Free Practice Question

PS · Problem Solving

705-805

Functions

[x] is the greatest integer less than or equal to the real number x. How many natural numbers n satisfy the equation $[\sqrt{n}] = 17$ ?

Answer Choices

Correct answer marked below

A

17

B

34

35

Correct

D

36

E

38

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Explanation

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Official Explanation

Official

From above we have that

17 \leq \sqrt{n} < 18

Square:

289 \leq n < 324

.…

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What this question tests

What it tests

Your ability to evaluate and compose functions, including unusual defined operations.

Common trap

Applying function operations in the wrong order or ignoring domain restrictions.

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[x] is the greatest integer less than or equal to the real number x. How many natural numbers n satisfy the equation [n]=17[\sqrt{n}] = 17[n​]=17?