Find all School-related info fast with the new School-Specific MBA Forum

It is currently 26 Jul 2014, 11:56

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A security agency assigns a two-digit code with distinct dig

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
User avatar
Joined: 01 Dec 2012
Posts: 39
Location: India
WE: Project Management (Retail)
Followers: 0

Kudos [?]: 11 [0], given: 10

A security agency assigns a two-digit code with distinct dig [#permalink] New post 04 Feb 2013, 04:58
Pemutations & Combinations Questions

Q1. A security agency assigns a two-digit code with distinct digits to each of its members using the digits 0,1,2,3....,9 such that the first digit of the code is not zero. However the code printed on a badge can potentially create confusion when read upside down. For example, the code 18 may appear as 81. How many codes are there for which there for which no such confusion can arise?
a. 69 b. 71 c. 81 d. 65 e. 68
[Reveal] Spoiler:
b


Q2. Find the number of ways of dividing 16 different books equally among
(i) 4 boys?
a. \frac{16!}{(4!)^4} b. \frac{16!}{(4!)^3} c. \frac{16!}{(4!)^5} d. \frac{16!}{4!}e. (4!)^4
[Reveal] Spoiler:
a


(ii) into 4 parcels?
a. \frac{16!}{(4!)^4} b. \frac{16!}{(4!)^3} c.\frac{16!}{(4!)^5} d. \frac{16!}{4!} e. (4!)^4
[Reveal] Spoiler:
c


Q3. Of twelve points on a plane, 5 points lie on a straight line and no other combination of 3 points lie on a straight line. Then, by joining these points how many quadrilaterals can be formed?
a. 495 b. 460 c. 490 d. 480 e. 420
[Reveal] Spoiler:
e


Q4. Let S be a set of all 5-digit numbers with distinct digits that can be formed using the digits 1,2,4,5 and 8 such that exactly two odd positions are occupied by the even digits. Find the sum of the digits in the rightmost position of all the numbers in S.
a. 296 b. 256 c. 316 d. 269 e. 329
[Reveal] Spoiler:
a


Q5. Ten points are plotted on a plane such that no three of them lie on a straight line. Four of these points are joined to each of the remaining six points and each of the remaining six points is joined to exactly five points. How many line segments are formed?
a. 28 b. 25 c. 29 d. 27 e. 24
[Reveal] Spoiler:
d


Q6. Using the first ten letters of the english alphabet how many strings of four letters can be formed such that each H is followed by B?
a. 6760 b. 6516 c. 6561 d. 240 e. 6805
[Reveal] Spoiler:
e


Q7. Mac has forgotten his friends 8-digit telephone number but remembers the following:
i) the first 3 digit are either 270 or 279.
ii) the digit 0 occurs exactly three times and the digit 9 occurs exactly one time.
iii) the number was an even number.
If he were to use a trial & error method to reach his friend, what is the minimum number of trials he has to make to be sure to succeed?
a. 1664 b. 1544 c. 832 d. 1280 e. 2000
[Reveal] Spoiler:
a


Q8. Two red, three balck & two white pencils are to be arrange in a row such that:
i) no two adjacent pencils are of the same color &
ii) the pencils at the two ends of the row are of same color.
In how many ways can the pencils be arranged?
a. 12 b. 8 c. 10 d. 9 e. 11
[Reveal] Spoiler:
c


Any shortcut for the above questions...??? pls help!!
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4579
Location: Pune, India
Followers: 1032

Kudos [?]: 4494 [0], given: 162

Re: A security agency assigns a two-digit code with distinct dig [#permalink] New post 04 Feb 2013, 19:46
Expert's post
pariearth wrote:
Pemutations & Combinations Questions

Q1. A security agency assigns a two-digit code with distinct digits to each of its members using the digits 0,1,2,3....,9 such that the first digit of the code is not zero. However the code printed on a badge can potentially create confusion when read upside down. For example, the code 18 may appear as 81. How many codes are there for which there for which no such confusion can arise?
a. 69 b. 71 c. 81 d. 65 e. 68
[Reveal] Spoiler:
b




First think of how the numbers change when the card is held upside down. The digit on the right comes to the left and the digit on the left goes to the right.

18 -> 81

Also the numbers turn upside down. Since 1 and 8 are symmetrical, turning them upside down doesn't change anything.
Now, 0, 1 and 8 are symmetrical. When you turn 6 upside down, it becomes 9 so it is a source of confusion too.
So how many numbers can create confusion? Since 0 cannot be on the left side in the number, a number that has 0 cannot create confusion (even if the 0 is on the right side, when you turn the card, it will come to the left which is not acceptable)
So the tens digit can take one of 4 values (1, 6, 8, 9) and the unit's digit can take one of the leftover 3 values in 4*3 = 12 ways
This 12 includes 69 and 96. Note that when you turn 69 upside down, it stays 69 (9 comes to the left and 6 goes to the right but 9 becomes 6 and 6 becomes 9)
Hence the numbers that can cause confusion = 12 - 2 = 10
Total numbers that can be formed = 9*9 = 81 (select tens digit in 9 ways and units in 9 ways)
No of numbers in which no confusion arises = 81 - 10 = 71
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Re: A security agency assigns a two-digit code with distinct dig   [#permalink] 04 Feb 2013, 19:46
    Similar topics Author Replies Last post
Similar
Topics:
1 Upset over the high-handedness of the security agencies, the getgyan 2 09 Oct 2012, 22:17
A company has assigned a distinct 3-digit code number to albany09 5 06 Oct 2008, 06:31
A company has assigned a distinct 3-digit code number to fiesta 4 01 Aug 2008, 04:13
A company has assigned a distinct 3-digit code number to gamjatang 1 24 Nov 2005, 04:30
A door can be opened only with a security code that consists cool_jonny009 8 14 Nov 2005, 18:53
Display posts from previous: Sort by

A security agency assigns a two-digit code with distinct dig

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.