can someone please explain..
is it 60?
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
Featured Course
Target Test Prep GMAT OnDemand
Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.
- 715+ score guarantee — highest in the industry (99th percentile)
- 52 chapters · 1,500+ lessons · 4,000+ practice questions
- 400 hours of video · 1,500+ instructor-led HD smartboard lessons
- 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
- 24/7 live support + weekly Zoom office hours with GMAT instructors
- TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
- 1,200+ flashcards + AI-powered study assistant & daily calendar
- OnDemand, LiveTeach & GMAT Bootcamp formats available
- Also: GRE, SAT Math & Executive Assessment courses
- MBA Admissions Consulting now available
- 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
- 200,000+ students served
- 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★
5.0
(559 reviews)
130-pt guarantee
$0 to start
then $127/mo
ps:pnc
Source: Beat The GMAT — Problem Solving |
-
manpsingh87
- Master | Next Rank: 500 Posts
- Posts: 436
- Thanked: 72 times
as you didn't specify what is palindrome in your question..so i will first of all like to give a bit definition of it..arjunshn wrote:How many 5 digit palindromes can be made using 1,2,3?
A palindrome is a word, phrase, number or other sequence of units that can be read the same way in either direction..!!
now coming to your number..!!!
case 1)
no. of palindromes that consist only one word e.g. 11111 would be 3, (other 2 would be 22222,33333);
case 2)
- - 1 - -; now first two and last two spaces must be same..;
21112;
12121;
13131;
31113;
23132;
32123;
- - 2 - -;
21212;
12221;
13231;
31213;
23232;
32223;
- - 3 - -;
21312;
12321;
13331;
31313;
23332;
32323;
hence total no. of palindrome would be 3+6+6+6=21;
O Excellence... my search for you is on... you can be far.. but not beyond my reach!
-
Stuart@KaplanGMAT
- GMAT Instructor
- Posts: 3225
- Location: Toronto
- Thanked: 1710 times
- GMAT Score:800
Not a real GMAT question (on the GMAT, "palindrome" would be defined, there would be more specificity regarding repeating numbers and, of course, there would be answer choices), but an interesting counting question nonetheless.arjunshn wrote:How many 5 digit palindromes can be made using 1,2,3?
Ignoring the actual numbers, let's use X, Y and Z to represent the 3 available digits and see how many patterns we can create.
XXXXX
(1 pattern * 3, since we can replace X with Y or Z, = 3 patterns)
XXYXX
XXZXX
(2 patterns * 3, since we can replace X with Y or Z and Y or Z with X, = 6 patterns)
XYYYX
XZZZX
XYZYX
XYXYX
XZYZX
XZXZX
(6 patterns *3, since we can replace X with Y or Z and Y or Z with X, = 18 patterns)
3 + 6 + 18 = 27 possible palindromes.
(manpsingh87 forgot about the second set of patterns above.)
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
-
manpsingh87
- Master | Next Rank: 500 Posts
- Posts: 436
- Thanked: 72 times
thanks a lot sir....!!!Stuart Kovinsky wrote:Not a real GMAT question (on the GMAT, "palindrome" would be defined, there would be more specificity regarding repeating numbers and, of course, there would be answer choices), but an interesting counting question nonetheless.arjunshn wrote:How many 5 digit palindromes can be made using 1,2,3?
Ignoring the actual numbers, let's use X, Y and Z to represent the 3 available digits and see how many patterns we can create.
XXXXX
(1 pattern * 3, since we can replace X with Y or Z, = 3 patterns)
XXYXX
XXZXX
(2 patterns * 3, since we can replace X with Y or Z and Y or Z with X, = 6 patterns)
XYYYX
XZZZX
XYZYX
XYXYX
XZYZX
XZXZX
(6 patterns *3, since we can replace X with Y or Z and Y or Z with X, = 18 patterns)
3 + 6 + 18 = 27 possible palindromes.
(manpsingh87 forgot about the second set of patterns above.)
O Excellence... my search for you is on... you can be far.. but not beyond my reach!
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Location: New York, NY
- Thanked: 13060 times
- GMAT Score:790
Using 1,2 and 3 only, we need to count how many ways we can build a 5-digit integer that is the same backwards and forwards, such as 12221, 32123, 22122, and so on.arjunshn wrote:How many 5 digit palindromes can be made using 1,2,3?
Ten-thousands digit can be 1,2, or 3 = 3 choices.
Units digit must be the same as the ten-thousands digit = 1 choice.
Thousands digit can be 1,2,or 3 = 3 choices.
Tens digit must be the same as the thousands digit = 1 choice.
Hundreds digit can be 1,2, or 3 = 3 choices.
To combine the number of choices for each digit, we multiply:
3*1*3*1*3 = 27.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
The key to solving such a question is to identify that we have to chose only three digits,
EITHER We chose the digits at the units, tens and the Hundredth place or we chose digits at the ten thousandth, thousandth and hundredth place -
Each of the digits can be chosen in 3 ways - i.e. the digits -1 or 2 or 3
thus the answer should be 3*3*3 = 27
EITHER We chose the digits at the units, tens and the Hundredth place or we chose digits at the ten thousandth, thousandth and hundredth place -
Each of the digits can be chosen in 3 ways - i.e. the digits -1 or 2 or 3
thus the answer should be 3*3*3 = 27
Using 1,2 and 3 only, we need to count how many ways we can build a 5-digit integer that is the same backwards and forwards, such as 12221, 32123, 22122, and so on.
Ten-thousands digit can be 1,2, or 3 = 3 choices.
Units digit must be the same as the ten-thousands digit = 1 choice.
Thousands digit can be 1,2,or 3 = 3 choices.
Tens digit must be the same as the thousands digit = 1 choice.
Hundreds digit can be 1,2, or 3 = 3 choices.
To combine the number of choices for each digit, we multiply:
3*1*3*1*3 = 27.
Thanks ! this is an awesome solution !
