## How many perfect squares are less than the integer $$d$$?

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### How many perfect squares are less than the integer $$d$$?

by BTGmoderatorLU » Wed May 08, 2019 1:34 pm

00:00

A

B

C

D

E

## Global Stats

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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by ceilidh.erickson » Thu May 16, 2019 10:46 am

00:00

A

B

C

D

E

## Global Stats

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.