BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Permutations Problem

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 379
Joined: Wed Jun 03, 2009 3:05 am
Thanked: 19 times
Followed by:1 members
GMAT Score:690

Permutations Problem

by sreak1089 » Wed Jan 20, 2010 12:18 am
A telephone company wanted to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. If the company used 122 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 124 signs?

A) 246
B) 248
C) 492
D) 15128
E) 30256
Top
Source: — Problem Solving |
User avatar
MBA Student
Posts: 403
Joined: Tue Dec 22, 2009 7:32 pm
Thanked: 98 times
Followed by:22 members

by fibbonnaci » Wed Jan 20, 2010 12:53 am
each letter can take 122 different signs.
total ways of forming 2 letters is 122*122

Now if the company wants to use 124 signs, then for 2 letters ,
total number of ways = 124*124.

Difference= (124)^2 - (122)^2
= (124+ 122) (124-122)
= 246*2 => 492 additional area codes can be created.

Answer = C
Top
Master | Next Rank: 500 Posts
Posts: 379
Joined: Wed Jun 03, 2009 3:05 am
Thanked: 19 times
Followed by:1 members
GMAT Score:690

by sreak1089 » Wed Jan 20, 2010 7:55 am
I am not able to figure out, how you got 122*122? can you please elaborate?

Is it because, you have 122 signs for the first letter and for each of the 122 letters you can have further 122 signs right?

To make it simple, let's say you have only 3 symbols (assume a, b, c) if you have two letter code then you have:

aa ba ca
ab bb cb
ac bc cc

Thus, 3 * 3 = 9 ways.

I thinking I am getting it, Am I correct?[/img]
Top
User avatar
MBA Student
Posts: 403
Joined: Tue Dec 22, 2009 7:32 pm
Thanked: 98 times
Followed by:22 members

by fibbonnaci » Wed Jan 20, 2010 7:58 am
exactly.
for the first letter- you have 3 ways.(a, b, c)
and for the next letter similiar 3 ways.
so total 3*3 ways.

Hope i have clarified ur doubt!
Top
Master | Next Rank: 500 Posts
Posts: 379
Joined: Wed Jun 03, 2009 3:05 am
Thanked: 19 times
Followed by:1 members
GMAT Score:690

by sreak1089 » Wed Jan 20, 2010 8:17 am
Yes, sir you have. Thank you so much.
fibbonnaci wrote:exactly.
for the first letter- you have 3 ways.(a, b, c)
and for the next letter similiar 3 ways.
so total 3*3 ways.

Hope i have clarified ur doubt!
Top
Post new topic Post Reply
• Page 1 of 1