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22 Feb 2021, 03:45
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A
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Difficulty:
85%
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Question Stats:
53% (02:34) correct
47%
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wrong
based on 111
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In certain strange languages, words are written with letters from the following six-letter alphabet: A, G, K, N, R, U. Each word consists of six letters and none of the letters repeat. Each combination of these six letters is a word in this language. The word “KANGUR” remains in the dictionary at,
(A) 248th
(B) 247th
(C) 246th
(D) 245rd
(D) 244rd
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
(A) 248th
(B) 247th
(C) 246th
(D) 245rd
(D) 244rd
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22 Feb 2021, 04:15
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Bunuel
The total words that can be made using six letters = 6!
In a dictionary, the arrangement of words is in an ordered way.
So with A as first letter, the remaining 5 can be filled in 5! ways => A, _, _, _, _, _
After these 5! ways, the 2nd letter in the order is G, which will now take the first position => G, _, _, _, _, _
Total ways till now = 5!+5!=2*5*4*3*2=240
After these 5! ways, the 3rd letter in the order is K, which will now take the first position => K, _, _, _, _, _
The 241st letter from A, G, K, N, R, U will be KAGNRU. But we are looking for KANGUR
KA are constant but G and N change places. The ways words can be made with G at third position, that is K, A, G, _, _, _, are 3!.
Total ways = 240+3!=246
So the 247th word will be KANGRU, but we require the word KANGUR, that is letters U and R are to be interchanged.
Thus 248th word will be KANGUR.
A
27 Feb 2021, 21:46
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Six-letter alphabets in order: A, G, K, N, R, U.
if A is fixed at first place = 5! = 120 words
if G is fixed at first place = 5! = 120 words
Now, the next word will be KAGNRU, but, we need to reach KANGUR, so last 3 places can be filled = 3! = 6 words
Further, 247th word will be KANGRU. We need to go one word more to interchange last 2 letters.
So, 248th word will be “KANGUR”.
I think A.
if A is fixed at first place = 5! = 120 words
if G is fixed at first place = 5! = 120 words
Now, the next word will be KAGNRU, but, we need to reach KANGUR, so last 3 places can be filled = 3! = 6 words
Further, 247th word will be KANGRU. We need to go one word more to interchange last 2 letters.
So, 248th word will be “KANGUR”.
I think A.
