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03 Apr 2009, 14:25
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Guys,
If I count numbers between 11 to 99, I can find it as 99-11+1 = 89. So, there are 89 numbers between 11 and 99 (both inclusive).
Is there a way to get the answer through counting methods. What I mean is that to calculate the numbers between 11 and 99, we have :
the unit digit changes from 1 - 9 , so a total of 9 ways I can fill the unit digit. I can also fill the tens digit in 9 ways. So, the total numbers between 11 and 99 = 9*9 = 81. This is not the correct answer. This is because I missed 20,30,40,50,60,70 and 80. How would I include these missed numbers (20,30..80) in my above calculation, so that I can find the answer just by multiplying numbers?
thanks
sanjay
If I count numbers between 11 to 99, I can find it as 99-11+1 = 89. So, there are 89 numbers between 11 and 99 (both inclusive).
Is there a way to get the answer through counting methods. What I mean is that to calculate the numbers between 11 and 99, we have :
the unit digit changes from 1 - 9 , so a total of 9 ways I can fill the unit digit. I can also fill the tens digit in 9 ways. So, the total numbers between 11 and 99 = 9*9 = 81. This is not the correct answer. This is because I missed 20,30,40,50,60,70 and 80. How would I include these missed numbers (20,30..80) in my above calculation, so that I can find the answer just by multiplying numbers?
thanks
sanjay
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03 Apr 2009, 16:46
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sanjay_gmat
Yes, you can use counting methods:
-there are 9 choices for the tens' digit (1-9)
-there are 10 choices for the units' digit (0-9)
-we therefore have 90 possible two digit numbers from 10 to 99
-from 11 to 99, we need to subtract one, because we don't want to count the number 10. We thus have 89 numbers between 11 and 99 (inclusive).
It is not straightforward, however, to adapt this method to other ranges of numbers, so the alternative approach you mentioned (largest - smallest + 1) is normally preferable.
03 Apr 2009, 22:27
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IanStewart
Ian, thanks for your inputs. You are right that counting method is not a preferable method in that it can involve lengthy calculations. However, y'day I came across a question on gmatclub's test m01. The question is :
How many integers between 324,700 and 458,600 have a 2 in the tens digit and a 1 in the units digit?
For this question, we need to count numbers from 324721 to 458521, which is basically the same as counting numbers from 3247 to 4586. This should be easy if one spots this pattern.
However, if I just tackle the question without giving too much thought to the pattern, it's going to be a nightmare trying to find the answer. Taking a look at these different digits :
hundredth digit varies from 7 to 6. - 10 ways
thousandth digit varies from 4 to 8. - 5 ways
ten thousandth digit varies from 2 to 5 - 14 ways
hundred thousandth digit varies from 3 to 4 - 2 ways .
total number of ways = 10*5*14*2 = 1400. However, this is not the right answer. Could you please point out the flaw in my calculations?
