A certain online form requires a 2-digit code for the day of the month

Question

A certain online form requires a 2-digit code for the day of the month to be entered into one of its fields, such as 04 for the 4th day of the month. The code is valid if it is 01, 02, 03, …, 31 and not valid otherwise. The transpose of a code xy is yx. For example, 40 is the transpose of 04. If N is the number of valid codes having a transpose that is not valid, what is the value of N ?

A. 12
B. 13
C. 18
D. 19
E. 20

PS92981.01

A. 12
B. 13
C. 18
D. 19
E. 20

PS92981.01

ScottTargetTestPrep · Accepted Answer

Let’s list all the valid codes that have transposes that are also valid:

01, 02, 03, 10, 11, 12, 13, 20, 21, 22, 30 and 31.

We see that there are 12 codes with valid transposes; therefore, there are 31 - 12 = 19 codes that have a transpose that is not valid.

Answer: D

Archit3110 · Answer

total valid codes with transpose ; 01,02,03,11,12,13,20,21,22 ; 12 options
total possible 31
31-12 ; 19 not possible
IMO D

Mohammadmo · Answer

Valid codes which are invalid when reversion incloud {04,05,06,07 08,09,14,15,16,17,18,19,23,24,25,26,27,28,29}
Hence option D

Posted from my mobile device

uchihaitachi · Answer

We need to find numbers whose transpose does not exist in the calendar. 
So the numbers possible are -->
04,05,06,07,08,09
14,15,16,17,18,19
23,24,25,26,27,28,29

IMO, Answer is D

Basshead · Answer

total days: 31

1-10 = 6 days (start from 04)
11-20 = 6 days (start from 14)
21-31 = 7 days (start from 23)

6 + 6 + 7 = 19

Answer is D.

Fdambro294 · Answer

The Set of Valid Codes ranges from:

01 ....... 02 ............30 ........31

Any Code that has a Units Digit > 3 will definitely NOT have a Valid "Transpose" (i.e., reversal of the Digits)

04 thru 09 ------> 6

14 thru 19 ------>6

24 thru 29 -------> 6

01 thru 03 ----> transpose valid
10 thru 13 -----> transpose valid
20 thru 22 ------> transpose valid

However, for the Number 23 --------> the Transpose would be the Number 32, which is INVALID --- Add +1 more Number to N

30 and 31 -----> transpose valid

N = 6 + 6 + 6 + 1 = 19 Numbers in which the "transpose" (reversal) of the Numbers will be Invalid

-D-

MathRevolution · Answer

Valid codes 04,05,06,07,08,09 will give invalid transpose. From 4 to 9 there are total 6 numbers.

Similarly, invalid codes will be formed from 14 to 19 and 24 to 29.

=> 6 * 3 = 18 numbers.

Number 23 will give invalid transpose (32).

=> 18 + 1 = 19

Answer D

daniformic · Answer

04,05,06,07,08,09
14,15,16,17,18,19
23,24,25,26,27,28,29

Answer is D

Pritishd · Answer

1. Considering there are only 30 numbers, we can quickly go through them and list the ones that meet the criterion

2. We are basically looking for transposes of numbers between 01, 02, 03, …, 31 (let's call this set x) that do belong to 01, 02, 03, …, 31. E.g. 13 belongs to the set x and its transpose 31 also belongs to set x. 17 belongs to set x but its transpose 71 does not belong to set x. In this question we are asked to list of examples such 17 in which the transpose does not belong to set x

3. 04, 05, 06, 07, 08, 09 | 14, 15, 16, 17, 18, 19 | 23, 24, 25, 26, 27, 28, 29 - A total of 19 numbers

Ans.  D

Vaishnavi12345 · Answer

found the answer 19, i.e. C by manually counting the numbers whose transpose exceeds 31. Any shortcut for this? Took me over 2.3 mins!

MBAB123 · Answer

You can/should look for patterns.
The units digit for numbers whose transpose exceeds 31 will start from 3 or 4 and go upto 9.
So from 1 to 10 - you'll have 6 numbers (4 - 9)
From 10-20 you'll have 6 numbers (14-19)
From 20-30 you'll have 7 numbers (23-29). 1 additional number here as transpose of 23 is 32 (this is catch you need to be vary of) 
 So 6+6+7 = 19

CrackverbalGMAT · Answer

The best way to solve is to find the no of valid codes having a valid transpose and subtract it from the total valid codes i.e 31 to get the number of valid codes with invalid transpose..

The valid codes that have valid transposes are:

01, 02, 03, 10, 11, 12, 13, 20, 21, 22, 30 and 31.

There are a total of 12 valid codes with valid transposes.
 We knew that the total valid codes are 31.

Then, no of valid codes with invalid transpose = 31 - 12= 19

Option D is the answer.

Thanks,
  Clifin J Francis,
GMAT SME

MonishaC · Answer

let transpose of a valid code xy be yx
y can take values 0123 only to be valid and x already has to be taking values 0123 as per the questions(the range is 01 to 31)
possible number of values yx can take is 4*4 = 16 
 invalid numbers (ie) 00,32,33,23(original code cannot be 32)is to be removed from the count.
16-4 = 12
valid codes where transposes are not valid is 31-12 = 19

thisisit25 · Answer

calculate numbers with valid transpose (T) instead and then remove.

numbers with 0 in tens place:
01, 02, 03 have valid T = three

numbers with 1 in tens place:
10, 11, 12, 13 have valid T = four

numbers with 2 in tens place:
20, 21, 22 have valid T = three

numbers with 3 in tens place:
30, 31 have valid T = two

Total = 3+4+3+2 = 12

Not valid = 31 (total codes) - 12 = 19

piyushnagre99 · Answer

#valid code & valid transpose =  01, 02, 03, 10, 11, 12, 13, 20, 21, 22, 30 and 31 ( total 12 ) 
 #valid codes =  31  
 #valid code & invalid transpose = 31 - 12 =  19  (option D)

A certain online form requires a 2-digit code for the day of the month

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A certain online form requires a 2-digit code for the day of the month

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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