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

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How many integers between 324,700 and 458,600 have tens [#permalink] New post 11 Mar 2011, 08:47
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Aug 2012, 14:06, edited 1 time in total.
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Re: integers [#permalink] New post 11 Mar 2011, 08:54
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Madelaine88 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


There is one number in hundred with 1 in th tens digit and 3 in the units digit: 13, 113, 213, 313, ...

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: E.
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Re: integers [#permalink] New post 12 Mar 2011, 13:31
is there another way to solve this?

I once saw someone solving this kind of questions by multiplying the amount of different number of digits u can put in each place (in each different digit)
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Re: integers [#permalink] New post 12 Mar 2011, 20:40
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144144 wrote:
is there another way to solve this?

I once saw someone solving this kind of questions by multiplying the amount of different number of digits u can put in each place (in each different digit)


You can but you would have to take multiple cases and that would be really cumbersome. The left most digit can be either a 3 or a 4 but then next digit depends on what the leftmost digit is. If left most digit is 3, next digit can be anything from 2 to 9. If the leftmost digit is 4, the next digit can be from 0 to 5. Similarly other digits too.
So preferably, focus on the approach given by Bunuel.
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Re: HELP Me on This . . . . [#permalink] New post 10 Aug 2012, 09:14
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mothergoose wrote:
How many integers between 324, 700 and 458, 600 have tens digit 1 and units digit 3 ?

1) 10, 300
2) 10,030
3) 1,353
4) 1,352
5)1,339


The numbers must be of the form ABCD13, where ABCD is any four-digit number between 3247 and 4585 inclusive.
ABCD cannot be 4586, as 458,613>458,600.

Therefore, the total number is 4585 - 3247 + 1 = 1339.

Answer E
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Re: How many integers between 324,700 and 458,600 have tens [#permalink] New post 10 Aug 2012, 17:59
+1 E

We have to count how many hundreds are from 324,700 to 458,600.
We substract 458,600 - 324,700 = 133,900
We divide, 133,900/100 = 1,339
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Re: HELP Me on This . . . . [#permalink] New post 19 Aug 2012, 21:46
EvaJager wrote:
mothergoose wrote:
How many integers between 324, 700 and 458, 600 have tens digit 1 and units digit 3 ?

1) 10, 300
2) 10,030
3) 1,353
4) 1,352
5)1,339


The numbers must be of the form ABCD13, where ABCD is any four-digit number between 3247 and 4585 inclusive.
ABCD cannot be 4586, as 458,613>458,600.

Therefore, the total number is 4585 - 3247 + 1 = 1339.

Answer E



Nice solution ...Bunuel and Eva ..
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How many integers between 324,700 and 458,600 have tens digit of [#permalink] New post 08 Apr 2013, 18:26
briks123 wrote:
Definitely A.

458,600-324,700=133,900-1=133,899.

So there are 133,899 integers between the two numbers. Now how many hundreds of numbers are there? There are 1338+1 (to account for the number 133,821).


m clear with the statement that there are 133,899 integers between the two numbers.
but how to calculate hundreds of numbers in them.....

There are 1338+1 (to account for the number 133,821-------cud not understand this particular step....

If anyone can explain me this step in little detail then plz explain coz i dont hv any idea :(

Thanks in advance! :)
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Re: Re: [#permalink] New post 08 Apr 2013, 22:48
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Perhaps wrote:
briks123 wrote:
Definitely A.

458,600-324,700=133,900-1=133,899.

So there are 133,899 integers between the two numbers. Now how many hundreds of numbers are there? There are 1338+1 (to account for the number 133,821).


m clear with the statement that there are 133,899 integers between the two numbers.
but how to calculate hundreds of numbers in them.....

There are 1338+1 (to account for the number 133,821-------cud not understand this particular step....

If anyone can explain me this step in little detail then plz explain coz i dont hv any idea :(

Thanks in advance! :)


When we have to find the numbers between A and B(where both A and B are included) = (B-A)/1 +1.

