then it will appear six times in T^2.

Fact #3: An even number, by definition, has at least one factor of 2 in its prime factorization.

Therefore, the square of any even number will have at least two factors of 2, and therefore will be divisible by 4.

The question "is y^2 divisible by 4?" is entirely equivalent to the question "is y an even integer?"

All of that was the mathematical heavy-lifting for the question. Now, the statements will be a piece of cake.

Statement #1: y is divisible by 4. Therefore y is even.

Sufficient.

Statement #2: y is divisible by 6. Therefore y is even.

Sufficient.

Both statements sufficient. Answer =

DDoes all that make sense?

Here's another odd/even DS question for practice.

http://gmat.magoosh.com/questions/868Please let me know if you have any questions.

Mike

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Mike McGarry

Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)