In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered

BTGmoderatorDC wrote: ↑

Mon Jan 27, 2020 5:42 pm

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

OA C

Source: Princeton Review

Since the codes must be ordered pairs, the length of coeds would be 2. Note that there is no restriction to not reuse the letters.

Say the minimum no. of letters needed is n, thus, the first letter for the code can be chosen in n ways; similarly, the second letter for the code can be chosen in n ways. Thus, the total no. of ways = n*n = n^2

=> n^2 ≥ 60 => minimum value of n = 8.

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorDC wrote: ↑

Mon Jan 27, 2020 5:42 pm

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



OA C

Source: Princeton Review

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 that 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