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LMP
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09 Aug 2018, 07:14
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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:
43% (00:29) correct
57%
(02:20)
wrong
based on 7
sessions
History
Date
Time
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Not Attempted Yet
An intelligence agency forms a code of two distinct digits selected from 0, 1, 2, …., 9 such that the first digit of the code is nonzero. The code, handwritten on a slip, can however potentially create confusion, when read upsidedown-for example, the code 91 may appear as 16. How many codes are there for which no such confusion can arise?
(a) 80
(b) 78
(c) 71
(d) 69
(e) 75
(a) 80
(b) 78
(c) 71
(d) 69
(e) 75
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vaibhav1221
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Schools: IIMA '25 (A) Columbia CBS'26 (D) Fuqua '26 (D) ISB '25 (WL) Darden '26 (D) Kenan-Flagler '26 (WL)
GMAT 1: 710 Q49 V38
Posts: 292
09 Aug 2018, 07:41
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I got 72 as the answer. Could you please double check the options? Thanks.
LMP
Joined: 29 Jun 2018
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09 Aug 2018, 07:42
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vaibhav1221
I am sure you might have missed out on 69/96.
The available digits are 0,1,2, ....9.
The first digit can be chosen in 9 ways (0 not acceptable), the second digit can be accepted in 9 ways (digits repetition not allowed).
Thus, the code can be made in 9 x 9 = 81 ways.
Now there are only 4 digits 1, 6, 8, 9 which can create confusion.
Hence, the total number of codes which create confusion are = 4 x 3 = 12.
Out of these 12 codes 69 and 96 will not create confusion.
Hence, in total 12 - 2 = 10 codes will create confusion.
Hence, the total codes without confusion are 81 -10 = 71.
