M18-22

Question

Are all elements of an infinite increasing sequence of positive integers odd?

(1) Every element of the sequence is divisible by the same odd integer greater than 1
 
(2) The difference between any consecutive elements of the sequence is even

Bunuel · Answer

Official Solution:

Are all elements of an infinite increasing sequence of positive integers odd? 
 
(1) Every element of the sequence is divisible by the same odd integer greater than 1.
 
This statement is insufficient. For instance, if "the same odd integer" is 5, the sequence can contain no odd integers, as in the sequence {10, 20, 30, ...}, or only odd integers, as in the sequence {5, 15, 25, ...}.
 
(2) The difference between any consecutive elements of the sequence is even.
 
This statement is also insufficient. For example, consider the sequences {3, 5, 9, ...} and {2, 4, 6, ...}.
 
(1)+(2) The examples from statement (1) are still valid and provide different answers to the question: if the sequence is {10, 20, 30, ...}, the answer is No; but if the sequence is {5, 15, 25, ...}, the answer is Yes. Not sufficient.

Answer: E

joker265 · Answer

Point 1: Insufficient bcz odd number greater than 1 can be a factor of even and odd positive numbers.
For eg: 5 can be factor of 5,15,25 as well as 10,20 and 30.

Point 2: Insufficient bcz neither the statement nor the argument says the sequence starts with a positive odd number. Hence, the first number can either be positive odd or positive even. If so, the sequence can be off positive even or positive odd numbers.
For eg: The sequence can be 2,4,6,8..... or 5,15,25,35 .....

Point 1 and 2 : Insufficient bcz there are different possible sequences 14,28,42 .. or 7,21,35 ...

shubhajit · Answer

Hi

In general, whenever a "sequence" is mentioned in the question stem on the GMAT, are we to assume a reference is being made specifically to an arithmetic progression? Although, for this question in particular, even if the reference were made to a GP, it would still not change the answer, but since the explanation offered exclusively refers to an AP, I thought it would be best to clarify.

Thanks
SN

Bunuel · Answer

A sequence of numbers is not necessarily an arithmetic or geometric progression.

A sequence, by definition, is an ordered list of terms. While, a set, by definition, is a collection of elements without any order.

graceltw · Answer

Great question. Answered C as I missed the two possible cases for stat 1+2

restretto · Answer

what if the sequence is 3,9,15,21,27,33,39,45,51,57,63,69.....

every element is divisible by same odd no (3) and 
the difference between any consecutive elements of the sequence is even (6);

hence option c ?

Bunuel · Answer

Your example set gives a YES answer to the question: all elements are odd. The point is that not all possible sets give a yes answer. For example, if our set is {10, 20, 30, ...}, then the answer is NO: not all all elements are odd. Since we can have both a YES and a NO answers to the question, the statements taken together are not sufficient, and the answer is E.

M18-22

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