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Re: A researcher plans to identify each participant in a certain medical
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06 Nov 2018, 10:11
sacmenon wrote: BunuelA,B,AD,C,BC, ABC,D,CD, ABCD,AD,AC,BD so effectively we have used 4 letters. Please read the question carefully: a code consists of either a single letter or a pair of distinct letters written in alphabetical order.
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Re: A researcher plans to identify each participant in a certain medical
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28 Jan 2019, 08:50
Got tripped up a bit on the wording, but saw the familiarity of the problem. The hard part is that these combination/permutation word problems express things in an particular way that doesn't always make it immediately clear whether order matters or not. The issue I had was with the use of the word order, which in my mind would typically be associated with permutations, but the restriction of the problem actually means it's a combination. "written in alphabetical order"  meaning that the letters have to be alphabetically ordered, but not necessarily consecutively next to each other on the alphabet. This actually makes it a combination and not a permutation question, because it removes all the other possibilities (i.e. we can have AB but not BA). Drawing it out makes sense: The fact that the letters have to be ordered alphabetically is a convoluted way of saying only unique combinations of letters matter. Hopefully my thinking is correct in this regard.



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Re: A researcher plans to identify each participant in a certain medical
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28 Jan 2019, 20:17
sarb wrote: A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
A. 4 B. 5 C. 6 D. 7 E. 8 Constraints: " Single Letter or a pair of distinct letters written in alphabetical order" List the possibilities out: A, AB, B, AC, BC, C, AD, BD, CD, D, AE, BE <= 12th combo A, B, C, D, E were used, 5 different letters. Answer is B



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Re: A researcher plans to identify each participant in a certain medical
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02 Apr 2019, 08:13
sarb wrote: A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
A. 4 B. 5 C. 6 D. 7 E. 8 Bunuel, chetan2uCan any one elaborate condition of highlighted part.



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Re: A researcher plans to identify each participant in a certain medical
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02 Apr 2019, 09:05
Gmatprep550 wrote: sarb wrote: A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
A. 4 B. 5 C. 6 D. 7 E. 8 Bunuel, chetan2uCan any one elaborate condition of highlighted part. It means that the letters we choose must be presented in alphabetical order. So, for example, EG is good, since E comes before G in the alphabet. Conversely, GE is not acceptable, since G does not come before E in the alphabet. Cheers, Brent
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A researcher plans to identify each participant in a certain medical
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20 Apr 2019, 19:47
A simpler way would be to see the first option, which says 4. If we take 4 alphabets then the number of words with one alphabet : 4 two alphabets(considering 4 & sequence) : 3 two alphabets(considering 3 & sequence) : 2 two alphabets(considering 2 & sequence) :1 Total =10 Hence the next higher to 4 ie 5 is the correct option



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Re: A researcher plans to identify each participant in a certain medical
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29 May 2019, 01:02
Bunuel, can you explain why this is a combination and not a permutation? Bunuel wrote: Almost identical question:
John has 12 clients and he wants to use color coding to identify each client. If either a single color or a pair of two different colors can represent a client code, what is the minimum number of colors needed for the coding? Assume that changing the color order within a pair does not produce different codes. A. 24 B. 12 C. 7 D. 6 E. 5
The concept is not that hard. We can use combination or trial and error approach.
Combination approach: Let # of colors needed be \(n\), then it must be true that \(n+C^2_n\geq{12}\) (\(C^2_n\)  # of ways to choose the pair of different colors from \(n\) colors when order doesn't matter) > \(n+\frac{n(n1)}{2}\geq{12}\) > \(2n+n(n1)\geq{24}\) > \(n(n+1)\geq{24}\) > as \(n\) is an integer (it represents # of colors) \(n\geq{5}\) > \(n_{min}=5\).
Trial and error approach: If the minimum number of colors needed is 4 then there are 4 single color codes possible PLUS \(C^2_4=6\) twocolor codes > 4+6=10<12 > not enough for 12 codes;
If the minimum number of colors needed is 5 then there are 5 single color codes possible PLUS \(C^2_5=10\) twocolor codes > 5+10=15>12 > more than enough for 12 codes.
Actually as the least answer choice is 5 then if you tried it first you'd get the correct answer right away.
Answer: E.
Hope it helps.



