There is a set of 10 letters: A, B, C, D, E, F, G, H, I, J.

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AAPL: Moderator; Posts: 2644; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Tue Oct 31, 2017 9:52 am

There is a set of 10 letters: A, B, C, D, E, F, G, H, I, J. There are five-character and four-character codes to be made out of these letters. Each of the codes can use any of the 10 letters without repeating them in any one code. What is the ratio of the total number of possible five-character codes to the number of possible four-character codes?

(A) 1:6
(B) 1:5
(C) 5:1
(D) 6:1
(E) 10:1

The OA is D.

I don't understand this PS question. Please, can any expert explain it for me? Thanks.

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Source: Beat The GMAT — Problem Solving | Tue Oct 31, 2017 9:52 am

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by [email protected] » Tue Oct 31, 2017 10:00 am

Hi AAPL,

To calculate the number of 5-letter codes and 4-letter codes, we have to set up 2 permutations. There's a 'shortcut' though - since the answer choices are RATIOS, we don't actually have to calculate the total number of each type of code.

Total 5-letter codes = (10)(9)(8)(7)(6)
Total 4-letter codes = (10)(9)(8)(7)

Notice how the number of 5-letter codes is the total of 4-letter codes multiplied by 6. Thus, the ratio of codes is 6:1

Final Answer: D

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Rich

Contact Rich at [email protected]

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by Scott@TargetTestPrep » Tue Dec 17, 2019 7:32 pm

AAPL wrote:There is a set of 10 letters: A, B, C, D, E, F, G, H, I, J. There are five-character and four-character codes to be made out of these letters. Each of the codes can use any of the 10 letters without repeating them in any one code. What is the ratio of the total number of possible five-character codes to the number of possible four-character codes?

(A) 1:6
(B) 1:5
(C) 5:1
(D) 6:1
(E) 10:1

The OA is D.

I don't understand this PS question. Please, can any expert explain it for me? Thanks.

The number of 5-letter codes that can be made is 10P5 = 10 x 9 x 8 x 7 x 6, and the number of 4-letter codes that can be made is 10P4 = 10 x 9 x 8 x 7. Therefore, the ratio of 5-letter codes to 4-letter codes is:

(10 x 9 x 8 x 7 x 6)/(10 x 9 x 8 x 7) = 6/1

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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