NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 03:30 It is currently 26 Apr 2024, 03:30
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

A palindrome is a number that reads the same backward and forward, suc

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92929
Own Kudos [?]: 619104 [5]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
A palindrome is a number that reads the same backward and forward, suc [#permalink] New post   18 Jan 2022, 03:00
5
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

63% (03:19) correct 38% (03:04) wrong based on 48 sessions
Hide Show timer Statistics
A palindrome is a number that reads the same backward and forward, such as 545. What is the sum of all three-digit palindromes?

A. 49320
B. 49410
C. 49500
D. 49590
E. 49680


Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
C
User avatar
S
Kalpit1212
Manager
Manager
Joined: 25 Sep 2019
Posts: 57
Own Kudos [?]: 29 [1]
Given Kudos: 103
Send PM
Re: A palindrome is a number that reads the same backward and forward, suc [#permalink] New post   21 Jan 2022, 01:12
I doubt it could be solved in under 3minutes!.. Please let me know if there is a shorter method

for 100s, we have following palindromes... 101 and 111,121, 131.... 191. We can split this as 100+11, 100+21, 100+31.. sum of this is equal to 100*9 + 11+21+...91

Similarly for 2s, we have 202, 212, 222, 232, 242... 292.. We can again split this as 200+11+1, 200+21+2, 200+11+3... This will result in 200 + 11, 200 +21... 200 +91, + 9. Sum of this is 200*9 + 11+21+31...+91 + 9

For 300s, this will result in 300+11, 300+21, 300+21 + 2*9..

Going for other numbers, we will find a similar pattern. So we will have 4 APs altogether...

101+202+303+...+909 ; 900+1800+2700...+8100; 11+21+31+...+91; and 0+9+18+..+72. Note that 11+21+31+..+91 series is repeated 9 times so we need to multiply sum of this series by 9.

Sum of AP = Middle term * no. of terms

Hence,

Sum of
AP 1 = 505*9; AP 2 = 4500*9; AP 3 = 51*9*9; AP 4 = 36*9

= 9 * (505+4500+459+35)
= 9* (5500)
= 495000
(C) IMO
avatar
B
akb8386
Intern
Intern
Joined: 25 Nov 2021
Posts: 5
Own Kudos [?]: 13 [2]
Given Kudos: 115
Send PM
Re: A palindrome is a number that reads the same backward and forward, suc [#permalink] New post   21 Jan 2022, 02:30
1
Kudos
1
Bookmarks
There will be 9 such series 1a1, 2a2 …. 9a9

For the first one - there will be 10 numbers and the sum can be written as 100*(1+1…. 10 times)+ 10*(0+1+2…9) + (1+1….. 10 times)

For the others, the form will be similar

100x (2+2+2… 10 times) + 10x (0+1+2….9) + (2+2… 10 times)

So the sum can be written as 100*10*(1+2+3….9) + 10*9*(1+2+3…..9) + 10*(1+2…..9)

= 1000*45 + 90*45 + 10*45 = 45000 + 4050 + 450 = 49500 …. (C)

Posted from my mobile device
User avatar
G
ChakAvi
Intern
Intern
Joined: 27 Jul 2020
Posts: 36
Own Kudos [?]: 60 [0]
Given Kudos: 33
Location: India
Send PM
Re: A palindrome is a number that reads the same backward and forward, suc [#permalink] New post   21 Jan 2022, 02:48
[quote="Bunuel"]A palindrome is a number that reads the same backward and forward, such as 545. What is the sum of all three-digit palindromes?

A. 49320
B. 49410
C. 49500
D. 49590
E. 49680

101+111+121+...............+191
202+212+222+...............+292
303+313+323+...............+393
....+...+...+.....................+...
....+...+...+......................+...
909+919+929+................+999
(Each Column is in AP with c.d. =101 & has 9 terms, while Each row is in AP with c.d. 10 & has 10 terms)
......................................................

(505*9)+(515*9)+(525*9)............(595*9)
=9(505+515+...595)
=9*(545+555)*10/2
=49500
Answer C.

**I took way long time to arrive at this solution :? **
User avatar
B
Yeetyeti38
Intern
Intern
Joined: 16 May 2023
Posts: 13
Own Kudos [?]: 2 [2]
Given Kudos: 3
Send PM
Re: A palindrome is a number that reads the same backward and forward, suc [#permalink] New post   28 Mar 2024, 12:28
1
Kudos
1
Bookmarks
I just used the ap formula summation

all the palindromes can be written out as: 1_1, 2_2, 3_3...9_9
each of those blanks represents 10 possible numbers (any of the 10 digits), so there are 90 terms total
the average value is: 999+111=1100 -> 1100/2=550

550*90 = 49500
GMAT Club Bot
gmatclubot
Re: A palindrome is a number that reads the same backward and forward, suc [#permalink]
28 Mar 2024, 12:28
Moderators:
Bunuel
Math Expert
92929 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions