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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

GMAT MATH

by BTGmoderatorRO » Fri Dec 29, 2017 4:53 am

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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

OA is C

Do I need a special formula to solve this? An Expert.

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Source: Beat The GMAT — Problem Solving | Fri Dec 29, 2017 4:53 am

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Tue Jan 02, 2018 9:34 am

Roland2rule 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

OA is C

Do I need a special formula to solve this? An Expert.

Since you can use either a 4 letter symbol or a 5 letter symbol, you add the number of symbols for each.

Since the question doesn't say a letter can't be used more than once, you are free to use any of the 26 letters in each position.

So, the number of four letter symbols is 26*26*26*26 = 26^4

The number of 5 letter symbols is as above multiplied by one more 26, or 26^5.

Adding the two gives the correct answer 26^4 + 26^5. Notice that this is not among the correct answers. Don't give up hope.

Factor out the 26^4 and rewrite: 26^4(1+26) = [spoiler](26^4)*27, C[/spoiler]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Aug 14, 2019 4:31 pm

BTGmoderatorRO 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

OA is C

Do I need a special formula to solve this? An Expert.

We need to determine the maximum number of different stocks that can be designated by a 4-letter or a 5-letter code that is created by using the 26 letters of the alphabet.

Number of 5-letter codes:

26 x 26 x 26 x 26 x 26 = 26^5

Number of 4-letter codes:

26 x 26 x 26 x 26 = 26^4

Since the stocks can be designated by a 4-letter OR 5-letter code, we must add our results together to determine the maximum number of codes that can be created. We note that 26^4 is a common factor of both 26^5 and 26^4, so we have:

26^5 + 26^4 = 26^4(26 + 1) = 26^4(27)

Answer: C

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