Find the sum of all odd three digit numbers

Question

Find the sum of all odd three digit numbers that are divisible by 5.

1) 49500
2) 50000
3) 50250
4) 50500
5) 51250

GMATinsight · Accepted Answer

Total 3 digit odd numbers = 9 (1 to 9)*10 (0 to 9)*1(odd digits 5) = 90

Smallest 3 digit odd number = 105
Biggest 3 digit odd number = 995
Sum of these two numbers = 1100

Second Smallest 3 digit odd number = 115
Second Biggest 3 digit odd number = 985
Sum of these two numbers = 1100

Third Smallest 3 digit odd number = 125
Third Biggest 3 digit odd number = 975
Sum of these two numbers = 1100

Total Numbers = 90

So total such Pairs of numbers = (90)/2
Each pair has sum = 1100
Sum of all pairs = (90/2)*1100 = 49500

Answer: Option A

janadipesh · Answer

Numbers divisible by 5 will end with 0 or 5
So,Odd Numbers divisible by 5 will end with 5
First Odd three digit number number divisible by 5 is 105 
second 115 , third 125 and so on ....
last odd three digit number divisible by 5 is 995

So the series 
105 +115+125.........+995

number of terms ={ (995-105)/10} +1 = 89+1=90

Sum = n/2   where n=90 ,a=105 & d=10
Sum = 49500

Ans:1

MathRevolution · Answer

The first odd three-digit number divisible by 5 is 105.

The last odd three-digit number divisible by 5 is 995.

Number of terms:  \frac{995 - 105 }{ 10} + 1 = 90

Sum =  \frac{n}{2 }

=> Sum =  \frac{90}{2}

=> Sum = 49,500

Answer A

BrushMyQuant · Answer

Find the sum of all odd three digit numbers that are divisible by 5.

All odd three digit numbers divisible by 5 will have 5 as the units' digit:

First number = 105
Last Number = 995
Common difference, d = 10 (as alternate multiples of 5 will be odd numbers)
Number of terms, n = (Last term - First Term)/d + 1 =  \frac{995 - 105}{10}  + 1 = 89 + 1 = 90
Sum = n * (First Term + Last Term)/2 = 90 *  \frac{(105 + 995)}{2}  = 49,500

So,  Answer will be A 
Hope it helps!

Watch the following video to MASTER Sequence problems

https://www.youtube.com/watch?v=EfNT2JoE5CM

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Find the sum of all odd three digit numbers

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Find the sum of all odd three digit numbers

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