Question

Ed has 93 marbles. In which sequence can he arrange them and use all the marbles?

A) a sequence with six terms that starts with 1 and has a common ratio of 2
B) a sequence with six terms that starts with 1 and has a common ratio of 3
C) a sequence with six terms that starts with 3 and has a common ratio of 2
D) a sequence with five terms that starts with 3 and has a common ratio of 2
E) a sequence with five terms that starts with 1 and has a common ratio of 3

Answer 1

@Klip

Answer 2

If you consider the options, note that sequences with a common ratio of two will be a multiple of 1,2,4,8,16,32,...
If the common ratio is three, the sequence will be a multiple of 1,3,9,27,81,...

Now, as the prime factorization of 93 is "3 * 31", you just need to consider which of the sequences (above) might add to 31. You can easily see that the first five terms of the first sequence accomplishes this task:

1 + 2 + 4 + 8 + 16 = 31

Therefore, you want a sequence starting with 3* and common ratio two.
(i.e. option "D" )

This is so that each term of the new sequence is tripled... we needed 3 * 31

Answer 3

mr smart .... XD

Answer 4

Not really :PP