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How many even multiples of 9 are there from 1–1,000, inclusive?

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How many even multiples of 9 are there from 1–1,000, inclusive?  [#permalink]

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New post 23 Jan 2019, 01:18
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Re: How many even multiples of 9 are there from 1–1,000, inclusive?  [#permalink]

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New post 23 Jan 2019, 05:58
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Bunuel wrote:
How many even multiples of 9 are there from 1–1,000, inclusive?

A 55
B 56
C 109
D 110
E 111


IMO A

Total terms will be 111 which could be multiple of 9

In 1st 10 numbers of this series will have 5 Even and 5 Odd

Now out of 100 terms, 55 terms will be even 55 terms will be odd

the 111th term will be odd.
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Re: How many even multiples of 9 are there from 1–1,000, inclusive?  [#permalink]

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New post 23 Jan 2019, 06:38
Bunuel wrote:
How many even multiples of 9 are there from 1–1,000, inclusive?

A 55
B 56
C 109
D 110
E 111



1000 / 9 = ~111
111 comprises of both odd & even integer values
so 111/2 = 55.5 ~ 56
since first term is odd and last term is also odd , so odd multiples +1 than even multiples
56 odd and 55 even
IMO A
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Re: How many even multiples of 9 are there from 1–1,000, inclusive?  [#permalink]

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New post 24 Jan 2019, 01:53
Bunuel wrote:
How many even multiples of 9 are there from 1–1,000, inclusive?

A 55
B 56
C 109
D 110
E 111


Bunuel where can I find some theory of these concepts?

Thank you!!!!!!!!
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Re: How many even multiples of 9 are there from 1–1,000, inclusive?  [#permalink]

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New post 24 Jan 2019, 07:39
The first even multiple of 9 is 18
The last even multiple of 9 is 990
\(\frac{990-18}{18}\)+1=55

We are dividing by 18 because there are 1 even multiple of 9 in every 18 numbers

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Re: How many even multiples of 9 are there from 1–1,000, inclusive?  [#permalink]

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New post 27 Jan 2019, 18:58
Bunuel wrote:
How many even multiples of 9 are there from 1–1,000, inclusive?

A 55
B 56
C 109
D 110
E 111


The number of even multiples of 9 (or, in other words, multiples of 18) from 1 to 1,000, inclusive, is determined by first finding the smallest multiple of 18 in the set and then finding the greatest multiple of 18. We see that these values are 18 and 990, respectively. Then we determine the number of multiples of 18 are in the set:

(990 - 18)/18 + 1 = 972/18 + 1 = 55

Answer: A
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Re: How many even multiples of 9 are there from 1–1,000, inclusive?  [#permalink]

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New post 27 Jan 2019, 20:28
Bunuel wrote:
How many even multiples of 9 are there from 1–1,000, inclusive?

A 55
B 56
C 109
D 110
E 111


The even multiples of 9 in the given range are : 9 * 2, 9 * 4, 9 * 6,......., 9 * 110

If you consider 2,4,6,.....,110 it can be seen that the nth term is 2n and hence 110 is the 55th term

Hence, there are 55 even multiples of 9

Choice A
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Re: How many even multiples of 9 are there from 1–1,000, inclusive?   [#permalink] 27 Jan 2019, 20:28
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