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How many integers between 324,700 and 458,600 have tens digit 2 and

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IrinaOK
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How many integers between 324,700 and 458,600 have tens digit 2 and [#permalink] How many integers between 324,700 and 458,600 have tens digit 2 and   Updated on: 21 May 2015, 10:22
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How many integers between 324,700 and 458,600 have tens digit 2 and units digit 1?

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

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A

Originally posted by IrinaOK on 14 Oct 2007, 00:39.
Last edited by Bunuel on 21 May 2015, 10:22, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Bunuel
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Re: How many integers between 324,700 and 458,600 have tens digit 2 and [#permalink] How many integers between 324,700 and 458,600 have tens digit 2 and   08 Jul 2010, 06:46
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bibha
How many integers between 324,700 and 458,600 have a 2 in the tens digit and a 1 in the units digit?
A 1,339
B 1,352
C 1,353
D 10,030
E 10,300

There is one number in hundred with 2 in th tens digit and 1 in the units digit: 21, 121, 221, 321, ...

The difference between 324,700 and 458,600 is 458,600-324,700=133,900 - one number per each hundred gives 133,900/100=1,339 numbers.

Answer: A.

Hope it's clear.
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Re: How many integers between 324,700 and 458,600 have tens digit 2 and [#permalink] How many integers between 324,700 and 458,600 have tens digit 2 and   14 Oct 2007, 01:00
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Using the probability method

N = 458,600 – 324,700 = 133,900
P = 1/10*1/10 = 1/100.

P*N = 1/100*133,900 = 1,339

And the answer is (A)

:)
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Re: How many integers between 324,700 and 458,600 have tens digit 2 and [#permalink] How many integers between 324,700 and 458,600 have tens digit 2 and   14 Oct 2007, 12:43
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Re: How many integers between 324,700 and 458,600 have tens digit 2 and [#permalink] How many integers between 324,700 and 458,600 have tens digit 2 and   08 Jul 2010, 08:03
Hey,
Great thinking.
Thx.
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Re: How many integers between 324,700 and 458,600 have tens digit 2 and [#permalink] How many integers between 324,700 and 458,600 have tens digit 2 and   08 Jul 2010, 12:51
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bibha
How many integers between 324,700 and 458,600 have a 2 in the tens digit and a 1 in the units digit?
A 1,339
B 1,352
C 1,353
D 10,030
E 10,300

Find the number of integers between the two.

458600-324700 = 133900. Now we need to figure out how many instances there will be a 2 in the tens and a 1 in the units. The easiest way to do this is to see that per 100 integers (0-100) only 21 suffices the conditions. Thus, per 100 integers there is only 1 instance.

133900/100 = 1339.

A
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Re: How many integers between 324,700 and 458,600 have tens digit 2 and [#permalink] How many integers between 324,700 and 458,600 have tens digit 2 and   27 Feb 2018, 10:07
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IrinaOK
How many integers between 324,700 and 458,600 have tens digit 2 and units digit 1?

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

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Attachment:
Untitled1.jpg


The first few integers that have this property are: 324,721, 324,821, 324,921, …. As we can see, this is an arithmetic sequence with common difference of 100. Since the last integer that has this property is 458,521, the number of integers that have this property is:

(458,521 - 324,721)/100 + 1 = 133,800/100 + 1 = 1,338 + 1 = 1,339

Answer: A
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Re: How many integers between 324,700 and 458,600 have tens digit 2 and [#permalink] How many integers between 324,700 and 458,600 have tens digit 2 and   07 Jan 2021, 02:45
The number of numbers in an interval between two different multiples of 100 which end in the two-digit number 21 is equal to the number of 100 digit intervals between those two multiples of 100.

Calculate the number of 100 digit intervals between those two numbers.

(458,600 - 324,700) / 100

= 4586 - 3247

= 1339
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Re: How many integers between 324,700 and 458,600 have tens digit 2 and [#permalink] How many integers between 324,700 and 458,600 have tens digit 2 and   24 Sep 2023, 14:52
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Since the questions asks about the no. between the two integers that means the first and last integer will not be included. How many integers are between 2 and 5 is not 5 -2 =3 because the no. of integers are 3 & 4 only. So, how did we derive at 133900?
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How many integers between 324,700 and 458,600 have tens digit 2 and [#permalink] How many integers between 324,700 and 458,600 have tens digit 2 and   06 Aug 2024, 21:59
<quote option=""Bunuel""><quote option=""bibha"">How many integers between 324,700 and 458,600 have a 2 in the tens digit and a 1 in the units digit?<br />
A 1,339<br />
B 1,352<br />
C 1,353<br />
D 10,030<br />
E 10,300</quote><br />
There is one number in hundred with 2 in th tens digit and 1 in the units digit: <b>21</b>, 1<b>21</b>, 2<b>21</b>, 3<b>21</b>, ...<br />
<br />
The difference between 324,700 and 458,600 is 458,600-324,700=133,900 - one number per each hundred gives 133,900/100=1,339 numbers.<br />
<br />
Answer: A.<br />
<br />
Hope it's clear.</quote>­Hello Bunuel, @ScottTargetTestPrep,<br />
While counting the number of integers between 324700 and 458600 --> We should count all the numbers between 324701 and 458599 inclusive both, Then the total number should be 133899 and not 133900, Am i mistaken, Can you please help why it is 133900?­
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How many integers between 324,700 and 458,600 have tens digit 2 and [#permalink]
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