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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? [#permalink]

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01 Aug 2010, 17:11
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How many perfect squares are less than the integer d?

(1) 23 < d < 33
(2) 27 < d < 37
[Reveal] Spoiler: OA

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Re: How many perfect squares are less than the integer d? [#permalink]

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01 Aug 2010, 17:27
dungtd wrote:
How many perfect squares are less than the integer d?

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

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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Re: How many perfect squares are less than the integer d? [#permalink]

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02 Aug 2010, 07:14
make sense. thks ~! phew.. finally remembered what is a perfect sq.

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Re: How many perfect squares are less than the integer d? [#permalink]

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06 Sep 2014, 00:48
dungtd wrote:
How many perfect squares are less than the integer d?

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

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.

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Re: How many perfect squares are less than the integer d? [#permalink]

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06 Sep 2014, 09:11
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dungtd wrote:
How many perfect squares are less than the integer d?

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

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.

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Re: How many perfect squares are less than the integer d? [#permalink]

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15 Apr 2017, 11:31
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Re: How many perfect squares are less than the integer d?   [#permalink] 15 Apr 2017, 11:31
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