| | Notices | Welcome to the PaGaLGuY.com MBA forums. You are currently viewing our boards as a guest which gives you limited access to view most discussions and access our other features. By joining our free community you will have access to post topics, communicate privately with other members (PM), respond to polls, upload content and access many other special features. Registration is fast, simple and absolutely free so please, join our community today! If you have any problems with the registration process or your account login, please contact us at info [at] pagalguy.com | Quantitative Questions and Answers Discuss Quantitative and other Math related questions. Post your math doubts and get it solved by the smartest brains this side of the universe ! | | | |
has no status.
Addicted PaGaL
Status: Offline Posts: 1,118 Thanks: 613
Thanked 586 Times in 287 Posts
Join Date: Feb 2007 Location: Hyd->Chn-> Del | Re: The Official CAT 2007 Quant Thread -
07-11-2007, 11:13 AM
Quote:
Originally Posted by getneonow  How many 7's are used in writing out all the positive integers from 1 to 10^8?
1)3 *10^7
2)10^7
3)7*10^7
4)8*10^7
5)6*10^7
Neo | No of 7s or 8s etc from 1 to 10^n is
n*10^(n-1).
NOTE :
1. This formula is applicable only when we have to find till 10^n. For other nos, we need to find till the nearest 10^n and then do the manual calculation.
2. If the no of 1s is asked, the answer is n*10^(n-1) + 1 ( The addlnal 1 bcos 10^n wud have the extra one.
At the age of 20 we always think of what others think of us; At the age of 40 we don’t care what others think of us; At the age of 60 we realize that nobody has been thinking of us Energy saved is equal to twice the energy produced. Save energy. | | | | | The Following 3 Users Say Thank You to kondapalli For This Useful Post: | | | | | |
has no status.
Newbie PaGaL
Status: Offline Posts: 3 Thanks: 0
Thanked 2 Times in 1 Post
Join Date: Feb 2005 Location: Noida Age: 24 | Re: The Official CAT 2007 Quant Thread -
07-11-2007, 11:38 AM
Quote:
Originally Posted by getneonow 304 is the right answer.. 
Hats off to ur patience dude..i just gave up understanding the complexity of the problem
Neo | Guess there's a easier approcah...u just need to check how many times a digit occurs at each position (100s, 10s and units)..
For first 299 numbers:
SOD = 100*(1+2) + 3*10*(1+2+3+...9) + 3*10*(1+2+3+..9)
(3 being for each of the hundres and units place each digit occurs 10 times in a hundred..)
= 300 + 2*30*45
= 300+2700
= 3000
Now moving from here to any of the options is easy...304 in this case strikes answer soon with 325 (3000 + 3*5 + 1+2+3+4) !! | | | | | The Following 2 Users Say Thank You to Man of Lamancha For This Useful Post: | | | | | |
has no status.
Expert PaGaL
Status: Offline Posts: 231 Thanks: 549
Thanked 106 Times in 65 Posts
Join Date: May 2007 Location: Bokaro | Re: The Official CAT 2007 Quant Thread -
07-11-2007, 11:56 AM
Quote:
Originally Posted by kondapalli No of 7s or 8s etc from 1 to 10^n is
n*10^(n-1).
NOTE :
1. This formula is applicable only when we have to find till 10^n. For other nos, we need to find till the nearest 10^n and then do the manual calculation.
2. If the no of 1s is asked, the answer is n*10^(n-1) + 1 ( The addlnal 1 bcos 10^n wud have the extra one. | it means
there r 20 (2 , 3 ,4 etc between 1 & 100
also, 300 ...........between 1 & 1000
etc
plz. confirm | | | | | | | |
SOM rocks!!!!!!
Addicted PaGaL
Status: Offline Posts: 1,049 Thanks: 701
Thanked 744 Times in 340 Posts
Join Date: May 2006 Location: delhi Age: 25 | Re: The Official CAT 2007 Quant Thread -
07-11-2007, 12:53 PM
Konda bhai Please solve this then.......
No of 3s required written from 1 to 1500....... | | | | | | | |
has no status.
Trainee PaGaL
Status: Offline Posts: 30 Thanks: 4
Thanked 20 Times in 11 Posts
Join Date: Jul 2005 Age: 22 | Re: The Official CAT 2007 Quant Thread -
07-11-2007, 01:09 PM
Quote:
Originally Posted by junoonmba Konda bhai Please solve this then.......
No of 3s required written from 1 to 1500....... | from 1 -1500, we can count the desired number of 3's taking units, tens and hundreds digits into consideration.
