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Find the sum of all positive integers less than $1000$ ending in $3$ or $4$ or $5$.

 Apr 2, 2024

Best Answer 

 #2
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https://web2.0calc.com/questions/sum_93

 

 

cool cool cool

 Apr 3, 2024
 #1
avatar+394 
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We want all numbers in this form:

_ _ 3

_ _ 4

_ _ 5

An integer can't be part of both groups, since an integer has only one ending number.

For all of these, the first two can cycle from 10 to 99 which is 90 numbers

Sum of numbers ending in 3 is (sum of numbers 10 - 99) * 10 + 90*3 = 49320

Sum of numbers ending in 4 is (sum of numbers 10 - 99) * 10 + 90*4 = 49410
Sum of numbers ending in 5 is (sum of numbers 10 - 99) * 10 + 90*5 = 49500

49320 + 49410 + 49500 = 148230.

 Apr 3, 2024
 #2
avatar+128399 
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Best Answer

https://web2.0calc.com/questions/sum_93

 

 

cool cool cool

CPhill Apr 3, 2024

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