GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Jun 2019, 08:24

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# A password of a computer used five digits where they are fro

Author Message
TAGS:

### Hide Tags

Intern
Status: MBA Aspirant
Joined: 24 Aug 2012
Posts: 40
Location: India
A password of a computer used five digits where they are fro  [#permalink]

### Show Tags

06 May 2014, 07:23
10
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:47) correct 32% (02:12) wrong based on 206 sessions

### HideShow timer Statistics

A password of a computer used five digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?

A. 1/32
B. 1/16
C. 1/8
D. 2/5
E. 1/2
Intern
Joined: 02 Nov 2013
Posts: 8

### Show Tags

06 May 2014, 07:47
4
We have five digits can be used for password -0,2,3,5,7.
Assuming that the numbers can be repeated any number of times in the password, probability of selecting any one of them is 5/10 (out of 10 digits from 0-9)
So, 5/10 * 5/10 * 5/10 * 5/10 * 5/10 =1/32 (A)
Intern
Status: MBA Aspirant
Joined: 24 Aug 2012
Posts: 40
Location: India

### Show Tags

06 May 2014, 07:55
How can we have probability for 1st digit as 5/10, if 0 gets selected at first place its no longer a 5 digit number...
Math Expert
Joined: 02 Sep 2009
Posts: 55631

### Show Tags

06 May 2014, 08:29
1
aniketb wrote:
A password of a computer used five digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?

A. 1/32
B. 1/16
C. 1/8
D. 2/5
E. 1/2

How can we have probability for 1st digit as 5/10, if 0 gets selected at first place its no longer a 5 digit number...

A 5-digit number cannot have 0 as its first digit while a 5-digit password can. For example, a password can be 00000.

Does this make sense?
_________________
Intern
Status: MBA Aspirant
Joined: 24 Aug 2012
Posts: 40
Location: India
Re: A password of a computer used five digits where they are fro  [#permalink]

### Show Tags

06 May 2014, 23:15
oh o..missed that. Thanks Bunuel.
Manager
Joined: 25 Apr 2014
Posts: 104
Re: A password of a computer used five digits where they are fro  [#permalink]

### Show Tags

27 Jun 2014, 16:36
For sure a stupid question but still... why are we not doing a 10C5 here for total possible outcomes ?
Math Expert
Joined: 02 Sep 2009
Posts: 55631
Re: A password of a computer used five digits where they are fro  [#permalink]

### Show Tags

28 Jun 2014, 04:58
1
1
maggie27 wrote:
For sure a stupid question but still... why are we not doing a 10C5 here for total possible outcomes ?

For two reasons.

1. 10C5 gives the number of groups of 5 possible out of 10 when the order of the selection is not important. In passwords the order of the numbers is important

2. 10C5 gives 5 different numbers out of 10, while the numbers in passwords can be repeated.

Thus the total number of passwords is 10*10*10*10*10 (10 options for each of the 5 digits we have in the password).

Hope it's clear.
_________________
Manager
Joined: 25 Apr 2014
Posts: 104
Re: A password of a computer used five digits where they are fro  [#permalink]

### Show Tags

28 Jun 2014, 07:13
Thank You so much Bunuel
Director
Joined: 23 Jan 2013
Posts: 547
Schools: Cambridge'16
Re: A password of a computer used five digits where they are fro  [#permalink]

### Show Tags

29 Sep 2014, 22:43
I got stuck looking for combination approach here, it was tempting. After shifting direct probability easily found that
it is just
(1/2)^5=1/32

i thing direct method is better anyway
Current Student
Status: Remember to Always Think Twice
Joined: 04 Nov 2014
Posts: 54
Location: India
GMAT 1: 740 Q49 V40
GPA: 3.51
Re: A password of a computer used five digits where they are fro  [#permalink]

### Show Tags

24 Feb 2016, 07:33
good question.. but it should be given that the numbers may repeat.
_________________
breathe in.. and breathe out!
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6522
Location: United States (CA)
Re: A password of a computer used five digits where they are fro  [#permalink]

### Show Tags

10 May 2018, 10:42
1
aniketb wrote:
A password of a computer used five digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?

A. 1/32
B. 1/16
C. 1/8
D. 2/5
E. 1/2

The total number of ways to select 5 digits to form a 5-digit password is 10^5. The number of ways to select the 5 digits that are either a prime (2, 3, 5, 7) or zero is 5^5. Therefore, the probability is 5^5/10^5 = (5/10)^5 = (1/2)^5 = 1/32.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Joined: 12 Jan 2017
Posts: 10
Re: A password of a computer used five digits where they are fro  [#permalink]

### Show Tags

22 May 2018, 05:03
How do we know whether the repetition of ghe digits are allowed or not.
Math Expert
Joined: 02 Sep 2009
Posts: 55631
Re: A password of a computer used five digits where they are fro  [#permalink]

### Show Tags

22 May 2018, 05:38
lincy93 wrote:
How do we know whether the repetition of ghe digits are allowed or not.

Restriction that the repetition is not allowed is not given so we can assume that it's allowed though proper GMAT question would make this issue clearer.
_________________
Manager
Joined: 18 Dec 2018
Posts: 50
Re: A password of a computer used five digits where they are fro  [#permalink]

### Show Tags

18 Dec 2018, 23:21
Total possible ways of designing a password = 105ways.
No of 0’s and prime no between 0 and 9 = 5 (1,2,3,5,7)
So, The probability of favorable arrangements = 105/55 = 1/32.
CEO
Joined: 18 Aug 2017
Posts: 3838
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: A password of a computer used five digits where they are fro  [#permalink]

### Show Tags

16 May 2019, 09:04
aniketb wrote:
A password of a computer used five digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?

A. 1/32
B. 1/16
C. 1/8
D. 2/5
E. 1/2

total such no
0,2,3,5,7
5/10 ; 1/2
for 5 digits; (1/2)^5 = 1/32
IMOA
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Re: A password of a computer used five digits where they are fro   [#permalink] 16 May 2019, 09:04
Display posts from previous: Sort by