When we have to find the numbers between A and B(where both A and B are excluded) = (B-A)/1 -1.

When we have to find the numbers between A and B(where either A or B is included) = (B-A)/1 .

For a number to keep having a 2 in the tens place and 1 in the units place, we have to keep adding 100 to that number. Thus, starting from 324,721, keep adding 100 to get the same units and digits place. Now to find the hundreds, all we have to do is find the number of hundreds between 458,521 and 324,721, where both are included : (458521-324721)/100+1 = 1338+1 = 1339.
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Re: How many integers between 324,700 and 458,600 have tens digi [#permalink] New post 09 Apr 2013, 02:33
Expert's post
Perhaps wrote:
briks123 wrote:
Definitely A.

458,600-324,700=133,900-1=133,899.

So there are 133,899 integers between the two numbers. Now how many hundreds of numbers are there? There are 1338+1 (to account for the number 133,821).


m clear with the statement that there are 133,899 integers between the two numbers.
but how to calculate hundreds of numbers in them.....

There are 1338+1 (to account for the number 133,821-------cud not understand this particular step....

If anyone can explain me this step in little detail then plz explain coz i dont hv any idea :(

Thanks in advance! :)


Merging similar topics. Please refer to the solutions above.
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Re: Re: [#permalink] New post 09 Apr 2013, 09:31
vinaymimani wrote:
Perhaps wrote:
briks123 wrote:
Definitely A.

458,600-324,700=133,900-1=133,899.

So there are 133,899 integers between the two numbers. Now how many hundreds of numbers are there? There are 1338+1 (to account for the number 133,821).


m clear with the statement that there are 133,899 integers between the two numbers.
but how to calculate hundreds of numbers in them.....

There are 1338+1 (to account for the number 133,821-------cud not understand this particular step....

If anyone can explain me this step in little detail then plz explain coz i dont hv any idea :(

Thanks in advance! :)


When we have to find the numbers between A and B(where both A and B are included) = (B-A)/1 +1.

When we have to find the numbers between A and B(where both A and B are excluded) = (B-A)/1 -1.

When we have to find the numbers between A and B(where either A or B is included) = (B-A)/1 .

For a number to keep having a 2 in the tens place and 1 in the units place, we have to keep adding 100 to that number. Thus, starting from 324,721, keep adding 100 to get the same units and digits place. Now to find the hundreds, all we have to do is find the number of hundreds between 458,521 and 324,721, where both are included : (458521-324721)/100+1 = 1338+1 = 1339.


what a wonderful explaination!!! :)

even after reading all the above solutions , things dint go in my mind ....... :?

but ur explaination ( specially the first three lines) made my basic concepts vivid.

thanks a lot for ur efforts Vinay .....

A big thanks to u :thumbup:
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Re: How many integers between 324,700 and 458,600 have tens [#permalink] New post 16 Jun 2014, 02:40
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Re: How many integers between 324,700 and 458,600 have tens [#permalink] New post 26 Jun 2014, 07:14
Bunuel wrote:
Madelaine88 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


There is one number in hundred with 1 in th tens digit and 3 in the units digit: 13, 113, 213, 313, ...

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: E.


Hi
Why you divided by 100..Please explain..I read all below comments but still can not understand the concept.

Thanks in advance
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Re: How many integers between 324,700 and 458,600 have tens [#permalink] New post 26 Jun 2014, 07:20
Expert's post
GGMAT730 wrote:
Bunuel wrote:
Madelaine88 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


There is one number in hundred with 1 in the tens digit and 3 in the units digit: 13, 113, 213, 313, ...

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: E.


Hi
Why you divided by 100..Please explain..I read all below comments but still can not understand the concept.

Thanks in advance


In each hundred there is only one number with 1 in the tens digit and 3 in the units digit. How many hundreds are in 133,900? 133,900/100=1,339. One number per hundred gives total of 1,339*1 numbers.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: How many integers between 324,700 and 458,600 have tens   [#permalink] 26 Jun 2014, 07:20
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