Integer Digit Problem

[wcheng57]

This was a real GMAT problem from an old GMAT Test Paper exam.

How many integers between 324,700 and 458,600 have tens digit 1 and units digit 3?

a) 10,300

b) 10,030

c) 1353

d) 1352

e) 1339


E is the correct answer. Could someone explain how one would do this problem in under 2 minutes? Thanks.

[pradeepkaushal9518]

imo E is answer 1339

as 458600-324700=133900

in every 100 there is one no having 13 so 133900/100=1339

it takes me only 1 min

[iikarthik]

The unit disgit -3 repeats itself for every 10 consecutive nos
But the tenth digit -1 repeats itself only for every 100 consecutive nos.
We need both the 1 and 3 to be present for that number to get counted.
so the counting of 3 can be ignored it can't be counted without the presence of digit 1 that repeats once in 100 numbers.

so 458600-324700 = 133900

since the required combination repeats itself once in 100 numbers

133900/100, we get 1339