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26 Nov 2018, 07:57
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
63% (01:37) correct
37%
(01:33)
wrong
based on 1453
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Are there 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) 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
26 Nov 2018, 11:22
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gmatbusters
(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.
27 Aug 2020, 00:34
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GMATBusters
Does the language Q have exactly 3 distinct symbols? (for example, English language has exactly 26 distinct letters)
Stmnt 1 tells us that code words are made by horizontal placement of 1 or more of these symbols. And stmnt 2 tells us that there are exactly 15 code words.
If we have 3 distinct symbols in a language (say @, #, $), how many code words can we make?
We can make a code word by selecting exactly 1 of these 3 symbols. So 3
We can make a code word by selecting exactly 2 of these symbols and arranging them in 2! ways. So 3C2 * 2!
We can make a code word by selecting all 3 of these symbols and arranging them in 3! ways. So 3!
Total = 3 + 3C2*2! + 3! = 15
So yes, language Q has exactly 3 distinct symbols.
Answer (C)
