dungtd wrote:

How many perfect squares are less than the integer d?

(1) 23 < d < 33

(2) 27 < d < 37

Please explain! Thanks a lot!

A perfect square is a number which is the square of an integer, so 0, 1, 4, 9, 16, 25, etc... are all perfect squares.

Using Statement 1 alone, d might be greater than 25, in which case the six perfect squares from 0 to 25 are all less than d. However, d might be 24 or 25, in which case only five perfect squares (0 through 16) are strictly less than d. So Statement 1 is not sufficient.

Statement 2, on the other hand, is sufficient; no matter what the value of d, we have exactly six perfect squares less than d, the squares from 0 to 25. Even if you make d as large as possible -- that is, you make d=36 (we know d is an integer, so if d < 37, then d can be at most 36) -- then only the squares up to 25 are strictly less than d.

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