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

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Re: How many integers between 324,700 and 458,600 have tens digit 2 and [#permalink]
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Re: How many integers between 324,700 and 458,600 have tens digit 2 and [#permalink]
Hey,
Great thinking.
Thx.
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Re: How many integers between 324,700 and 458,600 have tens digit 2 and [#permalink]
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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]
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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

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

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Re: How many integers between 324,700 and 458,600 have tens digit 2 and [#permalink]
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]
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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]
<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 />