Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43358

The country of Sinistrograde uses standard digits but writes its numbe [#permalink]
Show Tags
24 Apr 2015, 01:56
Question Stats:
52% (01:40) correct 48% (01:28) wrong based on 148 sessions
HideShow timer Statistics



Manager
Joined: 22 Jan 2014
Posts: 139
WE: Project Management (Computer Hardware)

Re: The country of Sinistrograde uses standard digits but writes its numbe [#permalink]
Show Tags
24 Apr 2015, 02:14
1
This post received KUDOS
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 “twentyone.” A fivedigit code from Sinistrograde is accidentally interpreted from left to right. If all possible fivedigit 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
_________________
Illegitimi non carborundum.



Senior Manager
Joined: 28 Feb 2014
Posts: 295
Location: United States
Concentration: Strategy, General Management

Re: The country of Sinistrograde uses standard digits but writes its numbe [#permalink]
Show Tags
24 Apr 2015, 07:06
1
This post received KUDOS
Total possible combinations is 10^5
Possible ways it is a palindrome is 10×10×10×1×1
10^3 / 10^5
= 1/100
Answer : B



Manager
Joined: 15 May 2014
Posts: 65

Re: The country of Sinistrograde uses standard digits but writes its numbe [#permalink]
Show Tags
25 Apr 2015, 07:28
2
This post received KUDOS
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
= \(\frac{10^3}{10^5}\)
= \(\frac{1}{100}\)
Answer B



Math Expert
Joined: 02 Sep 2009
Posts: 43358

Re: The country of Sinistrograde uses standard digits but writes its numbe [#permalink]
Show Tags
27 Apr 2015, 01:04
1
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
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 “twentyone.” A fivedigit code from Sinistrograde is accidentally interpreted from left to right. If all possible fivedigit 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 fivedigit 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 fivedigit 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. The correct answer is B.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 09 Nov 2013
Posts: 92

Re: The country of Sinistrograde uses standard digits but writes its numbe [#permalink]
Show Tags
27 May 2015, 11:13
1
This post received KUDOS
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 “twentyone.” A fivedigit code from Sinistrograde is accidentally interpreted from left to right. If all possible fivedigit 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 fivedigit 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 fivedigit 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. The correct answer is B. Dear Bunuel Pl make the change to OA as it shows "C" as the correct answer.



Math Expert
Joined: 02 Sep 2009
Posts: 43358

Re: The country of Sinistrograde uses standard digits but writes its numbe [#permalink]
Show Tags
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 “twentyone.” A fivedigit code from Sinistrograde is accidentally interpreted from left to right. If all possible fivedigit 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 fivedigit 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 fivedigit 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. The correct answer is B. Dear Bunuel Pl make the change to OA as it shows "C" as the correct answer. ____ Done. Thank you.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 04 May 2014
Posts: 30

The country of Sinistrograde uses standard digits but writes its numbe [#permalink]
Show Tags
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: 43358

Re: The country of Sinistrograde uses standard digits but writes its numbe [#permalink]
Show Tags
04 Jun 2015, 08:54



NonHuman User
Joined: 09 Sep 2013
Posts: 14162

Re: The country of Sinistrograde uses standard digits but writes its numbe [#permalink]
Show Tags
27 Aug 2017, 21:28
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: The country of Sinistrograde uses standard digits but writes its numbe
[#permalink]
27 Aug 2017, 21:28






