gmatbusters wrote:
Project DS Butler: Day 21: Data Sufficiency (DS41)
For DS butler Questions Click HereAre exactly 3 distinct symbols used to create the code words in language Q?
(1) The set of all code words in language Q is the set of all possible distinct horizontal arrangements of one or more symbols, with no repetition.
(2) There are exactly 15 code words in language Q
(1) So from this statement, we can get that:
if there are say 2 symbols, then all the possible code words will be formed by using either one symbol or two symbols (without repetition) taking all possible arrangements.
If there are say 3 symbols, then all the possible code words will be formed by using either one symbol or two symbols or three symbols, again without repetition, taking all possible arrangements. But this just explains how to form code words using symbols, doesnt tell us anything about number or symbols or number of words.
Not Sufficient.
(2) We are given number of code words, but no logic about how symbols are used to form code words.
Not Sufficient.
Combining the statements, we can do some trial/error. If say there are two symbols A & B, then taking one symbol at a time, we can form two words only:A and B (basically 2P1). Taking 2 symbols at a time, we can form AB or BA, so two more words (basically 2P2). Total 4 words, not 15.
Now lets take 3 symbols at a time, say A, B, C. Taking one symbol at a time, there are three words: A, B, C. (3P1)
Taking two symbols at a time, there are six words: AB, BA, AC, CA, BC, CB. (3P2)
Taking three symbols at a time, there are again six words: ABC, ACB, BAC, BCA, CAB, CBA. (3P3)
So total words = 3+6+6 = 15.
If we take more symbols, number of code words will definitely be more than 15. So the only possibility that leads of exactly 15 code words is with 3 symbols only.
Sufficient to answer the question with YES.
Hence
C answer.