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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # How many integers between 324,700 and 458,600 have tens

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Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10629
Location: Pune, India
Re: How many integers between 324,700 and 458,600 have tens  [#permalink]

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rahulk2801! wrote:
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 458-324 = 134.

Therefor total = 134 x 10 =1340

Total final possibilities = 1340 - 1 (1613 is not possible) = 1339

Yes, this is correct too. Note that you subtract 1 at the end because 458,613 is not included.
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Karishma
Veritas Prep GMAT Instructor

Intern  B
Joined: 21 Feb 2019
Posts: 29
Re: How many integers between 324,700 and 458,600 have tens  [#permalink]

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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.

Hi, I tried this method but got an incorrect answer. I saw someone else also did this but I didnt get the solution. Can you please help?

Here is what i did.

For numbers starting with the digit 3, it will be 1(because only 3 can come here)*8*(because any number above 2 can come here)*6(any number above 4 can come here)*3(any number above 7 can come here)*1*1.

Similarly for numbers starting with 4 using the same logic above - 1*6*9*7*1*1

The answer should be adding the 2 combinations and subtracting 1 from it which is 521
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10629
Location: Pune, India
Re: How many integers between 324,700 and 458,600 have tens  [#permalink]

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kanikab 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 tried this method but got an incorrect answer. I saw someone else also did this but I didnt get the solution. Can you please help?

Here is what i did.

For numbers starting with the digit 3, it will be 1(because only 3 can come here)*8*(because any number above 2 can come here)*6(any number above 4 can come here)*3(any number above 7 can come here)*1*1.

Similarly for numbers starting with 4 using the same logic above - 1*6*9*7*1*1

The answer should be adding the 2 combinations and subtracting 1 from it which is 521

Did you count in 333313 ?

When my second digit from the left is 3, my third and fourth digits can be anything, not necessarily greater than 4 and 7 respectively.
It is far too cumbersome.
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Karishma
Veritas Prep GMAT Instructor

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Joined: 28 Aug 2019
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How many integers between 324,700 and 458,600 have tens  [#permalink]

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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

Solution:
We just need 13, which is fixed, in the end. Am I correct?

Okay so just remove the last 00 subtract.

Example: How many integers between 700 and 800 have tens digit 1 and units digit 3?

subtract 7 from 8 i.e. 1 [We did this because 13, in the end, has an occurrence once in 100 numbers. 713 813 913 and so on...]

Main question. Subtract 3247 from 4586. Answer is 1339

Bunuel is my approach correct?
Intern  B
Joined: 11 Oct 2018
Posts: 3
Re: How many integers between 324,700 and 458,600 have tens  [#permalink]

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I saw this as an evenly spaced set and went from there. We know that the the next number to have a 1 in the tens digit and a 3 in the units digit is 100 away. So let's find the minimum and maximum number within the range that fit the parameters.

458,613 minus 324,713 equals 133,800. We divide by 100, the difference in the set, to get 1,338. Then add 1 to 1,338 because 458,613 is also included in the range. The answer is 1,339.

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