Bunuel wrote:
tonebeeze wrote:
What is the best approach to solve problems such as these two examples below. If someone can solve them and show me the steps they took, I would appreciate it greatly. The GMAT Club test explanations were a little difficult for me to digest.
"How many times will the digit 7 be written when listing the integers from 1 to 1000?"
"How many integers between 324,700 and 458,600 have a 2 in the tens digit and a 1 in the units digit?"
Answer: 1339
Thanks Club!
"How many times will the digit 7 be written when listing the integers from 1 to 1000?"
"How many integers between 324,700 and 458,600 have a 2 in the tens digit and a 1 in the units digit?"
Answer: 1339
Thanks Club!
1. How many times will the digit 7 be written when listing the integers from 1 to 1000?
Many approaches are possible. For example:
Consider numbers from 0 to 999 written as follows:
1. 000
2. 001
3. 002
4. 003
...
...
...
1000. 999
We have 1000 numbers. We used 3 digits per number, hence used total of 3*1000=3000 digits. Now, why should ANY digit have preferences over another? We used each of 10 digits equal # of times, thus we used each digit (including 7) 3000/10=300 times.
Answer: 300.
2. How many integers between 324,700 and 458,600 have a 2 in the tens digit and a 1 in the units digit?
There is one number in hundred with 2 in th tens digit and 1 in the units digit: 21, 121, 221, 321, ...
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: 1,339.
Hope it's clear.
Amazing thoughts....really brilliant...........splendid.............by Bunnel.
i just have one question and its about this line "Now, why should ANY digit have preferences over another?" .
Do you think from 1 to 1000, 1 and 0 haven't a little priority over others in aspects of their number ?
i am telling because of especially the last number that is 1000 . it's not a 3 digit number but still here.......
7 was not here that's why couldn't make problem.....
By the way, one thing to tell and it's day by day i am learning lot from your uploaded files...............thanks to you again bunnel.....