How many perfect squares are less than the integer d?

Question

(1) 23 < d < 33 
(2) 27 < d < 37

IanStewart · Answer

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.

ohfred · Answer

make sense. thks ~! phew.. finally remembered what is a perfect sq.

luckyme17187 · Answer

1. d is between 24 & 32 .. if d is 31 then 25, 16, 9, 4,1,0 are smaller than this. If d is 24 then different story. Not suff.

2. d is between 28 and 36 .. if d is 36 or less than that at max it could be 28 hence 25, 16, 9, 4,1,0 less that interval . we could able to get the exact count.

Hence B.

Bunuel · Answer

How many perfect squares are less than the integer d? First of all: a perfect square is a number which is the square of an integer. So, perfect squares are: 0 =0^2, 1 =1^2, 4 =2^2, 9 =3^2, ... (1) 23 < d < 33 --> if d>25 (for example 26, 27, ...) then there will be 6 perfect square less then d: 0, 1, 4, 9, 16, and 25 BUT if d\leq25 (for example 25 or 24) then there will be only 5 perfect square less then d: 0, 1, 4, 9, and 16. Not sufficient. (2) 27 < d < 37 --> no matter what the value of d is there will be 6 perfect square less then d: 0, 1, 4, 9, 16, and 25 (even for max and min values of d). Sufficient. Answer: B.

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How many perfect squares are less than the integer d?

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How many perfect squares are less than the integer d?

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