How many options are there for license plate number if each

This topic has expert replies
Moderator
Posts: 2505
Joined: Sun Oct 15, 2017 1:50 pm
Followed by:6 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Source: Economist GMAT

How many options are there for license plate numbers if each license plate can include 2 digits and 3 letters (in that order), or 3 digits and 2 letters (in that order)? (Note: there are 26 letters in the alphabet)

A. \(360\cdot 260^2\)
B. \(36\cdot 260^2\)
C. \(36\cdot 270^2\)
D. \(10^2 \cdot 26^3\)
E. \(10^3 \cdot 26^2\)

The OA is B
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Sat May 04, 2019 9:10 pm
BTGmoderatorLU wrote:Source: Economist GMAT

How many options are there for license plate numbers if each license plate can include 2 digits and 3 letters (in that order), or 3 digits and 2 letters (in that order)? (Note: there are 26 letters in the alphabet)

A. \(360\cdot 260^2\)
B. \(36\cdot 260^2\)
C. \(36\cdot 270^2\)
D. \(10^2 \cdot 26^3\)
E. \(10^3 \cdot 26^2\)

The OA is B
Number of ways each license plate can include 2 digits and 3 letters (in that order) = 10^2 * 26^3; (there are 10 digits, incl 0; note that digits and alphabets can repeat)

Number of ways each license plate can include 3 digits and 2 letters (in that order) = 10^3 * 26^2

Total number of ways = 10^2 * 26^3 + 10^3 * 26^2 = 10^2 * 26^2(26 + 10) = 36 * 10^2 * 26^2 = 36 * 260^2

The correct answer: B

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: GRE Manhattan | ACT Tutoring Houston | SAT Prep Courses Seattle | Charlotte IELTS Tutoring | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

GMAT/MBA Expert

User avatar
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 » Thu May 16, 2019 6:56 pm
BTGmoderatorLU wrote:Source: Economist GMAT

How many options are there for license plate numbers if each license plate can include 2 digits and 3 letters (in that order), or 3 digits and 2 letters (in that order)? (Note: there are 26 letters in the alphabet)

A. \(360\cdot 260^2\)
B. \(36\cdot 260^2\)
C. \(36\cdot 270^2\)
D. \(10^2 \cdot 26^3\)
E. \(10^3 \cdot 26^2\)

The OA is B
The number of ways to create the license plate with 2 digits followed by 3 letters is 10^2 x 26^3.

The number of ways to create the license plate with 3 digits followed by 2 letters is 10^3 x 26^2.

So we have:

10^2 x 26^3 + 10^3 x 26^2

This expression is not one of the answer choices, so we simplify it by factoring the common (10^2) and (26^2) from each term. Thus, we have:

10^2 x 26^2 x (26 + 10) = (26^2)(10^2)(36) = (260^2)(36)

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage