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How many perfect squares are less than the integer d?

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Tue Oct 08, 2019 10:07 pm
BTGmoderatorDC wrote:How many perfect squares are less than the integer d?

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

OA B

Source: Princeton Review
Let's take each statement one by one.

(1) 23 < d < 33

=> d is one among 24, 25, 26, 27, 28, 29, 30 31, and 32.

There's only one perfect square (25) between 24 and 32, inclusive.

Case 1: Say 24 ≤ d ≤ 25. Then the answer is no. No perfect square is less than d.
Case 2: Say 26 ≤ d ≤ 32. Then the answer is ONE (25). One perfect square (25) is less than d.

No unique answer. Insufficient.

(2) 27 < d < 37

=> d is one among 28, 29, 30 31, 32, 33, 34, 35, and 36.

There's only one perfect square (36) between 28 and 36, inclusive.

Case 1: Say 28 ≤ d ≤ 35. Then the answer is no. No perfect square is less than d.
Case 2: Say d = 36. Then the answer is still no since 36 is not greater than 36.

Unique answer. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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