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# The Quest for 700: Weekly GMAT Challenge (Answer)

Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:

Label the keys A, B, C, and D, such that key A fits the first lock, key B fits the second lock, and so on.  Each possible reassignment of the keys can then be seen as a rearrangement of the four letters.  For instance, the “word” BCAD would correspond to the reassigning key B to the first lock, key C to the second lock, key A to the third lock, and key D to the fourth lock.  In this particular case, only key D would fit its lock.

Thus, we should compute the number of anagrams of ABCD in which exactly two of the letters are in their original alphabetic positions.

There are at least two ways to compute this number:

1) Simply try listing the possibilities.  First place two letters in correct positions, then fill in the others.  The letters in their correct positions will be written in uppercase; letters out of position will be written in lowercase.

Correct letters     Anagram

A and B               ABdc
A and D               AcbD
B and C               dBCa