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10 Nov 2022, 07:59
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
63% (01:51) correct
37%
(01:45)
wrong
based on 192
sessions
History
Date
Time
Result
Not Attempted Yet
In how many ways can letters a, b and c be assigned into a nine places such that no letter is used more than once in each column and each row?
A. 9
B. 10
C. 11
D. 12
E. 13
Attachment:
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11 Nov 2022, 00:54
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This kind of question could seem very daunting. However, if you are ready to think through and approach them logically, these can actually be much easier.
To start with, there could be multiple possibilities. I am just drawing one to show how it happens.
ABC
BCA
CAB
Here we have the top row as ABC.
Now since there's no bias against A B or C we can say that the first row can be assigned in 3! ways.
Now that straight away suggests that the answer is a multiple of 6. And we can simply mark 12 and go ahead.
However, to see how it happens I am showing a couple of cases
We start with ABC
ABC
BCA
CAB
Or
ABC
CAB
BCA
The answer is D. 12
To start with, there could be multiple possibilities. I am just drawing one to show how it happens.
ABC
BCA
CAB
Here we have the top row as ABC.
Now since there's no bias against A B or C we can say that the first row can be assigned in 3! ways.
- ABC or ACB or BCA or BAC or CAB or CBA
Now that straight away suggests that the answer is a multiple of 6. And we can simply mark 12 and go ahead.
However, to see how it happens I am showing a couple of cases
We start with ABC
ABC
BCA
CAB
Or
ABC
CAB
BCA
The answer is D. 12
miag
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Schools: Anderson '26 (A) Haas '26 (A) Kellogg '26 (A)
GMAT Focus 1: 675 Q87 V83 DI80
Posts: 404
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159
17 Feb 2025, 06:16
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Hi SaquibHGMATWhiz - can you explain how you got from the 3!=6 to the answer = 12?
Is it because each of the 6 have 2 possible ways of rearranging (the second and third rows can switch) so it becomes 6*2 = 12?
Thank you!
Is it because each of the 6 have 2 possible ways of rearranging (the second and third rows can switch) so it becomes 6*2 = 12?
Thank you!
SaquibHGMATWhiz
