BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

A palindrome is a number that reads the same forward and

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2599
Joined: Sun Oct 29, 2017 2:08 pm
Followed by:2 members

A palindrome is a number that reads the same forward and

by AAPL » Tue Dec 11, 2018 5:04 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

GMAT Prep

A palindrome is a number that reads the same forward and backward. For example. 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits, 1, 2, 3, how many such palindromes are possible?

A. 12
B. 15
C. 18
D. 24
E. 27

OA E.
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pm
Thanked: 59 times
Followed by:33 members

by fskilnik@GMATH » Tue Dec 11, 2018 6:37 am
AAPL wrote:GMAT Prep

A palindrome is a number that reads the same forward and backward. For example. 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits, 1, 2, 3, how many such palindromes are possible?

A. 12
B. 15
C. 18
D. 24
E. 27
$$\matrix{
{\underline {{\rm{A}}\,\,{\rm{free}}} } \cr
3 \cr

} \,\,\,\matrix{
{\underline {{\rm{B}}\,\,{\rm{free}}} } \cr
3 \cr

} \,\,\,\matrix{
{\underline {{\rm{C}}\,{\rm{free}}} } \cr
3 \cr

} \,\,\,\matrix{
{\underline {{\rm{D}}\,{\rm{ = }}\,{\rm{B}}\,{\rm{copy}}} } \cr
1 \cr

} \,\,\,\matrix{
{\underline {{\rm{E}}\,{\rm{ = }}\,{\rm{A}}\,{\rm{copy}}} } \cr
1 \cr

} \,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = {3^3} = 27$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Tue Dec 11, 2018 7:27 am
A palindrome is a number that reads the same forward and backward. For example. 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits, 1, 2, 3, how many such palindromes are possible?

A) 12
B) 15
C) 18
D) 24
E) 27
Take the task of building palindromes and break it into stages.

Stage 1: Select the ten-thousands digit
We can choose 1, 2, or 3
So, we can complete stage 1 in 3 ways

Stage 2: Select the thousands digit
We can choose 1, 2, or 3
So, we can complete stage 2 in 3 ways

Stage 3: Select the hundreds digit
We can choose 1, 2, or 3
So, we can complete stage 3 in 3 ways

IMPORTANT: At this point, the remaining digits are already locked in.

Stage 4: Select the tens digit
This digit must be the SAME as the thousands digit (which we already chose in stage 2)
So, we can complete this stage in 1 way.

Stage 5: Select the units digit
This digit must be the SAME as the ten-thousands digit (which we already chose in stage 1)
So, we can complete this stage in 1 way.

By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus build a 5-digit palindrome) in (3)(3)(3)(1)(1) ways (= 27 ways)

Answer: E
--------------------------

Note: the FCP can be used to solve the majority of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat-counting?id=775

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html
- https://www.beatthegmat.com/mouse-pellets-t274303.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/ps-counting-t273659.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/please-solve ... 71499.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/laniera-s-co ... 15764.html

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

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 » Fri Mar 15, 2019 5:35 pm
AAPL wrote:GMAT Prep

A palindrome is a number that reads the same forward and backward. For example. 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits, 1, 2, 3, how many such palindromes are possible?

A. 12
B. 15
C. 18
D. 24
E. 27

OA E.
We have 3 options for the first digit, 3 options for the second, 3 options for the third, 1 option for the fourth (since it has to be the same as the second), and 1 option for the fifth (since it has to be the same as the first). Thus, there are 3 x 3 x 3 = 27 possible palindromes.

Answer: E

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
Top
Post new topic Post Reply
• Page 1 of 1