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# The country of Sinistrograde uses standard digits but writes its numbe

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Math Expert
Joined: 02 Sep 2009
Posts: 62434
The country of Sinistrograde uses standard digits but writes its numbe  [#permalink]

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24 Apr 2015, 01:56
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Difficulty:

65% (hard)

Question Stats:

60% (02:06) correct 40% (02:03) wrong based on 169 sessions

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The country of Sinistrograde uses standard digits but writes its numbers from right to left, so that place values are reversed. For instance, 12 means “twenty-one.” A five-digit code from Sinistrograde is accidentally interpreted from left to right. If all possible five-digit codes (including zeroes in all positions) are equally likely, what is the probability that the code is in fact interpreted correctly?

A. 1/10
B. 1/100
C. 1/1,000
D. 1/10,000
E. 1/100,000

Kudos for a correct solution.

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Joined: 22 Jan 2014
Posts: 165
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Re: The country of Sinistrograde uses standard digits but writes its numbe  [#permalink]

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24 Apr 2015, 02:14
2
1
Bunuel wrote:
The country of Sinistrograde uses standard digits but writes its numbers from right to left, so that place values are reversed. For instance, 12 means “twenty-one.” A five-digit code from Sinistrograde is accidentally interpreted from left to right. If all possible five-digit codes (including zeroes in all positions) are equally likely, what is the probability that the code is in fact interpreted correctly?

A. 1/10
B. 1/100
C. 1/1,000
D. 1/10,000
E. 1/100,000

Kudos for a correct solution.

1/100

total possible cases = 10^5

for the code to be interpreted correctly the code needs to be a palindrome. so we just need to choose the first 3 numbers.
for instance: if the number if xyzyx then we just need to choose x,y,and z. which can be done in 10^3 ways.
so prob = 10^3/10^5 = 1/100
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Joined: 28 Feb 2014
Posts: 288
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Re: The country of Sinistrograde uses standard digits but writes its numbe  [#permalink]

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24 Apr 2015, 07:06
1
Total possible combinations is 10^5

Possible ways it is a palindrome is 10×10×10×1×1

10^3 / 10^5

= 1/100

Manager
Joined: 15 May 2014
Posts: 61
Re: The country of Sinistrograde uses standard digits but writes its numbe  [#permalink]

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25 Apr 2015, 07:28
2
a b c b a

if the five digit number is of the form above, then the value will be the same when it is reversed
a, b, and c each can take 10 values
p = favorable/total

= $$\frac{10^3}{10^5}$$

= $$\frac{1}{100}$$

Math Expert
Joined: 02 Sep 2009
Posts: 62434
Re: The country of Sinistrograde uses standard digits but writes its numbe  [#permalink]

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27 Apr 2015, 01:04
1
2
Bunuel wrote:
The country of Sinistrograde uses standard digits but writes its numbers from right to left, so that place values are reversed. For instance, 12 means “twenty-one.” A five-digit code from Sinistrograde is accidentally interpreted from left to right. If all possible five-digit codes (including zeroes in all positions) are equally likely, what is the probability that the code is in fact interpreted correctly?

A. 1/10
B. 1/100
C. 1/1,000
D. 1/10,000
E. 1/100,000

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

First, figure out how many possible five-digit codes there are in general. Since there are ten digits (0 through 9) and five different positions, the number of possible codes is 10 × 10 × 10 × 10 × 10, or 10^5 = 100,000.

Now, what must be true about five-digit codes that could be interpreted correctly either way (left to right or right to left)? These codes must be palindromes—they must be the same forward and backwards. If you represent each digit with a letter, then the code must be of the form xyzyx. The first and last digits must be the same (x), and the second and fourth digits must be the same (y). The middle digit can be anything.

Since you now only can determine three digits independently, you only have 10 × 10 × 10, or 10^3 = 1,000 possible palindromic codes.

The chance of choosing such a code at random is 1,000/100,000, or 1/100.

