In a certain appliance store, each model of television

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Sat Mar 24, 2018 4:29 am

In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 60 different models of televisions, what is the minimum number of letters that must be used to make the codes?

A. 6
B. 7
C. 8
D. 9
E. 10

[spoiler]OA=C[/spoiler].

Should I use combinations or permutations? What is the best approach to solve this PS question?

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Source: Beat The GMAT — Problem Solving | Sat Mar 24, 2018 4:29 am

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by [email protected] » Sat Mar 24, 2018 10:11 am

Hi Gmat_mission,

We're told that each model of television is uniquely designated by a code made up of a particular ordered PAIR of letters and the store has 60 different models of televisions. We're asked for the minimum number of letters needed to make the 60 codes. Since the answers are numbers, we can use them 'against' the prompt and TEST THE ANSWERS.

To start, although this prompt does NOT state it, we're meant to assume that a letter CAN be used TWICE. For example, with the letters A and B, we could create 4 unique codes:
AA, AB, BA, BB

The question asks for the MINIMUM number of letters needed, so we'll start with the SMALLEST answer and work our way up...

Answer A: 6 letters --> with 6 letters, we could create (6)(6) = 36 codes. This is TOO SMALL though (we need to create 60 codes)

Answer B: 7 letters --> with 7 letters, we could create (7)(7) = 49 codes. This is TOO SMALL though (we need to create 60 codes)

Answer C: 8 letters --> with 8 letters, we could create (8)(8) = 64 codes. This covers the 60 codes we need to create, so this is the answer.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Thu Mar 29, 2018 3:02 pm

Gmat_mission wrote:In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 60 different models of televisions, what is the minimum number of letters that must be used to make the codes?

A. 6
B. 7
C. 8
D. 9
E. 10

We can analyze each answer choice, but we will start at 8 (choice C) first. (If 8 letters are too many, we will go lower; if they are too few, we will go higher.)

We will assume that we can repeat the letters since the problem doesn't say the letters can't be repeated. Thus the number of codes can be created using 8 letters is:

8 x 8 = 64

This is just enough for the 60 different models of televisions. If we go lower to 7, we will have 7 x 7 = 49, which is not enough for the 60 different models of televisions. So the answer must be 8.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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