Gmat_mission wrote:Which of the following is not a perfect square?

1. 100856
2. 325137
3. 945729
4. All of these
5. None of these

We know that a perfect square must end with 0, 1, 4, 5, 6, or 9, so we can see choice 2 is not a perfect square.

Now let's check choice 1. Since 310^2 = 96,100 and 320^2 = 102,400, then, if 100,856 is a perfect square, it must be the square of either 314 or 316 since either one of these integers will produce a units digit of 6 when squared. However, since 314^2 = 98,596 and 316^2 = 99,856, we see that choice 1 is a not a perfect square, either.

Since both choices 1 and 2 are not perfect squares, we will conclude that the correct answer must be choice 4 (even though we have not verified that choice 3 is not a perfect square).

Answer: 4