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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  [#permalink]

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New post 31 Aug 2018, 08:04
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A
B
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D
E

Difficulty:

  65% (hard)

Question Stats:

53% (02:43) correct 47% (02:33) wrong based on 38 sessions

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

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

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Re: Find the sum of all odd three digit numbers  [#permalink]

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New post 31 Aug 2018, 08:31
Afc0892 wrote:
Find the sum of all odd three digit numbers that are divisible by 5.

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


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
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Re: Find the sum of all odd three digit numbers  [#permalink]

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New post 31 Aug 2018, 11:32
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Afc0892 wrote:
Find the sum of all odd three digit numbers that are divisible by 5.

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


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 [2a+(n-1)d] where n=90 ,a=105 & d=10
Sum = 49500

Ans:1
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Re: Find the sum of all odd three digit numbers   [#permalink] 31 Aug 2018, 11:32
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