stocks

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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Wed May 23, 2012 12:04 pm

All of the stocks on the over the counter market are designated by either a 4 letter or a 5 letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be desgnated with these codes?

1.2(26^5)
2.26(26^4)
3.27(26^4)
4.26(26^5)
5.27(26^5)

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Source: Beat The GMAT — Problem Solving | Wed May 23, 2012 12:04 pm

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Wed May 23, 2012 12:52 pm

GmatKiss wrote:All of the stocks on the over the counter market are designated by either a 4 letter or a 5 letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be desgnated with these codes?

A. 2(26^5)
B. 26(26^4)
C. 27(26^4)
D. 26(26^5)
E. 27(26^5)

Hi!

At first glance this may look like a permutations question, but it's actually an exponent question with a tiny bit of permutations thrown in.

Since there's no restriction on how many times we use each letter in each code, the number of possible 5 letter codes is simply 26^5 and the number of possible 4 letter codes is 26^4. Since we want the total number of possible codes, we sum those two numbers.

So, the question is really asking:

Which of the following is equivalent to 26^5 + 26^4?

There are simple rules for multiplying and dividing exponents, but no easy way to add or subtract them. The only time you can add or subtract exponents is when both the base and the power are the same - in that case, you simply add or subtract the coefficients.

For example: 3(x^4) + 7(x^4) = 10(x^4).

Accordingly, if we want to add or subtract exponents with the same base but different powers, we need to equalize the powers. We do so by factoring down to the smaller power.

Let's leave 26^4 alone and rewrite 26^5 as a multiple of 26^4:

26^5 = 26^1 * 26^4 = 26(26^4)

Now we can do our sum:

26^5 + 26^4 = 26(26^4) + 1(26^4) = 27(26^4)... choose C!

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed May 23, 2012 9:41 pm

GmatKiss wrote:All of the stocks on the over the counter market are designated by either a 4 letter or a 5 letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be desgnated with these codes?

1.2(26^5)
2.26(26^4)
3.27(26^4)
4.26(26^5)
5.27(26^5)

There are 26 alphabets, so in 4-digit code, each digit can take 26 values, so total number of 4-digits code possible = 26^4
Again for 5-digit code, each digit can take 26 values, so total number of 5-digits code possible = 26^5

Total = 26^4 + 26^5 = 26^4(1 + 26) = [spoiler]27 * 26^4[/spoiler]

The correct answer is C.

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

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