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Posts: 61
Re: The country of Sinistrograde uses standard digits but writes its numbe  [#permalink]

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27 May 2015, 11:13
1
Bunuel wrote:
Bunuel wrote:
The country of Sinistrograde uses standard digits but writes its numbers from right to left, so that place values are reversed. For instance, 12 means “twenty-one.” A five-digit code from Sinistrograde is accidentally interpreted from left to right. If all possible five-digit codes (including zeroes in all positions) are equally likely, what is the probability that the code is in fact interpreted correctly?

A. 1/10
B. 1/100
C. 1/1,000
D. 1/10,000
E. 1/100,000

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

First, figure out how many possible five-digit codes there are in general. Since there are ten digits (0 through 9) and five different positions, the number of possible codes is 10 × 10 × 10 × 10 × 10, or 10^5 = 100,000.

Now, what must be true about five-digit codes that could be interpreted correctly either way (left to right or right to left)? These codes must be palindromes—they must be the same forward and backwards. If you represent each digit with a letter, then the code must be of the form xyzyx. The first and last digits must be the same (x), and the second and fourth digits must be the same (y). The middle digit can be anything.

Since you now only can determine three digits independently, you only have 10 × 10 × 10, or 10^3 = 1,000 possible palindromic codes.

The chance of choosing such a code at random is 1,000/100,000, or 1/100.

Dear Bunuel Pl make the change to OA as it shows "C" as the correct answer.
Math Expert
Joined: 02 Sep 2009
Posts: 62434
Re: The country of Sinistrograde uses standard digits but writes its numbe  [#permalink]

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27 May 2015, 11:40
Sidhrt wrote:
Bunuel wrote:
Bunuel wrote:
The country of Sinistrograde uses standard digits but writes its numbers from right to left, so that place values are reversed. For instance, 12 means “twenty-one.” A five-digit code from Sinistrograde is accidentally interpreted from left to right. If all possible five-digit codes (including zeroes in all positions) are equally likely, what is the probability that the code is in fact interpreted correctly?

A. 1/10
B. 1/100
C. 1/1,000
D. 1/10,000
E. 1/100,000

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

First, figure out how many possible five-digit codes there are in general. Since there are ten digits (0 through 9) and five different positions, the number of possible codes is 10 × 10 × 10 × 10 × 10, or 10^5 = 100,000.

Now, what must be true about five-digit codes that could be interpreted correctly either way (left to right or right to left)? These codes must be palindromes—they must be the same forward and backwards. If you represent each digit with a letter, then the code must be of the form xyzyx. The first and last digits must be the same (x), and the second and fourth digits must be the same (y). The middle digit can be anything.

Since you now only can determine three digits independently, you only have 10 × 10 × 10, or 10^3 = 1,000 possible palindromic codes.

The chance of choosing such a code at random is 1,000/100,000, or 1/100.

Dear Bunuel Pl make the change to OA as it shows "C" as the correct answer.

____
Done. Thank you.
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The country of Sinistrograde uses standard digits but writes its numbe  [#permalink]

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04 Jun 2015, 08:47
This is a very good question, but in the answer explanation I did not read anything about the possibility of having similar digits on all places, which should also be interpreted the same way.
Codes such as 11111 or 22222.
Shouldn't this be included in the probability?

UPDATE: Oh wait never mind, this is also included with 10x10x10.
Math Expert
Joined: 02 Sep 2009
Posts: 62434
Re: The country of Sinistrograde uses standard digits but writes its numbe  [#permalink]

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04 Jun 2015, 08:54
tjerkrintjema wrote:
This is a very good question, but in the answer explanation I did not read anything about the possibility of having similar digits on all places, which should also be interpreted the same way.
Codes such as 11111 or 22222.
Shouldn't this be included in the probability?

UPDATE: Oh wait never mind, this is also included with 10x10x10.

Yes, they are also included.

Hope it helps.
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Re: The country of Sinistrograde uses standard digits but writes its numbe  [#permalink]

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22 Jul 2019, 11:22
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Re: The country of Sinistrograde uses standard digits but writes its numbe   [#permalink] 22 Jul 2019, 11:22
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