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

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S is the set of all positive 3-digit integers. How many integers in S  [#permalink]

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New post 29 Nov 2018, 01:16
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  15% (low)

Question Stats:

76% (01:37) correct 24% (02:16) wrong based on 50 sessions

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Re: S is the set of all positive 3-digit integers. How many integers in S  [#permalink]

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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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Re: S is the set of all positive 3-digit integers. How many integers in S  [#permalink]

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New post 29 Nov 2018, 04:47
2
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]

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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]

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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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S is the set of all positive 3-digit integers. How many integers in S   [#permalink] 01 Dec 2018, 04:53
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S is the set of all positive 3-digit integers. How many integers in S

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