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Re: A researcher plans to identify each participant in a certain medical
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29 May 2019, 19:32
Hi crushorange, The last sentence in the prompt tells us: "Assume that changing the color order within a pair does NOT produce different codes." This means that two different colors will only produce ONE code. For example BlueGreen and GreenBlue are the SAME code. Thus, the order of the colors does NOT matter and we're dealing with a Combination. GMAT assassins aren't born, they're made, Rich
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Re: A researcher plans to identify each participant in a certain medical
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12 Jul 2019, 10:20
A,B,AB,C,AC,BC,D,AD,BD,CD,E,AE....
5 Letters and we can get 12 code in alphabetical order.
Is it the right way of doing it?



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Re: A researcher plans to identify each participant in a certain medical
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12 Jul 2019, 11:43
Hi sk710, Based on the work that you've shown, you used a 'brute force' approach (re: you just 'mapped out' the possibilities without the need of a formula or any excessive 'math'). That's actually a great way to approach this question  and you'll find that a certain number of Quant questions (including many DS questions) can be solved by taking that same general approach. GMAT assassins aren't born, they're made, Rich
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A researcher plans to identify each participant in a certain medical
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14 Sep 2019, 14:50
I recommend do not go for the Formula, because it may confuse some people. Follow the Basic Logic, and solve it in 1 Min. Ans. Requirement  1.) It should be a SINGLE letter or a PAIR. 2.) The code should be in Alphabetical Order. So, let's start a Quick count  A  Letters Used = 1 B  Letters Used = 2 AB  Letters Used = 2 C  Letters Used = 3 AC  Letters Used = 3 BC  Letters Used = 3 D  Letters Used = 4 AD  Letters Used = 4 BD  Letters Used = 4 CD  Letters Used = 4 E  Letters Used = 5 AE  Letters Used = 5 12 Participants have been Covered and Letter Used Till Now is 5 i.e. (A, B, C, D, E) Forget the Formulas in Quant, just go for the Logic, think how you could solve any question if it were a reallife Problem



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Re: A researcher plans to identify each participant in a certain medical
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18 Sep 2019, 09:42
sarb wrote: A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
A. 4 B. 5 C. 6 D. 7 E. 8 With 4 letters say A B C D A B C D AB AC AD BC BD CD 10 Possible codes. With 5 you will definitely have more, but just to list A B C D E AB AC AD AE BC BD BE and so on.. So 6 will be sufficient for 12 participants.
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Re: A researcher plans to identify each participant in a certain medical
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10 Oct 2019, 21:13
Bunuel wrote: eaakbari wrote: Bunuel wrote: Practice: try to use the same concept.
Okay here goes, The # of single letter codes possible would be \(n\) itself; The # of pair of distinct letters codes possible would be (in alphabetical order); \(nC2\) The # of Triples of distinct letters codes possible would be (in alphabetical order); \(nC3\) Thus \(nC3 + nC2 + n\) > \(12\) \(n*(n1)/2 + n*(n1)*(n2)/3*2 + n\) > \(12\) Simplifying \(n*(n^2 +5)\) > \(72\) Only sufficient value of \(n = 4\) Is it correct? Correct. Three letters A, B, and C, are enough for 7<12 codes: A; B; C; AB; AC; BC; ABC. Four letters A, B, C, and D are enough for 15>12 codes: A; B; C; D; AB; AC; AD; BC; BD; CD; ABC; ABD; ACD; BCD; ABCD. Bunuel plz claer this : i though alphabetial menas AB,BC ,CD only AC ,AD also alphabetical?



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Re: A researcher plans to identify each participant in a certain medical
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10 Oct 2019, 21:18
vanam52923 wrote: Bunuel wrote: eaakbari wrote: Okay here goes,
The # of single letter codes possible would be \(n\) itself; The # of pair of distinct letters codes possible would be (in alphabetical order); \(nC2\) The # of Triples of distinct letters codes possible would be (in alphabetical order); \(nC3\)
Thus
\(nC3 + nC2 + n\)> \(12\)
\(n*(n1)/2 + n*(n1)*(n2)/3*2 + n\)> \(12\)
Simplifying
\(n*(n^2 +5)\)> \(72\)
Only sufficient value of \(n = 4\)
Is it correct? Correct. Three letters A, B, and C, are enough for 7<12 codes: A; B; C; AB; AC; BC; ABC. Four letters A, B, C, and D are enough for 15>12 codes: A; B; C; D; AB; AC; AD; BC; BD; CD; ABC; ABD; ACD; BCD; ABCD. Bunuel plz claer this : i though alphabetial menas AB,BC ,CD only AC ,AD also alphabetical? I think my post answers your question.
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Re: A researcher plans to identify each participant in a certain medical
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