For units digit alone, number of 3's range from 3,13,.........1493
therefore total number of 3's in units place = [(1493-3)/10] +1 = 150
For tens place, numbers can range from 30,31,...,130,...1439
Total number of 3's in tens place = 10*[(1430-30)/100] = 150
For the hundreds place, we have 300-399 = 100 numbers
1300-1399 = 100 numbers
Therefore total no: of 3's = 500
| | | | | | | |
..Filling Fire in Lungs
Hardcore PaGaL
Status: Offline Posts: 587 Thanks: 556
Thanked 489 Times in 209 Posts
Join Date: Aug 2005 Location: Hyderabad | Re: The Official CAT 2007 Quant Thread -
07-11-2007, 01:50 PM
Quote:
Originally Posted by kondapalli No of 7s or 8s etc from 1 to 10^n is
n*10^(n-1).
NOTE :
1. This formula is applicable only when we have to find till 10^n. For other nos, we need to find till the nearest 10^n and then do the manual calculation.
2. If the no of 1s is asked, the answer is n*10^(n-1) + 1 ( The addlnal 1 bcos 10^n wud have the extra one. | Konda bhai ..according to ur formula No. of 7's from 1 to 10^8 = 8*10^7
BUT the given ans is 7*10^7 !! 
plz confirm the answer.
Neo | | | | | | | |
SOM rocks!!!!!!
Addicted PaGaL
Status: Offline Posts: 1,049 Thanks: 701
Thanked 744 Times in 340 Posts
Join Date: May 2006 Location: delhi Age: 25 | Re: The Official CAT 2007 Quant Thread -
07-11-2007, 01:51 PM
Quote:
Originally Posted by the_fence_crosser from 1 -1500, we can count the desired number of 3's taking units, tens and hundreds digits into consideration.
For units digit alone, number of 3's range from 3,13,.........1493
therefore total number of 3's in units place = [(1493-3)/10] +1 = 150
For tens place, numbers can range from 30,31,...,130,...1439
Total number of 3's in tens place = 10*[(1430-30)/100] = 150
For the hundreds place, we have 300-399 = 100 numbers
1300-1399 = 100 numbers
Therefore total no: of 3's = 500 | Check the red part.... | | | | | | | |
..Filling Fire in Lungs
Hardcore PaGaL
Status: Offline Posts: 587 Thanks: 556
Thanked 489 Times in 209 Posts
Join Date: Aug 2005 Location: Hyderabad | Re: The Official CAT 2007 Quant Thread -
07-11-2007, 01:53 PM
While kondapalli confirms the ans to the prev qn, here's the next one
How many composite numbers between 420 and 715 are co prime to 420 as well as 715?
1)12
2)8
3)10
4)9
5)11
Neo | | | | | | | |
has no status.
Trainee PaGaL
Status: Offline Posts: 30 Thanks: 4
Thanked 20 Times in 11 Posts
Join Date: Jul 2005 Age: 22 | Re: The Official CAT 2007 Quant Thread -
07-11-2007, 02:01 PM
Quote:
Originally Posted by junoonmba Check the red part.... | The red part amounts to counting number of 3's in tens place.
from 30-39, there are 10 3's
so are 10 3's from 130-139, 230-239, etc....
therefore total no: of 3's = 10 times the number of 3's in tens place in the series [30, 130,.....1430] Therefore, total no: of 3's in Tens place = 10[{(1430-30)/100} +1] = 150
I had missed typing the '+1' inside the bracket in my previous post
| | | | | | | |
has no status.
Trainee PaGaL
Status: Offline Posts: 30 Thanks: 4
Thanked 20 Times in 11 Posts
Join Date: Jul 2005 Age: 22 | Re: The Official CAT 2007 Quant Thread -
07-11-2007, 02:10 PM
Quote:
Originally Posted by getneonow While kondapalli confirms the ans to the prev qn, here's the next one
How many composite numbers between 420 and 715 are co prime to 420 as well as 715?
1)12
2)8
3)10
4)9
5)11
Neo | 5)11
the nos: being 437,493,527,529,551,589,629,667,697,703,713
Last edited by the_fence_crosser; 07-11-2007 at 02:26 PM..
| | | | | The Following User Says Thank You to the_fence_crosser For This Useful Post: | | | Thread Tools | | | | Display Modes |  Linear Mode | 
Posting Rules
| You may not post new threads You may not post replies You may not post attachments You may not edit your posts
HTML code is Off | | | |
| |
