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How many multiples of 7 between 100 and 150?

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How many multiples of 7 between 100 and 150? [#permalink]  10 May 2012, 05:45
Hey everyone. As you can see, I need help with something so simple. I'm sure the answer is right in front of me and I can't see it. They use the above question in Manhattan Number Properties. They start listing multiples: 105, 112,119,126, 133, 140, 147. The thing that is not clear to me is how I know to start with 105 instead of say, 103 or 101.
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Re: How many multiples of 7 between 100 and 150? [#permalink]  10 May 2012, 06:22
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The first multiple of 7 that is greater than 100, is 105. (70+35 = 105).
The one before that is 98, and that's less than 100.

This is the most reliable way to solve the question (listing).
Another is to subtract 100 from 150 and divide that by 7 but that does not always work well. In this case, it does since 50 divided by 7 is 7.

Hope this helps.
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Re: How many multiples of 7 between 100 and 150? [#permalink]  10 May 2012, 06:37
bb wrote:
The first multiple of 7 that is greater than 100, is 105. (70+35 = 105).
The one before then is 98, and that's less than 100.

This is the most reliable way to solve the question (listing).
Another is to subtract 100 from 150 and divide that by 7 but that does not always work well. In this case, it does since 50 divided by 7 is 7.

Hope this helps.

Wow. Makes perfect sense. Thanks a lot.
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Re: How many multiples of 7 between 100 and 150? [#permalink]  11 May 2012, 11:26
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My thought process:
Smallest multiple > 100 = 105, multiple 105/7 = 15
greatest multiple < 150 = 147, multiple 147/7 = 21, Therefore total number of multiples = 21-15 +1 = 7
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Re: How many multiples of 7 between 100 and 150? [#permalink]  11 May 2012, 18:40
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Response in attached images.
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Re: How many multiples of 7 between 100 and 150? [#permalink]  11 May 2012, 18:47
Slightly different approach, once the beginning and ends are established.
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Re: How many multiples of 7 between 100 and 150? [#permalink]  20 May 2012, 20:58
mdavidm531 wrote:
gmatz101 wrote:
Hey everyone. As you can see, I need help with something so simple. I'm sure the answer is right in front of me and I can't see it. They use the above question in Manhattan Number Properties. They start listing multiples: 105, 112,119,126, 133, 140, 147. The thing that is not clear to me is how I know to start with 105 instead of say, 103 or 101.

Per Manhattan GMAT:

(last - first) / multiple + 1

Hm.... so that would be
Step 1: (150 - 100) = 50
Step 2: \frac{50}{7} = 7
Step 3: 7+1 = 8 ?

I think you meant (Last - First +1)/Multiple
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Re: How many multiples of 7 between 100 and 150?   [#permalink] 20 May 2012, 20:58
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