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The security gate at a storage facility requires a fivE

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The security gate at a storage facility requires a fivE [#permalink] New post 23 Feb 2011, 21:05
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

67% (02:09) correct 33% (00:57) wrong based on 90 sessions
The security gate at a storage facility requires a five-digit lock code. If the lock code must consist only of digits from 1 through 7, inclusive, with no repeated digits, and the first and last digits of the code must be odd, how many lock codes are possible?

A. 120
B. 240
C. 360
D. 720
E. 1440
[Reveal] Spoiler: OA

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Re: 5-digit security code [#permalink] New post 24 Feb 2011, 03:16
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IndigoIntentions wrote:
The security gate at a storage facility requires a five-digit lock code. If the lock code
must consist only of digits from 1 through 7, inclusive, with no repeated digits, and
the first and last digits of the code must be odd, how many lock codes are possible?

a)120
b)240
c)360
d)720
e)1440


X-X-X-X-X --> there are 4 odd digits from 1 to 7, inclusive thus options for the first and the last X's are: 4-X-X-X-3. Other X's can take following values: 4-5-4-3-3 --> 4*5*4*3*3=720.

Answer: D.
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Re: 5-digit security code [#permalink] New post 24 Feb 2011, 03:21
Start with the most restricted digits first.

Digit #1: has to be odd => 4 possibilities (1,3,5,7)

Digit #5: has to be odd => 3 possiblities left (one possibility has already been used for digit #1)

Digit #2: any of the 7 possible digits (1,2,...7) less the 2 that have already been used for Digits #1 & #5 => 5 possibilities

Digit #3: any of the 7 possible digits (1,2,...7) less the 3 that have already been used for Digits #1, #2 & #5 => 4 possibilities

Digit #4: any of the 7 possible digits (1,2,...7) less the 4 that have already been used for Digits #1, #2, #3 & #5 => 3 possiblities

Thus, the number of possiblities is 4*3*5*4*3 = 720
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Re: 5-digit security code [#permalink] New post 24 Feb 2011, 03:57
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4 * 3 * 5!/2!

= 12 * (5 * 4 * 3* 2!)/2!

= 12 * 60 = 720

Answer D
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Re: 5-digit security code [#permalink] New post 18 Apr 2013, 21:17
Bunuel wrote:
IndigoIntentions wrote:
The security gate at a storage facility requires a five-digit lock code. If the lock code
must consist only of digits from 1 through 7, inclusive, with no repeated digits, and
the first and last digits of the code must be odd, how many lock codes are possible?

a)120
b)240
c)360
d)720
e)1440


X-X-X-X-X --> there are 4 odd digits from 1 to 7, inclusive thus options for the first and the last X's are: 4-X-X-X-3. Other X's can take following values: 4-5-4-3-3 --> 4*5*4*3*3=720.

Answer: D.


Hi bunuel,


I have a small doubt , why not we are considering that the first and last digit can occur in 2 ways and the middle 3 digits can occur in 6 ways.

for example middle 3 digits can be arranged in 3! ways among themselves after selecting 5c1 4c1 3c1 .

My question may be stupid, please correct my doubt.

Thanks
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Re: 5-digit security code [#permalink] New post 19 Apr 2013, 02:28
Expert's post
tarunjagtap wrote:
Bunuel wrote:
IndigoIntentions wrote:
The security gate at a storage facility requires a five-digit lock code. If the lock code
must consist only of digits from 1 through 7, inclusive, with no repeated digits, and
the first and last digits of the code must be odd, how many lock codes are possible?

a)120
b)240
c)360
d)720
e)1440


X-X-X-X-X --> there are 4 odd digits from 1 to 7, inclusive thus options for the first and the last X's are: 4-X-X-X-3. Other X's can take following values: 4-5-4-3-3 --> 4*5*4*3*3=720.

Answer: D.


Hi bunuel,


I have a small doubt , why not we are considering that the first and last digit can occur in 2 ways and the middle 3 digits can occur in 6 ways.

for example middle 3 digits can be arranged in 3! ways among themselves after selecting 5c1 4c1 3c1 .

My question may be stupid, please correct my doubt.

Thanks


Consider this: two digit code XX, each digit must be distinct and can be 1, 2 or 3.

First digit can take 3 values (1, 2, or 3) and the second can take 2 values, total 3*2=6 codes:
12
13
21
23
31
32.

Similarly, for the original question: the first digit can take 4 values and the last digit can take 3 values, total 4*3. The same way for the middle 3 digits: the second digit can take 5 values (7 minus two we already used for first and last), the third 4 and the fourth 3.

Total: (4*3)*5*4*3=720.

Hope it's clear.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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Re: The security gate at a storage facility requires a fivE [#permalink] New post 24 Apr 2013, 22:13
IndigoIntentions wrote:
The security gate at a storage facility requires a five-digit lock code. If the lock code must consist only of digits from 1 through 7, inclusive, with no repeated digits, and the first and last digits of the code must be odd, how many lock codes are possible?

A. 120
B. 240
C. 360
D. 720
E. 1440



1. There is one large group i.e., digits 1 through 7, from which 5 digits should be selected.
2. The first and the last digits have a constraint that they should be odd. There is also a general constraint that each digit should be different.
3. Considering the above constraints the first and the last digits can be selected in 4P2 ways. 4 because there are 4 odd digits out of which they can be selected and because there should be no repetition it is 4P2 ways for those 2 positions.
4. The second digit cannot have the same digit as the first and the last digit. Therefore it can be chosen out of 7-2=5 digits. Similarly the third digit cannot have the same digit as the first, second and last. So it can be chosen in 4 ways and the fourth digit similarly in 3 ways.
5. So the number of lock codes possible is 4P2 * 5* 4*3 = 720

Therefore the answer is D.
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Re: The security gate at a storage facility requires a fivE [#permalink] New post 20 Jun 2013, 16:23
We have four odd numbers in this set 1, 3, 5, 7

First digit is 4C1 = 4
Last digit is 3C1 = 3 (we have to exclude the odd digit selected in the previous step.

mid digits are 3 of the remaining 5 digits (2, 4 , 6, in addition to two not selected odd digits) for the 2nd, 3rd and 4th digits in the code

mid digits 5C3 = 60

4*60*3= 720

Answer is D
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Re: The security gate at a storage facility requires a fivE [#permalink] New post 25 Aug 2013, 02:56
Odd digits between 1 and 7
1 3 5 7 ==> 4
first and last place being fixed, can be filled with Odd number is
4* 5 *4* 3* 3

Total 720 combinations

Ans: D
Re: The security gate at a storage facility requires a fivE   [#permalink] 25 Aug 2013, 02:56
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