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2006 iTest Problems/Problem 15 - Revision history
2024-03-28T11:40:33Z
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Rockmanex3: Solution to Problem 15 — PS from 1 to 2006
2018-11-28T03:31:08Z
<p>Solution to Problem 15 — PS from 1 to 2006</p>
<p><b>New page</b></p><div>==Problem==<br />
<br />
How many integers between <math>1</math> and <math>2006</math>, inclusive, are perfect squares?<br />
<br />
<math>\text{(A) }37\qquad<br />
\text{(B) }38\qquad<br />
\text{(C) }39\qquad<br />
\text{(D) }40\qquad<br />
\text{(E) }41\qquad<br />
\text{(F) }42\qquad<br />
\text{(G) }43\qquad<br />
\text{(H) }44\qquad</math><br />
<br />
<math>\text{(I) }45\qquad<br />
\text{(J) }46\qquad<br />
\text{(K) }47\qquad<br />
\text{(L) }48\qquad<br />
\text{(M) }49\qquad<br />
\text{(N) }50\qquad<br />
\text{(O) }\text{none of the above}\qquad</math><br />
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==Solution==<br />
<br />
Note that <math>1600 < 2006 < 2500</math>, so the number of perfect squares must be around 40 to 50. With some trial and error, we found that <math>44^2 = 1936</math> and <math>45^2 = 2025</math>, so the perfect squares between 1 and 2006 are <math>1^2, 2^2, 3^2, \cdots 44^2</math>. There are <math>\boxed{\textbf{(H) } 44}</math> integers in the set.<br />
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==See Also==<br />
<br />
{{iTest box|year=2006|num-b=14|num-a=16|ver=[[2006 iTest Problems/Problem U1|U1]] '''•''' [[2006 iTest Problems/Problem U2|U2]] '''•''' [[2006 iTest Problems/Problem U3|U3]] '''•''' [[2006 iTest Problems/Problem U4|U4]] '''•''' [[2006 iTest Problems/Problem U5|U5]] '''•''' [[2006 iTest Problems/Problem U6|U6]] '''•''' [[2006 iTest Problems/Problem U7|U7]] '''•''' [[2006 iTest Problems/Problem U8|U8]] '''•''' [[2006 iTest Problems/Problem U9|U9]] '''•''' [[2006 iTest Problems/Problem U10|U10]]}}<br />
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[[Category:Introductory Combinatorics Problems]]</div>
Rockmanex3