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

 It is currently 16 Nov 2018, 08:06

### 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

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

November 17, 2018

November 17, 2018

07:00 AM PST

09:00 AM PST

Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
• ### GMATbuster's Weekly GMAT Quant Quiz # 9

November 17, 2018

November 17, 2018

09:00 AM PST

11:00 AM PST

Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

# An employee identification code consists of a vowel followed by a 3-di

Author Message
TAGS:

### Hide Tags

Manager
Joined: 21 Sep 2012
Posts: 216
Location: United States
Concentration: Finance, Economics
Schools: CBS '17
GPA: 4
WE: General Management (Consumer Products)
An employee identification code consists of a vowel followed by a 3-di  [#permalink]

### Show Tags

10 Dec 2014, 02:24
1
14
00:00

Difficulty:

85% (hard)

Question Stats:

53% (02:42) correct 47% (02:54) wrong based on 135 sessions

### HideShow timer Statistics

An employee identification code consists of a vowel followed by a 3-digit number greater than 200. Exactly 2 of the 3 digits in the code should be identical. How many different codes is it possible to form?

A) 211
B) 216
C) 1075
D) 1080
E) 2160
Math Expert
Joined: 02 Sep 2009
Posts: 50619
An employee identification code consists of a vowel followed by a 3-di  [#permalink]

### Show Tags

10 Dec 2014, 04:02
3
6
desaichinmay22 wrote:
An employee identification code consists of a vowel followed by a 3-digit number greater than 200. Exactly 2 of the 3 digits in the code should be identical. How many different codes is it possible to form?

A) 211
B) 216
C) 1075
D) 1080
E) 2160

For the case when the hundreds digit is repeated: XXY or XYX
X can take 8 values (2, 3, 4, 5, 6, 7, 8, 9).
Y can take 9 values (10 digits minus the one we used for X).
To account for XXY or XYX case we are multiplying by 2.
So, for this case we'd have 8*9*2.

For the case when the tens and units digits are repeated: XYY
X can take 8 values (2, 3, 4, 5, 6, 7, 8, 9).
Y can take 9 values (10 digits minus the one we used for X).
Now, 8*9 also give number 200 and we need numbers greater than 200, so for this case we'd have 8*9 - 1.

Last step, since there are 5 vowels, then the final answer would be 5*(8*9*2 + 8*9 - 1) = 1,075.

Check Constructing Numbers, Codes and Passwords in our Special Questions Directory.
_________________
##### General Discussion
Senior Manager
Joined: 13 Jun 2013
Posts: 276
Re: An employee identification code consists of a vowel followed by a 3-di  [#permalink]

### Show Tags

10 Dec 2014, 04:13
1
desaichinmay22 wrote:
An employee identification code consists of a vowel followed by a 3-digit number greater than 200. Exactly 2 of the 3 digits in the code should be identical. How many different codes is it possible to form?

A) 211
B) 216
C) 1075
D) 1080
E) 2160

identification code will be of the type -,-,-,-
first digit can be selected from any of the 5 vowels in 5C1 ways

now for the remaining three digit lets consider the following two cases

case 1: when the number is greater than 200 but less than 300

number will be of the type 2,_,_. now suppose repeating number is same as first digit number i.e. 2. and the third number is one of the remaining 9 numbers (we are rejecting 2 here, because it will result in 222, which is not acceptable as per the given condition). thus these two number can arrange themselves in two blank spaces in 2! ways. hence total number of numbers in which repeating digit is same as the first digit = 1.9.2! =18

now, suppose that repeating number is different than first digit. thus possible case in this case are 8 as listed below:
211
233
244
255
266
277
288
299

here again we have rejected 200( because number must be greater than 200) and 222 ( exactly two repeating digits are allowed)

thus total possible cases are 18 + 8 =26

case 2: number ranging from 300 to 999
here for first digit we have 7 cases (3,4,5,6,7,8,9)
now if the repeating number is same as the first number then we will have 18 cases ( same reasoning as mentioned in the previous case)

if the repeating number is different than first digit number then we will have 9 cases ( because here number ending with two zeros are allowed)

hence total number of ways = 7(18+9) = 189

thus different number of codes = 5(189+26) = 1075

hence C
Intern
Joined: 27 Nov 2014
Posts: 49
Re: An employee identification code consists of a vowel followed by a 3-di  [#permalink]

### Show Tags

10 Dec 2014, 07:41
For the case when the tens and units digits are repeated: XYY
X can take 8 values (2, 3, 4, 5, 6, 7, 8, 9).
Y can take 9 values (10 digits minus the one we used for X).
Now, 8*9 also give number 200 and we need numbers greater than 200, so for this case we'd have 8*9 - 1.

Last step, since there are 5 vowels, then the final answer would be 5*(8*9*2 + 8*9 - 1) = 1,075.

--------------------------------------------------------------------------------------------------------------------------------------------------
Hi Bunuel

Can you plz explain the highlighted part why did we minus 1 and how does it gives number 200.

Regards
SG
Intern
Joined: 14 Jul 2014
Posts: 2
An employee identification code consists of a vowel followed by a 3-di  [#permalink]

### Show Tags

10 Dec 2014, 09:26
Can you plz explain the highlighted part why did we minus 1 and how does it gives number 200.

Regards
SG[/quote]

As X can take any number from (2, 3, 4, 5, 6, 7, 8, 9) and Y can take any number other than the one chosen for X.

So 200(X=2,Y=0,Y=0) is also included in 8*9 , hence we have to subtract 1
Intern
Joined: 19 Dec 2013
Posts: 11
GPA: 4
Re: An employee identification code consists of a vowel followed by a 3-di  [#permalink]

### Show Tags

10 Apr 2015, 12:22
Very elegant solution Bunuel. An alternate solution:

Required no. of ways (R)=Total no. of ways - (no. ways of ways when all digits are different + no. of ways when 3 digits are identical) -5 cases when vowel is combined with 200
R=5*8*10*10 - (5*8*9*8 + 5*8) - 5
= 5*8(100-72-1)-5
=40*27-5=1080-5=1075
Director
Joined: 07 Aug 2011
Posts: 539
GMAT 1: 630 Q49 V27
Re: An employee identification code consists of a vowel followed by a 3-di  [#permalink]

### Show Tags

10 Apr 2015, 21:11
1
1
desaichinmay22 wrote:
An employee identification code consists of a vowel followed by a 3-digit number greater than 200. Exactly 2 of the 3 digits in the code should be identical. How many different codes is it possible to form?

A) 211
B) 216
C) 1075
D) 1080
E) 2160

total number of 3-digit number greater than 200 are 799( 8*10*10 -1 )
numbers of the form XXX (all 3 repeated, 222, 333 ...) = 8
numbers of the form XYZ (all 3 digits different) =8*9*8 = 576
so numbers which will have 2 digit repeated are 799 - 8 - 576 = 215

finally considering 5 vowels we will have 5*215 = 1075 as answer
_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the to appreciate my post !!

Non-Human User
Joined: 09 Sep 2013
Posts: 8786
Re: An employee identification code consists of a vowel followed by a 3-di  [#permalink]

### Show Tags

12 Oct 2017, 10:18
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.
_________________
Re: An employee identification code consists of a vowel followed by a 3-di &nbs [#permalink] 12 Oct 2017, 10:18
Display posts from previous: Sort by