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I was thinking there are 50,000 odd numbers less than 100,000 but how many of those start with an even number?

thanks

- Thread starter blumfeld0
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- #1

- 148

- 0

I was thinking there are 50,000 odd numbers less than 100,000 but how many of those start with an even number?

thanks

- #2

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- #3

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not sure if you have learnt how to use AP to tackle this qns.

I was thinking there are 50,000 odd numbers less than 100,000 but how many of those start with an even number?

thanks

2 4 6 8

For numbers starting with 2, we have 2, (20-29) , (200-299), (2000-2999), (20000-29999)

same for 4 6 and 8

For odd # starting with 2 :

For 2,

0

For 20-29,

1st odd term is 21 , d is 2, last term is 29

Tn = a + (n -1 )d

29 = 21 + (n-1)2

n = 5

For 200 to 299,

1st odd term is 201 , d is 2, last term is 299

Tn = a + (n -1 )d

299 = 201 + (n-1)2

n = 50

For 2000 to 2999,

1st odd term is 2001 , d is 2, last term is 2999

Tn = a + (n -1 )d

2999 = 2001 + (n-1)2

n = 500

For 20000 to 29999,

1st odd term is 20001 , d is 2, last term is 29999

Tn = a + (n -1 )d

29999 = 20001 + (n-1)2

n = 5000

Total # of terms = 4 x (5 + 50 + 500 + 5000) = 22220

I hope this will be of some help

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