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All employees at Company W are assigned unique employee ID

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Author Message
TAGS:
CEO
CEO
User avatar
Joined: 07 Jun 2014
Posts: 3819
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 72

Kudos [?]: 1217 [0], given: 257

CAT Tests
All employees at Company W are assigned unique employee ID [#permalink] New post 30 Dec 2017, 13:56
Expert's post
00:00

Question Stats:

66% (01:10) correct 33% (03:26) wrong based on 3 sessions
All employees at Company W are assigned unique employee ID codes that consist of numbers and letters from the alphabet. If letters can be repeated within the same code but numbers
cannot, which of the following must be true?

A. There are 2,600 possible different 3 digit codes consisting of 1 letter and 2 digits.
B. There are 60,840 possible different 4 digit codes consisting of 2 letters and 2 numbers.
C. There are 650 possible 2 digit codes consisting of 1 letter and 1 digit.

Drill 2
Question: 12
Page: 565

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Sandy
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1 KUDOS received
CEO
CEO
User avatar
Joined: 07 Jun 2014
Posts: 3819
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 72

Kudos [?]: 1217 [1] , given: 257

CAT Tests
Re: All employees at Company W are assigned unique employee ID [#permalink] New post 12 Jan 2018, 15:35
1
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KUDOS
Expert's post
Explanation

This is a permutation problem, so lay out your slots to fill and then multiply.

For choice (A) you have 1 slot for a letter and two slots for digits. There are 26 choices for your letter and 10 choices for your first digit. Because you can’t repeat digits, there are 9 choices for your second digit. Thus, the number of different codes that can be made is 26 × 10 × 9 = 2,340.Eliminate choice (A).

For correct choice (B), you have two spots for letters and two for digits, so you have 26 × 26 (letters can repeat) × 10 × 9 = 60,840.

Choice (C) is incorrect because the number of different codes consisting of one letter and one digit is 26 × 10 = 260. The only correct answer is choice (B).
_________________

Sandy
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Re: All employees at Company W are assigned unique employee ID   [#permalink] 12 Jan 2018, 15:35
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All employees at Company W are assigned unique employee ID

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