how many integers between

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msbelasco: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Fri Jul 27, 2012 10:18 am; Thanked: 1 times

by msbelasco » Sat Sep 08, 2012 11:53 am

How many integers between 324,700 and 458,600 have tens digit 1 and units digit 3?

(A) 10,300
(B) 10,030
(C) 1,353
(D) 1,352
(E) 1,339

Can someone please explain to me how to do this kind of problem? Thanks

Answer e

Last edited by msbelasco on Sat Sep 08, 2012 1:07 pm, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Sat Sep 08, 2012 11:53 am

rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Sat Sep 08, 2012 12:07 pm

How many integers between 324,700 and 458,600 have tens digit 1 and units digit 3?

The integers would be 324713,324813,324913,........,458513
The number of integers = 4585-3247+1 = 1338+1 = 1339

The answer should be E
Are you sure about the answer provided by you? :-/

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adthedaddy: Master | Next Rank: 500 Posts; Posts: 167; Joined: Fri Mar 09, 2012 8:35 pmFollowed by: 3 members; Thanked: 39 times

by adthedaddy » Sat Sep 08, 2012 12:41 pm

rijul007 wrote:How many integers between 324,700 and 458,600 have tens digit 1 and units digit 3?

The integers would be 324713,324813,324913,........,458513
The number of integers = 4585-3247+1 = 1338+1 = 1339

The answer should be E
Are you sure about the answer provided by you? :-/

Hi rijul,
I agree with you on the 1339 as answer... just clarify one thing -

I subtracted 324713 from 458513 and got it as 1338... why have you added a "1" to 1338 ?
Ofcourse as 1338 is not in the answer list, it has to be 1339 but plz help me with the logic of adding one to 1338.

"Your time is limited, so don't waste it living someone else's life. Don't be trapped by dogma - which is living with the results of other people's thinking. Don't let the noise of others' opinions drown out your own inner voice. And most important, have the courage to follow your heart and intuition. They somehow already know what you truly want to become. Everything else is secondary" - Steve Jobs

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rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Sat Sep 08, 2012 1:00 pm

adthedaddy wrote: Hi rijul,
I agree with you on the 1339 as answer... just clarify one thing -

I subtracted 324713 from 458513 and got it as 1338... why have you added a "1" to 1338 ?
Ofcourse as 1338 is not in the answer list, it has to be 1339 but plz help me with the logic of adding one to 1338.

Subtracting 324713 from 458513 does not include the integer 324713.

Lets say you want the number of integers from 1 to 10.
Number of integers would be 10-1+1. It is incremented by one to include the integer 1.

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msbelasco: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Fri Jul 27, 2012 10:18 am; Thanked: 1 times

by msbelasco » Sat Sep 08, 2012 1:09 pm

rijul007,
Thanks. You were right. I fixed the answer in the spoiler

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adthedaddy: Master | Next Rank: 500 Posts; Posts: 167; Joined: Fri Mar 09, 2012 8:35 pmFollowed by: 3 members; Thanked: 39 times

by adthedaddy » Sat Sep 08, 2012 2:28 pm

Subtracting 324713 from 458513 does not include the integer 324713.

Lets say you want the number of integers from 1 to 10.
Number of integers would be 10-1+1. It is incremented by one to include the integer 1.

Thanks for clarifying rijul

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Shalini Suresh: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Thu Dec 22, 2011 10:22 pmFollowed by: 1 member; Thanked: 4 times

by Shalini Suresh » Thu Sep 13, 2012 1:56 am

Hi Rijul

You have mentioned :
The integers would be 324713,324813,324913,........,458513
The number of integers = 4585-3247+1 = 1338+1 = 1339

how did you arrive at 4585-3247 ?
COuld you please explain the logic behind this ?

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subhash.sonu39: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Sun Aug 12, 2012 9:30 pmFollowed by: 1 member; Thanked: 2 times

by subhash.sonu39 » Thu Sep 13, 2012 3:57 am

Shalini Suresh wrote:Hi Rijul

You have mentioned :
The integers would be 324713,324813,324913,........,458513
The number of integers = 4585-3247+1 = 1338+1 = 1339

how did you arrive at 4585-3247 ?
COuld you please explain the logic behind this ?

Nice question, I want to ask the same question, I am not getting it correctly, please provide the results with proper solution.relations and functions

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Thu Sep 13, 2012 4:15 am

Shalini Suresh wrote:Hi Rijul

You have mentioned :
The integers would be 324713,324813,324913,........,458513
The number of integers = 4585-3247+1 = 1338+1 = 1339

how did you arrive at 4585-3247 ?
COuld you please explain the logic behind this ?

324713
324813
324913
325013
325113
......
......
458513
Let the first number in the sequence be a1 = 324713, last term = an = a1 +(n-1)* 100
Last term = 458513 = 324713 + (n-1)*100
458513 = 324713 + (n-1)*100
458513 - 324713 = (n-1)*100 - [This is what Rijul simplied, 458513 - 324713 = (n-1)*100; Subtracting 13 from the first term and adding 13 to the second term, 458500 - 324700 = (n-1)*100; 4585 - 3247 = (n-1)]
133800 = (n-1)*100
1338 = n -1
n = 1339

Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
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Shalini Suresh: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Thu Dec 22, 2011 10:22 pmFollowed by: 1 member; Thanked: 4 times

by Shalini Suresh » Thu Sep 13, 2012 5:07 am

Thanks Neelgandham .

I did not think of using AP to find n . Now I get it.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Sep 13, 2012 8:59 am

msbelasco wrote:How many integers between 324,700 and 458,600 have tens digit 1 and units digit 3?
(A) 10,300
(B) 10,030
(C) 1,353
(D) 1,352
(E) 1,339

Quick approach:

First: How many integers are there between (but not including) 324,700 and 458,600?
There are about 133,900 such integers (133,899 to be exact)
We want those integers that end in 13.
Example, 327,913

Now notice that 1 out of every 100 integers will end in 13.
So, of the approximately 133,900 integers in question, 1/100 of then will end in 13.
(133,900)/100 = 1339
Since no other answer choices are very close to 1339, E must be the answer.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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