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.
ANSWER IS C
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