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How many integers between 324,700 and 458,600 have tens
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Updated on: 10 Aug 2012, 14:06
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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
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Originally posted by Madelaine88 on 11 Mar 2011, 08:47.
Last edited by Bunuel on 10 Aug 2012, 14:06, edited 1 time in total.
Edited the question.




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How many integers between 324,700 and 458,600 have tens
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11 Mar 2011, 08:54
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, 1 13, 2 13, 3 13, ... The difference between 324,700 and 458,600 is 458,600324,700=133,900  one number per each hundred gives 133,900/100=1,339 numbers. Answer: E.
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How many integers between 324,700 and 458,600 have tens
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Updated on: 01 Jul 2020, 10:23
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 A nice rule says: the number of integers from x to y inclusive equals y  x + 1So, the number of integers from 324,700 to 458,600 = 458,600  324,700 + 1 = 133901ASIDE: We can safely round this number 133900 (you'll see why shortly) Now let's look at how frequently we have a 1 in the tens digit and 3 in the units digit. Integers from 1 to 100: 13 (1 integer) Integers from 101 to 200: 1 13 (1 integer) Integers from 201 to 300: 2 13 (1 integer) Integers from 301 to 400: 3 13 (1 integer) . . . As we can see, for every 100 integers, there's 1 integer with a 1 in the tens digit and 3 in the units digit. In other words, 1/100 of all integers have a 1 in the tens digit and 3 in the units digit. So, among the 133900 integers in question 1/100 of them meet the given condition. (1/100)( 133900) = 1339 Answer: E Cheers, Brent
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Re: HELP Me on This . . . .
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10 Aug 2012, 09:14
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 fourdigit 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: integers
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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
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12 Mar 2011, 20:40
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: How many integers between 324,700 and 458,600 have tens
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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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How many integers between 324,700 and 458,600 have tens digit of
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08 Apr 2013, 18:26
briks123 wrote: Definitely A.
458,600324,700=133,9001=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 133,821cud 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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Perhaps wrote: briks123 wrote: Definitely A.
458,600324,700=133,9001=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 133,821cud 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) = (BA)/1 +1. When we have to find the numbers between A and B(where both A and B are excluded) = (BA)/1 1. When we have to find the numbers between A and B(where either A or B is included) = (BA)/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 : (458521324721)/100+1 = 1338+1 = 1339.
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vinaymimani wrote: Perhaps wrote: briks123 wrote: Definitely A.
458,600324,700=133,9001=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 133,821cud 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) = (BA)/1 +1. When we have to find the numbers between A and B(where both A and B are excluded) = (BA)/1 1. When we have to find the numbers between A and B(where either A or B is included) = (BA)/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 : (458521324721)/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



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Re: How many integers between 324,700 and 458,600 have tens
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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, 1 13, 2 13, 3 13, ... The difference between 324,700 and 458,600 is 458,600324,700=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
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26 Jun 2014, 07:20
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, 1 13, 2 13, 3 13, ... The difference between 324,700 and 458,600 is 458,600324,700=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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Re: How many integers between 324,700 and 458,600 have tens
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20 Feb 2015, 08:03
I guess possibility of 1 in the tens is 1/10 and possibility of 23 in the unit digit is 1/10, so number of the way is 458,600324,700=133,900/100 = 1,339
Answer: E.[/quote]



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Re: How many integers between 324,700 and 458,600 have tens
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14 Dec 2015, 10:09
Dear Bunuel,Karishma/others
I might be overthinking here.
Getting confused. I reached till the step of calculating hundreds i.e 458600324700 = 133900; Next I got confused and was trying to find hunders using LastFirst +1 > 133901
How are the above two concepts different. If we take 1200 range to calculate 100's we can do 2001 +1 > total integers/100
Kindly help in clarifying.



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Re: How many integers between 324,700 and 458,600 have tens
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12 Mar 2016, 09:00
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 I think there is an easier way to answer this question. Please let me know if I am wrong. As you can see there are 4 different units digits in the answer choice. So It would help to find the units digit. To get the units digits we know between 324,700 and 458,600. There are 9 numbers that fall under the requirements asked in the question. xxx,713 xxx,813 xxx,913 xx1,013 xx1,113 xx1,213 xx1,313 xx1,413 xx1,513 So with that fact we get E as the answer.



