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deleted.

 Oct 29, 2019
edited by sinclairdragon428  Nov 20, 2019, 6:50:10 AM
 #1
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+1

There are: 5^4 = 625 odd integers

There are 9000 / 5 =1,800 multiple of 5 integers

900 + 625 =1525 Total integers

 Oct 29, 2019
 #2
avatar+23337 
+3

let a equal the number of four digit odd numbers. let b equal the number of four digit multiples of 5. find a+b.

 

I assume:

These are two arithmetic series.

\(\begin{array}{|rcll|} \hline 1001 + (a-1)\cdot 2 &=& 9999 \quad | \quad \small \text{first odd four digit number }=1001,\ \text{last odd four digit number }=9999\\ (a-1)\cdot 2 &=& 9999 - 1001 \\ (a-1)\cdot 2 &=& 8998 \\ a-1 &=& 4499 \\ a &=& 4499+1 \\ \mathbf{a} &=& \mathbf{4500} \\\\ 1000 + (b-1)\cdot 5 &=& 9995 \quad | \quad \small \text{first four digit number multiples of 5}=1000,\ \text{last four digit number }=9995\\ (b-1)\cdot 5 &=& 9995 - 1000 \\ (b-1)\cdot 5 &=& 8995 \\ b-1 &=& 1799 \\ b &=& 1799+1 \\ \mathbf{b} &=& \mathbf{1800} \\ \hline \end{array} \)

 

\(a+b = 4500+1800 = 6300\)

 

laugh

 Oct 29, 2019
 #3
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heureka: Isn't the number of odd integers from the left: 5(1,3,5,7,9) x 5 x 5 x 5 =5^4 =625 such numbers.

 Oct 29, 2019
 #4
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heureka: You counted 4,500 ODD digits. He/she wants "four-digit odd numbers", which is 5^4 =625 odd numbers.

Guest Oct 29, 2019
 #5
avatar+397 
+1

Thank you to everyone! 6300 is the answer, so special thanks to heureka

 Oct 29, 2019
 #6
avatar+23337 
+2

Thank you, sinclairdragon428 !

 

laugh

heureka  Oct 29, 2019

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