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An intelligence agency forms a code of two distinct digits selected fr

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An intelligence agency forms a code of two distinct digits selected fr  [#permalink]

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New post 09 Aug 2018, 06:14
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Question Stats:

27% (00:28) correct 73% (01:58) wrong based on 11 sessions

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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
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Re: An intelligence agency forms a code of two distinct digits selected fr  [#permalink]

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New post 09 Aug 2018, 06:41
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I got 72 as the answer. Could you please double check the options? Thanks.
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Re: An intelligence agency forms a code of two distinct digits selected fr  [#permalink]

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New post 09 Aug 2018, 06:42
vaibhav1221 wrote:
I got 72 as the answer. Could you please double check the options? Thanks.


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.
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Re: An intelligence agency forms a code of two distinct digits selected fr  [#permalink]

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New post 09 Aug 2018, 06:48
Totally forgot about 9! Thanks.

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Re: An intelligence agency forms a code of two distinct digits selected fr  [#permalink]

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New post 09 Aug 2018, 07:00
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71 seems to be correct

Out of 90 two digit numbers we can elimate
1. the 9 non distict intergers (11,22,33...99)
2. The 10 confusing numbers (16,18,19,61,68,81,86,89,91,98)

90-9-10 = 71

PS: The part that's tricky about this question is when we count the confusing numbers. We have the four digits 1,6,8 and 9 that are contenders to form the confusing numbers. Total number of distinct confusing numbers formed are therefore (4x3 = 12). But 69 and 96 when read upside down are not confusing as they read the same number both ways. So total confusing numbers are 12-2 = 10

Hope this helps
;)

[size=80][b][i]Posted from my mobile device[/i][/b][/size]
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Re: An intelligence agency forms a code of two distinct digits selected fr &nbs [#permalink] 09 Aug 2018, 07:00
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