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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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Source: Princeton Review

How many perfect squares are less than the integer d?

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

The OA is B

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The best way to approach this problem is to test cases:

How many perfect squares are less than the integer d?

1) 23 < d < 33
if d = 32, there are 5 perfect squares less than d: 1, 4, 9, 16, 25
if d = 24, there are 4 perfect squares less than d: 1, 4, 9, 16
Insufficient

2) 27 < d < 37
if d = 36, there are 5 perfect squares less than d: 1, 4, 9, 16, 25. Be careful! We can't actually count 36 itself, because we're looking for "less than d"
if d = 28, there are 5 perfect squares less than d: 1, 4, 9, 16, 25
Since we get a result of 5 for any integer in this range, this statement is sufficient.

The answer is B.

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