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A unique code is assigned to all test takers of the GNAT exam on a spe
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11 Sep 2021, 03:43
11 Sep 2021, 03:43
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A unique code is assigned to all test takers of the GNAT exam on a specific day in a centre. On 12 Jan 2021, there were 32 test takers with the codes. The codes are either 2-letter codes or 3-letter codes in the alphabetical order. How many letters will the centre need at a minimum to give all the test takers a unique code?
A. 5
B. 6
C. 7
D. 8
E. 9
A. 5
B. 6
C. 7
D. 8
E. 9
Re: A unique code is assigned to all test takers of the GNAT exam on a spe
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12 Sep 2021, 03:37
12 Sep 2021, 03:37
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Expert Reply
Kushchokhani wrote:
A unique code is assigned to all test takers of the GNAT exam on a specific day in a centre. On 12 Jan 2021, there were 32 test takers with the codes. The codes are either 2-letter codes or 3-letter codes in the alphabetical order. How many letters will the centre need at a minimum to give all the test takers a unique code?
A. 5
B. 6
C. 7
D. 8
E. 9
A. 5
B. 6
C. 7
D. 8
E. 9
Let the number of alphabets be n, and since we are looking at alphabetical order, each combination will just give one way.
So, we are looking at ways to choose 2 or 3 alphabets out of n.
\(nC2+nC3\geq 32\)
Use options to ease calculations.
1) 5:
\(5C2+5C3\geq 32………..10+10\geq 32\)…..NO
2) 6:
\(6C2+6C3\geq 32………..15+20\geq 32\)…..YES
B
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Re: A unique code is assigned to all test takers of the GNAT exam on a spe
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12 Sep 2021, 08:51
12 Sep 2021, 08:51
nC2+nC3 >= 32
5 - 10+10 = 20
6 works - 15+20 = 35 >= 32
B
5 - 10+10 = 20
6 works - 15+20 = 35 >= 32
B