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Re: How many integers between 324,700 and 458,600 have tens
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13 Mar 2016, 20:04
Hi,
I have 3 questions.
1/ Here is how I approach the problem. Please check if it is correct. Find multiples of 100 between 324,700 and 458,600: (458,600324,700)/100  1 = 13391=1338 There are 1338 multiples of 100 starting from 324800. However, since 324700 is a legitimate multiple of 100 (because 324721 satisfies the stem) but 458600 is not (458621>458600), we have 1338+1=1339 as the answer. Is there anything incorrect?
2/ I dont understand why Bunuel subtract 324700 from 458600. What does 133900 refer to?
3/ I found this type of question quite challenging. Can anyone post the links to similar gmat problems in which the same concept is tested?
Thank you very much!



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Re: How many integers between 324,700 and 458,600 have tens
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14 Mar 2016, 01:24
truongynhi wrote: Hi,
I have 3 questions.
1/ Here is how I approach the problem. Please check if it is correct. Find multiples of 100 between 324,700 and 458,600: (458,600324,700)/100  1 = 13391=1338 There are 1338 multiples of 100 starting from 324800. However, since 324700 is a legitimate multiple of 100 (because 324721 satisfies the stem) but 458600 is not (458621>458600), we have 1338+1=1339 as the answer. Is there anything incorrect?
2/ I dont understand why Bunuel subtract 324700 from 458600. What does 133900 refer to?
3/ I found this type of question quite challenging. Can anyone post the links to similar gmat problems in which the same concept is tested?
Thank you very much! Hi, you are also doing the same thing what has been done in prior solution.. we have to find numbers that have 13 in the end.. 324700 will have 324713.. 324800 will have 324813.. so The number of 100s from 324700 to 458600 is found by subtrcting these two and then dividing by 100.. so difference in numbers= 458600324700=133900.. How many 100s does it contain 133900/100=1339 each of these 1339 100s has one 13 in it so ans 1339
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Re: How many integers between 324,700 and 458,600 have tens
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27 Mar 2016, 02:43
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, 1 13, 2 13, 3 13, ... The difference between 324,700 and 458,600 is 458,600324,700=133,900  one number per each hundred gives 133,900/100=1,339 numbers. Answer: E. Bunel I understood the concept of for every hundred digits we will have only one digit with tens digit 1 and units digit 3. But The number of digits between 324,700 and 458,600 should be (458,600324,700)1=133,9001=133899. You have calculated it for only 133900 how?



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How many integers between 324,700 and 458,600 have tens
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08 Jul 2016, 14:44
Hi chetan2u, If I want to calculate how many integers between 324,700 and 458,600 have tens digits 1 ( without the unit digit restriction), how can I use the same approach? Would it be 458,600  324,700 = (133,900 / 100 (happens every 100 numbers)) * 10 (happens 10 times every 100) = 133,900/10 = 13,390 Could you let me know if I am doing right, please? I want to grasp the concept for other problems (if you have other problems I can use to practice, I would appreciate it). Thank you! chetan2u wrote: truongynhi wrote: Hi,
I have 3 questions.
1/ Here is how I approach the problem. Please check if it is correct. Find multiples of 100 between 324,700 and 458,600: (458,600324,700)/100  1 = 13391=1338 There are 1338 multiples of 100 starting from 324800. However, since 324700 is a legitimate multiple of 100 (because 324721 satisfies the stem) but 458600 is not (458621>458600), we have 1338+1=1339 as the answer. Is there anything incorrect?
2/ I dont understand why Bunuel subtract 324700 from 458600. What does 133900 refer to?
3/ I found this type of question quite challenging. Can anyone post the links to similar gmat problems in which the same concept is tested?
Thank you very much! Hi, you are also doing the same thing what has been done in prior solution.. we have to find numbers that have 13 in the end.. 324700 will have 324713.. 324800 will have 324813.. so The number of 100s from 324700 to 458600 is found by subtrcting these two and then dividing by 100.. so difference in numbers= 458600324700=133900.. How many 100s does it contain 133900/100=1339 each of these 1339 100s has one 13 in it so ans 1339



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Re: How many integers between 324,700 and 458,600 have tens
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10 Aug 2017, 03:46
VeritasPrepKarishma wrote: 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. Hi! I did it this way. Though i am getting the same answer, is it a correct approach? For, 713  1613 1 x 10 x 1 x 1 = 10 Now 458324 = 134. Therefor total = 134 x 10 =1340 Total final possibilities = 1340  1 (1613 is not possible) = 1339




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