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# If S is a sequence of consecutive multiples of 7, how many multiples o

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If S is a sequence of consecutive multiples of 7, how many multiples o  [#permalink]

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27 Jun 2015, 02:05
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61% (01:27) correct 39% (01:14) wrong based on 196 sessions

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If S is a sequence of consecutive multiples of 7, how many multiples of 14 are there in S?

(1) The greatest term of S is even.

(2) There are 21 terms in S.

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Re: If S is a sequence of consecutive multiples of 7, how many multiples o  [#permalink]

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27 Jun 2015, 03:27
reto wrote:
If S is a sequence of consecutive multiples of 7, how many multiples of 14 are there in S?

(1) The greatest term of S is even.

(2) There are 21 terms in S.

Similar questions to practice: if-s-is-a-sequence-of-consecutive-multiples-of-172766.html
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Re: If S is a sequence of consecutive multiples of 7, how many multiples o  [#permalink]

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27 Jun 2015, 04:04
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reto wrote:
If S is a sequence of consecutive multiples of 7, how many multiples of 14 are there in S?

(1) The greatest term of S is even.

(2) There are 21 terms in S.

CONCEPT: If the number of terms in the sequence is Even then Multiple of 7 will be half of the terms
CONCEPT: If the number of terms in the sequence is Odd then Multiple of 7 will depend on how many terms are in sequence and first ters is even/odd

Statement 1: The greatest term of S is even

No. of terms in the sequence is unknown which may result in different answers so
NOT SUFFICIENT

Statement 2: There are 21 terms in S

It is unknown whether the series is starting with even term or odd hence no. of multiples of 14 may be 10 or 11 hence,
NOT SUFFICIENT

Combining the two statements
No. of terms = 21
Greatest term = Even
i.e. The series will have 11 even terms and 10 odd terms
All even Terms are multiple of 7 and 2 both i.e. Multiple of 14

SUFFICIENT

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Re: If S is a sequence of consecutive multiples of 7, how many multiples o  [#permalink]

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16 Jul 2016, 03:02
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reto wrote:
If S is a sequence of consecutive multiples of 7, how many multiples of 14 are there in S?

(1) The greatest term of S is even.

(2) There are 21 terms in S.

Every even multiple of 7 is also a multiple of 14 {14,28,56,70}
If we can know how many even numbers or even multiples are in the set then that number will be our answer.

(1) The greatest term of S is even.
Nice but insufficient. We know the biggest term/LAST TERM is even but we do not know how many other even terms are there in the set
S={7,14,21,28} Two even multiple of 14 present in the set; They are 14 and 28
S={7,14,21,28,35,42} Three even multiple of 14 present in the set; They are 14,28,42
INSUFFICIENT

(2) There are 21 terms in S
Nice but insufficient. These 21 terms will be consecutive multiples of 7 but If the first (and also Last) term is odd ; then odd multiple =11 even multiple =10
. If the first (and also last) term is even ; then odd multiple =10 even multiple =11
INSUFFICIENT

Merging both We know total multiples are 21 and that last term is even ==> Even Multiples are =11
All Even multiples are also multiple of 14
So multiple of 14 are 11 in number.

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Re: If S is a sequence of consecutive multiples of 7, how many multiples o  [#permalink]

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19 Sep 2018, 00:25
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Re: If S is a sequence of consecutive multiples of 7, how many multiples o   [#permalink] 19 Sep 2018, 00:25
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