fiza gupta wrote:How many integers between 324,700 and 458,600 have a 2 in the tens digit and 1 in the units digit?

(A) 1,339
(B) 1.352
(C) 1,353
(D) 10,030
(E) 10,300

A nice rule says: the number of integers from x to y inclusive equals y - x + 1
So, the number of integers from 324,700 to 458,600 = 458,600 - 324,700 + 1 = 133901
ASIDE: We can safely round this number 133900 (you'll see why shortly)

Now let's look at how frequently we have a 2 in the tens digit and 1 in the units digit.
Integers from 1 to 100: 21 - 1 integer
Integers from 101 to 200: 121 - 1 integer
Integers from 201 to 300: 221 - 1 integer
Integers from 301 to 400: 321 - 1 integer
.
.
.
As we can see, for every 100 integers, there's 1 integer with a 2 in the tens digit and 1 in the units digit.
In other words, 1/100 of all integers have a 2 in the tens digit and 1 in the units digit.

So, among the 133900 integers in question 1/100 of them meet the given condition.
(1/100)(133900) = 1339
Answer: A

Cheers,
Brent $$$$

santhosh_katkurwar wrote:Hi Brent,

Is it possible to find through method after finding the number of integers?

Thanks,
Santosh

Hi Santosh,

I'm not sure what you're asking.
Once I determined that there are 133901 integers from 324,700 to 458,600, I used the fact that 1/100 of those integers end in 21 to arrive at the correct answer.

Cheers,
Brent