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S is the set of all positive 3-digit integers. How many integers in S

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Bunuel
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S is the set of all positive 3-digit integers. How many integers in S [#permalink] New post   29 Nov 2018, 01:16
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S is the set of all positive 3-digit integers. How many integers in S are multiples of both 7 and 13 ?

A. 6
B. 9
C. 12
D. 15
E. 18
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B
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Re: S is the set of all positive 3-digit integers. How many integers in S [#permalink] New post   29 Nov 2018, 04:29
Bunuel wrote:
S is the set of all positive 3-digit integers. How many integers in S are multiples of both 7 and 13 ?

A. 6
B. 9
C. 12
D. 15
E. 18



chetan2u : how can we determine all integer values 3 digit those are multiples of both 7 & 13 is there any formula for such questions??
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chetan2u
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Re: S is the set of all positive 3-digit integers. How many integers in S [#permalink] New post   29 Nov 2018, 04:47
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Archit3110 wrote:
Bunuel wrote:
S is the set of all positive 3-digit integers. How many integers in S are multiples of both 7 and 13 ?

A. 6
B. 9
C. 12
D. 15
E. 18



chetan2u : how can we determine all integer values 3 digit those are multiples of both 7 & 13 is there any formula for such questions??



Hi..

multiple of both 7 and 13 means multiple of LCM of 3 and 17, which is 91..
so the smallest 3-digit number that is multiple of 91 will be 91*2 and the largest that should come to your mind is 91*10=910, the next after 910 is 910+91=1001
so multiples are 91*2 to 91*10, so (10-2)+1=9
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Re: S is the set of all positive 3-digit integers. How many integers in S [#permalink] New post   30 Nov 2018, 12:01
chetan2u wrote:
Archit3110 wrote:
Bunuel wrote:
S is the set of all positive 3-digit integers. How many integers in S are multiples of both 7 and 13 ?

A. 6
B. 9
C. 12
D. 15
E. 18



chetan2u : how can we determine all integer values 3 digit those are multiples of both 7 & 13 is there any formula for such questions??



Hi..

multiple of both 7 and 13 means multiple of LCM of 3 and 17, which is 91..
so the smallest 3-digit number that is multiple of 91 will be 91*2 and the largest that should come to your mind is 91*10=910, the next after 910 is 910+91=1001
so multiples are 91*2 to 91*10, so (10-2)+1=9



chetan2u

Thank you..
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S is the set of all positive 3-digit integers. How many integers in S [#permalink] New post   01 Dec 2018, 04:53
the mimum multiple of 7 and 13 is 91

so we have three digit integer xyz

in other words how many times does 91 go into three digit integer xyz

91*9 =819

Clearly option B
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Re: S is the set of all positive 3-digit integers. How many integers in S [#permalink] New post   14 Nov 2022, 11:27
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Bunuel wrote:
S is the set of all positive 3-digit integers. How many integers in S are multiples of both 7 and 13 ?

A. 6
B. 9
C. 12
D. 15
E. 18


If an integer is a multiple of both 7 and 13, that integer must be a multiple of LCM(7, 13) = 91. To find the number of three-digit multiples of 91, we will use the formula 1 + [(largest 3-digit multiple of 91 - smallest 3-digit multiple of 91)/(common difference)].

The smallest three-digit multiple of 91 is 182, and the largest three-digit multiple of 91 is 910. Since we are interested in multiples of 91, common difference is 91. Thus, there are 1 + [(910 - 182)/91] = 1 + 728/91 = 1 + 8 = 9 three-digit integers which are multiples of both 7 and 13.

Answer: B
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Re: S is the set of all positive 3-digit integers. How many integers in S [#permalink]
14 Nov 2022, 11:27
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