Difference between revisions of "2023 AMC 12A Problems/Problem 3"

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==Problem==
 
==Problem==
 
How many positive perfect squares less than <math>2023</math> are divisible by <math>5</math>?
 
How many positive perfect squares less than <math>2023</math> are divisible by <math>5</math>?
  
<cmath>\textbf{(A) } 8 \qquad\textbf{(B) }9 \qquad\textbf{(C) }10 \qquad\textbf{(D) }11 \qquad\textbf{(E) } 12</cmath>
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<math>\textbf{(A) } 8 \qquad\textbf{(B) }9 \qquad\textbf{(C) }10 \qquad\textbf{(D) }11 \qquad\textbf{(E) } 12</math>
  
 
==Solution 1==
 
==Solution 1==
Note that <math>45^{2}=2025</math> so the list is <math>5,10,15,20,25,30,35,40</math> there are <math>8</math> elements so the answer is <math>\text{\boxed{(A)}}</math>
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Note that <math>45^{2}=2025</math> so the list is <math>5,10,15,20,25,30,35,40</math> there are <math>8</math> elements so the answer is <math>\boxed{\textbf{(A) 8}}</math>.
  
 
~zhenghua
 
~zhenghua
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==Solution 2 (slightly refined)==
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Since <math>\left \lfloor{\sqrt{2023}}\right \rfloor = 44</math>, there are <math>\left \lfloor{\frac{44}{5}}\right \rfloor = \boxed{\textbf{(A) 8}}</math> perfect squares less than 2023.
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~not_slay
  
 
==See Also==
 
==See Also==

Revision as of 22:08, 9 November 2023

Problem

How many positive perfect squares less than $2023$ are divisible by $5$?

$\textbf{(A) } 8 \qquad\textbf{(B) }9 \qquad\textbf{(C) }10 \qquad\textbf{(D) }11 \qquad\textbf{(E) } 12$

Solution 1

Note that $45^{2}=2025$ so the list is $5,10,15,20,25,30,35,40$ there are $8$ elements so the answer is $\boxed{\textbf{(A) 8}}$.

~zhenghua

Solution 2 (slightly refined)

Since $\left \lfloor{\sqrt{2023}}\right \rfloor = 44$, there are $\left \lfloor{\frac{44}{5}}\right \rfloor = \boxed{\textbf{(A) 8}}$ perfect squares less than 2023.

~not_slay

See Also

2023 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 2
Followed by
Problem 4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 12 Problems and Solutions
2023 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 2
Followed by
Problem 4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 10 Problems and Solutions

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